Statistica Sinica 16(2006), 847-860
PSEUDO-R
2
IN LOGISTIC REGRESSION MODEL
Bo Hu, Jun Shao and Mari Palta
University of Wisconsin-Madison
Abstract: Logistic regression with binary and multinomial outcomes is commonly
used, and researchers have long searched for an interpretable measure of the strength
of a particular logistic model. This article describes the large sample properties
of some pseudo-R2 statistics for assessing the predictive strength of the logistic
regression model. We present theoretical results regarding the convergence and
asymptotic normality of pseudo-R2s. Simulation results and an example are also
presented. The behavior of the pseudo-R2s is investigated numerically across a
range of conditions to aid in practical interpretation.
Key words and phrases: Entropy, logistic regression, pseudo-R2
1. Introduction
Logistic regression for binary and multinomial outcomes is commonly used
in health research. Researchers often desire a statistic ranging from zero to one
to summarize the overall strength of a given model, with zero indicating a model
with no predictive value and one indicating a perfect fit. The coefficient of deter-
mination R2 for the linear regression model serves as a standard for such measures
(Draper and Smith (1998)). Statisticians have searched for a corresponding in-
dicator for models with binary/multinomial outcome. Many different R2 statis-
tics have been proposed in the past three decades (see, e.g., McFadden (1973),
McKelvey and Zavoina (1975), Maddala (1983), Agresti (1986), Nagelkerke
(1991), Cox and Wermuch (1992), Ash and Shwartz (1999), Zheng and Agresti
(2000)). These statistics, which are usually identical to the standard R2 when
applied to a linear model, generally fall into categories of entropy-based and
variance-based (Mittlböck and Schemper (1996)). Entropy-based R2 statistics,
also called pseudo-R2s, have gained some popularity in the social sciences (Mad-
dala (1983), Laitila (1993) and Long (1997)). McKelvey and Zavoina (1975)
proposed a pseudo-R2 based on a latent model structure, where the binary/
multinomial outcome results from discretizing a continuous latent variable that
is related to the predictors through a linear model. Their pseudo-R2 is defined
as the proportion of the variance of the latent variable that is explained by the
848 BO HU, JUN SHAO AND MARI PALTA
covariate. McFadden (1973) suggested an alternative, known as “likelihood-
ratio index”, comparing a model without any predictor to a model including all
predictors. It is defined as one minus the ratio of the log likelihood with inter-
cepts only, and the log likelihood with all predictors. If the slope parameters
are all 0, McFadden’s R2 is 0, but it is never 1. Maddala (1983) developed
another pseudo-R2 that can be applied to any model estimated by the maximum
likelihood method. This popular and widely used measure is expressed as
R2M = 1 −
(
L(θ̃)
L(θ̂)
)
2
n
, (1)
.
1. Regression analysis is a statistical technique used to model relationships between variables and make predictions. It can be used to describe relationships, estimate coefficients, make predictions, and control systems.
2. Linear regression models describe straight-line relationships between variables, while non-linear models describe curved relationships. The goodness of fit of a model can be evaluated using the coefficient of determination.
3. The least squares method is used to fit regression lines by minimizing the sum of the squared vertical distances between observed and estimated y-values for a regression of y on x, or minimizing the sum of squared horizontal distances for a regression of x on y.
STATISTICAL ANALYSIS OF FUZZY LINEAR REGRESSION MODEL BASED ON DIFFERENT DIST...Wireilla
Using fuzzy linear regression model, the least squares estimation for linear regression (LR) fuzzy number is studied by Euclidean distance, Y-K distance and Dk distance respectively. It is concluded that the three different distances have the same coefficient of the least squares estimation. The data simulation shows the correctness of this conclusion.
This document discusses multiple linear regression analysis. It begins by introducing the basic multiple regression model that includes more than one predictor variable. It then discusses the assumptions of multiple regression including adequate sample size, absence of outliers and multicollinearity, and normality, linearity and homoscedasticity of residuals. The document provides an example of predicting house prices using living area and distance from the city center as predictor variables. It shows how to check assumptions, interpret the regression output and make predictions using the fitted model.
This document discusses correlation, regression, and issues that can arise when performing regression analysis. It defines correlation and covariance, and how to interpret a scatter plot. It explains how to test for statistical significance of correlation and establish if a linear relationship exists between variables. Simple and multiple linear regression are explained, including assumptions, model construction, and importance of regression coefficients. It discusses how to assess the importance of independent variables in explaining the dependent variable using t-tests, F-tests, R-squared, and adjusted R-squared. Potential issues like heteroskedasticity and multicollinearity are also summarized.
STATISTICAL ANALYSIS OF FUZZY LINEAR REGRESSION MODEL BASED ON DIFFERENT DIST...ijfls
This document summarizes a study on statistical analysis of fuzzy linear regression models based on different distance measures. It analyzes least squares estimations and error terms for fuzzy linear regression models using Euclidean distance, Y-K distance, and kD distance. The study finds that the three distances produce the same coefficient estimates for the least squares regression model. Simulation data is used to validate this conclusion.
Data Science - Part IV - Regression Analysis & ANOVADerek Kane
This lecture provides an overview of linear regression analysis, interaction terms, ANOVA, optimization, log-level, and log-log transformations. The first practical example centers around the Boston housing market where the second example dives into business applications of regression analysis in a supermarket retailer.
1. Regression analysis is a statistical technique used to model relationships between variables and make predictions. It can be used to describe relationships, estimate coefficients, make predictions, and control systems.
2. Linear regression models describe straight-line relationships between variables, while non-linear models describe curved relationships. The goodness of fit of a model can be evaluated using the coefficient of determination.
3. The least squares method is used to fit regression lines by minimizing the sum of the squared vertical distances between observed and estimated y-values for a regression of y on x, or minimizing the sum of squared horizontal distances for a regression of x on y.
STATISTICAL ANALYSIS OF FUZZY LINEAR REGRESSION MODEL BASED ON DIFFERENT DIST...Wireilla
Using fuzzy linear regression model, the least squares estimation for linear regression (LR) fuzzy number is studied by Euclidean distance, Y-K distance and Dk distance respectively. It is concluded that the three different distances have the same coefficient of the least squares estimation. The data simulation shows the correctness of this conclusion.
This document discusses multiple linear regression analysis. It begins by introducing the basic multiple regression model that includes more than one predictor variable. It then discusses the assumptions of multiple regression including adequate sample size, absence of outliers and multicollinearity, and normality, linearity and homoscedasticity of residuals. The document provides an example of predicting house prices using living area and distance from the city center as predictor variables. It shows how to check assumptions, interpret the regression output and make predictions using the fitted model.
This document discusses correlation, regression, and issues that can arise when performing regression analysis. It defines correlation and covariance, and how to interpret a scatter plot. It explains how to test for statistical significance of correlation and establish if a linear relationship exists between variables. Simple and multiple linear regression are explained, including assumptions, model construction, and importance of regression coefficients. It discusses how to assess the importance of independent variables in explaining the dependent variable using t-tests, F-tests, R-squared, and adjusted R-squared. Potential issues like heteroskedasticity and multicollinearity are also summarized.
STATISTICAL ANALYSIS OF FUZZY LINEAR REGRESSION MODEL BASED ON DIFFERENT DIST...ijfls
This document summarizes a study on statistical analysis of fuzzy linear regression models based on different distance measures. It analyzes least squares estimations and error terms for fuzzy linear regression models using Euclidean distance, Y-K distance, and kD distance. The study finds that the three distances produce the same coefficient estimates for the least squares regression model. Simulation data is used to validate this conclusion.
Data Science - Part IV - Regression Analysis & ANOVADerek Kane
This lecture provides an overview of linear regression analysis, interaction terms, ANOVA, optimization, log-level, and log-log transformations. The first practical example centers around the Boston housing market where the second example dives into business applications of regression analysis in a supermarket retailer.
This chapter discusses linear regression and the least squares regression line (LSRL). The LSRL is a straight line that minimizes the vertical distance between the data points and the line. It serves as a mathematical model for predicting a response variable (y) based on an explanatory variable (x). The coefficient of determination (r^2) indicates how much of the variation in y is explained by the linear relationship with x. Residual plots and identifying outliers and influential points are also covered.
In this paper we focus on mixed model analysis for regression model to take account of over dispersion in random effects. Moreover, we present the Data Exploration, Box plot, QQ plot, Analysis of variance, linear models, linear mixed –effects model for testing the over dispersion parameter in the mixed model. A mixed model is similar in many ways to a linear model. It estimates the effects of one or more explanatory variables on a response variable. In this article, the mixed model analysis was analyzed with the R-Language. The output of a mixed model will give you a list of explanatory values, estimates and confidence intervals of their effect sizes, P-values for each effect, and at least one measure of how well the model fits. The application of the model was tested using open-source dataset such as using numerical illustration and real datasets
This document provides an overview of simple linear regression and correlation analysis. It defines regression as estimating the relationship between two variables and correlation as measuring the strength and direction of that relationship. The key points covered include:
- Regression finds an estimating equation to relate known and unknown variables. Correlation determines how well that equation fits the data.
- Pearson's correlation coefficient r measures the linear relationship between two variables on a scale from -1 to 1.
- The coefficient of determination r2 indicates what percentage of variation in the dependent variable is explained by the independent variable.
- Statistical tests can evaluate whether a correlation is statistically significant or could be due to chance.
The document discusses maximum likelihood estimation. It begins by explaining that maximum likelihood chooses parameter values that make the observed data most probable given a statistical model. This provides a justification for estimation techniques like least squares regression. The document provides an example of estimating a population proportion from a sample. It then generalizes maximum likelihood to cover a wide range of models and estimation problems. It discusses properties like consistency, efficiency, and how to conduct hypothesis tests based on maximum likelihood. Numerical optimization techniques are often required to find maximum likelihood estimates for complex models.
This document discusses analyzing and summarizing relationships between two quantitative variables (bivariate data) using scatterplots. It covers key topics like correlation, linear regression lines, residuals, outliers and influential points. Scatterplots display the relationship between two variables and can show positive or negative linear associations or no relationship. Correlation coefficients measure the strength and direction of linear relationships, while regression lines predict variable relationships. Residual plots assess linearity and outliers.
Regression analysis is used to establish relationships between variables and make predictions. It can be used to estimate dependent variables from independent variables, extend analysis to multiple variables, and show the nature of relationships. The key objectives are establishing if relationships exist and making forecasts. Regression requires interval scale data and establishes parameters and an error term in the regression equation. The least squares method chooses parameters that minimize errors between observed and estimated dependent variable values. Goodness of fit is measured by R-squared and F-tests and t-tests determine statistical significance.
This document discusses multiple linear regression analysis performed using SAS. It begins by outlining the assumptions of linear regression, including a linear relationship between variables, normality, no multicollinearity, and homoscedasticity. It then explains that multiple linear regression attempts to model the relationship between multiple explanatory variables and a response variable by fitting a linear equation to observed data. The document goes on to describe the regression analysis process, model selection, interpretation of outputs like R-squared and p-values, and evaluation of diagnostics like autocorrelation. It concludes by listing the predictor variables selected by the stepwise regression model and interpreting their parameter estimates.
Discriminant analysis (DA) is a statistical technique used to predict group membership when the dependent variable is categorical and the independent variables are continuous. It identifies which variables discriminate between two or more naturally occurring groups. DA develops a linear equation to predict group membership based on weighted combinations of predictor variables. It aims to maximize the distance between group means to achieve strong discriminatory power. Like regression, DA assumes variables are normally distributed, cases are randomly sampled, and groups are mutually exclusive and collectively exhaustive. It requires at least two groups with minimal overlap and similar group sizes of at least five cases. DA can classify new cases into groups based on the discriminant functions derived from existing data.
This document discusses linear regression analysis. It defines simple and multiple linear regression, and explains that regression examines the relationship between independent and dependent variables. The document provides the equations for linear regression analysis, and discusses calculating the slope, intercept, standard error of the estimate, and coefficient of determination. It explains that regression analysis is widely used for prediction and forecasting in areas like advertising and product sales.
Linear regression is an approach for modeling the relationship between one dependent variable and one or more independent variables.
Algorithms to minimize the error are
OLS (Ordinary Least Square)
Gradient Descent and much more.
Let me know if anything is required. Ping me at google #bobrupakroy
This document summarizes techniques for diagnosing regression models, including checking for normality of errors, detecting outliers and influential observations, addressing collinearity issues, and handling missing data. It discusses plotting residuals against fitted values to check for constant error variance, transforming predictors using Box-Cox or polynomials to address nonlinear relationships, and imputing missing values using mean or regression imputation. Diagnostics help validate model assumptions and identify issues requiring attention, improving model fit and reliability.
The document discusses correlation and linear regression. It defines Pearson and Spearman correlation as statistical techniques to measure the relationship between two variables. Pearson correlation measures the linear association between interval variables, while Spearman correlation measures statistical dependence between two variables using their rank order. Linear regression finds the best fit linear relationship between a dependent and independent variable to predict changes in one based on the other. The key assumptions and interpretations of correlation coefficients and regression lines are also covered.
Stuck with your Regression Assignment? Get 24/7 help from tutors with Phd in the subject. Email us at support@helpwithassignment.com
Reach us at http://www.HelpWithAssignment.com
Regression analysis is used to identify relationships between variables and make predictions. Simple linear regression fits a straight line to data using one independent variable to predict a dependent variable. Multiple linear regression uses more than one independent variable to explain variance in the dependent variable. The goal is to select variables that sufficiently explain variation in the dependent variable to allow for accurate prediction. Key outputs of regression include coefficients, R-squared, standard error, and significance values.
This document provides an overview of regression analysis and two-way tables. It defines key concepts such as regression lines, correlation, residuals, and marginal and conditional distributions. Regression finds the linear relationship between two variables to make predictions. The least squares regression line minimizes the vertical distance between the data points and the line. Correlation and the coefficient of determination r2 measure how well the regression line fits the data. Two-way tables summarize the relationship between two categorical variables through marginal and conditional distributions.
This document proposes generalized additive models (GAMs) to model conditional dependence structures between random variables. Specifically, it develops a GAM framework where a dependence or concordance measure between two variables is modeled as a parametric, non-parametric, or semi-parametric function of explanatory variables. It derives the root-n consistency and asymptotic normality of the maximum penalized log-likelihood estimator for the proposed GAMs. It also discusses details of the estimation procedure and selection of smoothing parameters.
This document discusses various types and methods of measuring correlation between two variables. It describes correlation as a statistical tool to measure the degree of relationship between variables. Some key methods covered include scatter diagrams, Karl Pearson's coefficient of correlation, and Spearman's rank correlation coefficient. Positive and negative correlation examples are provided. The document also differentiates between simple, multiple, partial, and total correlation, as well as linear and non-linear correlation.
This document discusses methods for analyzing the relationship between two quantitative variables, including:
- Scatter diagrams can show the relationship and be used to identify if the variables are positively or negatively correlated.
- The linear correlation coefficient, r, quantifies the strength of the linear relationship between -1 and 1, where values closer to -1 or 1 indicate a stronger negative or positive correlation, respectively.
- Least-squares regression finds the best-fitting straight line to describe the linear relationship between two variables by minimizing the sum of the squared residuals. It can be used to make predictions, but may not be accurate far outside the original data range.
This document discusses methods for analyzing the relationship between two quantitative variables, including:
- Scatter diagrams can show the relationship and be used to identify if the variables are positively or negatively correlated.
- The linear correlation coefficient, r, quantifies the strength of the linear relationship between -1 and 1, with values closer to 1 or -1 indicating a stronger linear relationship.
- Least-squares regression finds the best-fitting straight line to describe the linear relationship between two variables by minimizing the sum of the squared residuals. It can be used to make predictions, but may not be accurate far outside the original data range.
This document discusses correlation and regression analysis. It defines correlation as assessing the relationship between two variables, while regression determines how well one variable can predict another. Correlation does not imply causation. Pearson's r standardizes the covariance between variables and ranges from -1 to 1, indicating the strength and direction of their linear relationship. Regression finds the best-fitting linear relationship through the least squares method to minimize residuals and predict one variable from another. It provides the slope and intercept of the regression line. The coefficient of determination, r-squared, indicates how well the regression model fits the data.
Stations yourself somewhere (library, cafeteria, etc.) and observe.docxrafaelaj1
Stations yourself somewhere (library, cafeteria, etc.) and observe the nonverbal communication that occurs.
What do people say with their bodies?
What messages are implicit in vocal expressions, clothes, make-up and so on?
Take notes on five of the most eloquent messages sent nonverbally.
*one page.
*Read the instructions then write about 5 difeerent people
.
StatementState legislatures continue to advance policy proposals.docxrafaelaj1
Statement
State legislatures continue to advance policy proposals to address cyber threats directed at governments and private businesses. As threats continue to evolve and expand and as the pace of new technologies accelerates, legislatures are making cybersecurity measures a higher priority.
Assignment
You are to author a 2-page (maximum) paper about the “failed” amendments proposed by the Kentucky legislature in 2019 with respect to Cyber Policy. APA format – 1 cover page, 2 content pages, and 1 reference page.
You are to answer two questions in your individual papers.
Brief background of the proposed amendment and “researched” speculation as to why it failed?
What would you propose for them to pass in 2020?
Remember to cite your sources appropriately and turn in original work!
Section 54
KY S 14
Status: Failed - Adjourned
Provides definitions relating to personal information, provides certain personal information that shall be protected from disclosure by a public agency or third-party contractor through redaction or other means, provides a list of covered persons, provides guidelines for contracts between a public agency and a third-party contractor.
.
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- Pearson's correlation coefficient r measures the linear relationship between two variables on a scale from -1 to 1.
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Regression analysis is used to establish relationships between variables and make predictions. It can be used to estimate dependent variables from independent variables, extend analysis to multiple variables, and show the nature of relationships. The key objectives are establishing if relationships exist and making forecasts. Regression requires interval scale data and establishes parameters and an error term in the regression equation. The least squares method chooses parameters that minimize errors between observed and estimated dependent variable values. Goodness of fit is measured by R-squared and F-tests and t-tests determine statistical significance.
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Linear regression is an approach for modeling the relationship between one dependent variable and one or more independent variables.
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This document proposes generalized additive models (GAMs) to model conditional dependence structures between random variables. Specifically, it develops a GAM framework where a dependence or concordance measure between two variables is modeled as a parametric, non-parametric, or semi-parametric function of explanatory variables. It derives the root-n consistency and asymptotic normality of the maximum penalized log-likelihood estimator for the proposed GAMs. It also discusses details of the estimation procedure and selection of smoothing parameters.
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- Scatter diagrams can show the relationship and be used to identify if the variables are positively or negatively correlated.
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Stations yourself somewhere (library, cafeteria, etc.) and observe.docxrafaelaj1
Stations yourself somewhere (library, cafeteria, etc.) and observe the nonverbal communication that occurs.
What do people say with their bodies?
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Take notes on five of the most eloquent messages sent nonverbally.
*one page.
*Read the instructions then write about 5 difeerent people
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Statement
State legislatures continue to advance policy proposals to address cyber threats directed at governments and private businesses. As threats continue to evolve and expand and as the pace of new technologies accelerates, legislatures are making cybersecurity measures a higher priority.
Assignment
You are to author a 2-page (maximum) paper about the “failed” amendments proposed by the Kentucky legislature in 2019 with respect to Cyber Policy. APA format – 1 cover page, 2 content pages, and 1 reference page.
You are to answer two questions in your individual papers.
Brief background of the proposed amendment and “researched” speculation as to why it failed?
What would you propose for them to pass in 2020?
Remember to cite your sources appropriately and turn in original work!
Section 54
KY S 14
Status: Failed - Adjourned
Provides definitions relating to personal information, provides certain personal information that shall be protected from disclosure by a public agency or third-party contractor through redaction or other means, provides a list of covered persons, provides guidelines for contracts between a public agency and a third-party contractor.
.
StatementState legislatures continue to advance policy propo.docxrafaelaj1
Statement
State legislatures continue to advance policy proposals to address cyber threats directed at governments and private businesses. As threats continue to evolve and expand and as the pace of new technologies accelerates, legislatures are making cybersecurity measures a higher priority.
Assignment
You are to author a 2-page (maximum) paper about the “failed” amendments proposed by the Kentucky legislature in 2019 with respect to Cyber Policy. APA format – 1 cover page, 2 content pages, and 1 reference page.
You are to answer two questions in your individual papers.
Brief background of the proposed amendment and “researched” speculation as to why it failed?
What would you propose for them to pass in 2020?
Remember to cite your sources appropriately and turn in original work!
KY S 14
Status: Failed - Adjourned
Provides definitions relating to personal information, provides certain personal information that shall be protected from disclosure by a public agency or third-party contractor through redaction or other means, provides a list of covered persons, provides guidelines for contracts between a public agency and a third-party contractor.
.
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• Other Relevant Experiences or Personal Qualities: Discuss any experiences or
personal attributes that may illuminate your commitment to the study of history
and to the successful completion of the graduate program.
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Statement of Interest (This is used to apply for Graduate Schoo.docxrafaelaj1
Statement of Interest: (This is used to apply for Graduate School, digital media program)
Length: 2 pages. (500-750 words)
Area of interest in digital media.
-computational arts.
I did a mix media group exhibition in Feb. 2018 called What Makes You You. Half of my show is a sculpture-based installation. The other half is an interactive digital programed art(using Processing software). The visual of human evolution ties these two park together. See details at https://dongpu.weebly.com/what-makes-you-you.html
-short videos (documentary production).
I love shooting short videos. I formed a Youtube team called 2037 Club last year. https://www.youtube.com/channel/UCmtUQfDMvL9iE8IOy9oshSA
The latest documentary I did is called Liang(Grain). Video Statement:This documentary discovers the Chinese planned economy history period, which starts at the 1950s. People were given a certain amount of coupons to buy food and daily needs because of the limitation of products. Since this is a historical theme, reference images are included to support the concept of buying food today and before 1990. Other than that, the visuals are mainly about common people’s daily routine nowadays. Along with the visual, the most artistic part in this video is Shanghainese dialogue, which explained food coupons in the way of storytelling. “I accidentally found many food coupons in my grandparents’ house this summer, so I went to ask them about the experiences they had with these coupons. My curiosity leads me to the theme.” said by the producer.
This particular video also has a different meaning to me. My Grandmother passed away one week before the video published at the film festival (at Scottsdale Museum of Commemoratory Art). This piece becomes memorable to me, sadly, my grandmother never had a chance to see the whole piece.
https://www.youtube.com/watch?v=fD0Y-BXDfnY
-3D animation for games
I learned Maya in an animation course. Like editing videos, I soon full in love with 3D modeling.
https://www.youtube.com/watch?v=nGIRxaUdYiY
Business idea, if an applicant has one. It is fine if an applicant is unsure when applying to the program. It is also fine if an applicant is interested in the artistic aspect of digital media and not the entrepreneurial aspect.
I would like to complete a mobile game project in my Graduate studies period and start a game company after graduation. Meanwhile, still active in the art field being an intermedia artist.
Goals or expectations upon completion of the digital media program.
-I want to learn more about computer technologies to create artistic works. Focusing on the field of game development.
-Do more social, get to know people in my field
-Get professional advices of my projects
Here is my cover letter, you can utilize this for the statement of interest.
As a creative and passionate professional with a rich history of developing creative materials, I am eager to submit my resume for consideration for the (Position Title) position .
StatementState legislatures continue to advance policy prop.docxrafaelaj1
Statement
State legislatures continue to advance policy proposals to address cyber threats directed at governments and private businesses. As threats continue to evolve and expand and as the pace of new technologies accelerates, legislatures are making cybersecurity measures a higher priority.
Assignment
You are page amendments to author a 2-page (maximum) paper about the “failed” amendments proposed by the Kentucky legislature in 2019 with respect to Cyber Policy. APA format – 1 cover page, 2 content pages, and 1 reference pageamendments proposed.
You are to answer two questions in your individual papers.
Brief background of the proposed amendment and “researched” speculation as to why it failed?
What would you propose for them to pass in 2020?
.
Statement of cash flows (indirect method) Cash flows from ope.docxrafaelaj1
Statement of cash flows (indirect method)
Cash flows from operating activities
Net income
72,600
adjustments to net income
depreciation
4,000
Gan on sale of investments
-7,000
Increase in AR
-36,000
Decrease in inventory
40,000
Increased in Accounts payable
13,000
Decrease in Accrued liabilities
-3,100
net cash provided by operating activities
83,500
Cash flows from investing activities
Purchase of Plant assets
-16,000
Sale of long-term investments
20,000
net cash provided by investing activities
4,000
Cash flows from financing activities
retiement of bonds
-31,000
payment of dividend
-32,500
sale of common stock
6,000
net cash provided by financing activities
-57,500
net increase in cash
30,000
Cash balance, beginning
230,000
cash balance, ending
260,000
Statement of Cash flows (direct method)
Cash flows from operating activities
cash received from customers
714,000
(sales - increase in AR)
cash paid for merchandise
477,000
(cogs - decrease in invnetory - increase in AP)
cash paid for other operating expenes
105,100
(selling & admin exp + decrease in accrued liab - depreciation)
cash paid for income taxes
48,400
net cash provided b oeprating activities
83,500
Cash flows from investing activities
Purchase of Plant assets
-16,000
Sale of long-term investments
20,000
net cash provided by investing activities
4,000
Cash flows from financing activities
retiement of bonds
-31,000
payment of dividend
-32,500
sale of common stock
6,000
net cash provided by financing activities
-57,500
net increase in cash
30,000
Cash balance, beginning
230,000
cash balance, ending
260,000
.
Stateline Shipping and Transport CompanyRachel Sundusky is the m.docxrafaelaj1
Stateline Shipping and Transport Company
Rachel Sundusky is the manager of the South-Atlantic office of the Stateline Shipping and Transport Company. She is in the process of negotiating a new shipping contract with Polychem, a company that manufactures chemicals for industrial use. Polychem want Stateline to pick up and transport waste products from its six plants to three waste disposal sites. Rachel is very concerned about this proposed arrangement. The chemical wastes that will be hauled can be hazardous to humans and the environment if they leak. In addition, a number of towns and communities in the region where the plants are located prohibit hazardous materials from being shipped through their municipal limits. Thus, not only will the shipments have to be handled carefully and transported at reduced speeds, they will also have to traverse circuitous routes in many cases. Rachel has estimated the cost of shipping a barrel of waste from each of the six plants to each of the three waste disposal sites as shown in the following table:
Waste Disposal Site
Plant
Whitewater
Los Canos
Duras
Kingsport
$12
$15
$17
Danville
14
9
10
Macon
13
20
11
Selma
17
16
19
Columbus
7
14
12
Allentown
22
16
18
The plants generate the following amounts of waste products each week:
Plant
Waste per Week (bbl)
Kingsport
35
Danville
26
Macon
42
Selma
53
Columbus
29
Allentown
38
The three waste disposal sites at Whitewater, Los Canos, and Duras can accommodate a maximum of 65, 80, and 105 barrels per week respectively. In addition to shipping directly from each of the six plants to one of the three waste disposal sites, Rachel is also considering using each of the plants and waste disposal sites as intermediate shipping points. Trucks would be able to drop a load at a plant or disposal site to be picked up and carried on to the final destination by another truck, and vice versa. Stateline would not incur any handling costs because Polychem has agreed to take care of all local handling of the waste materials at the plants and the waste disposal sites. In other words, the only cost Stateline incurs is the actual transportation cost. So Rachel wants to be able to consider the possibility that it may be cheaper to drop and pick up loads at intermediate points rather than ship them directly. Rachel estimates the shipping costs per barrel between each of the six plants to be as follows:
Plant
Plant
Kingsport
Danville
Macon
Selma
Columbus
Allentown
Kingsport
$ __
$6
$4
$9
$7
$8
Danville
6
__
11
10
12
7
Macon
5
11
__
3
7
15
Selma
9
10
3
__
3
16
Columbus
7
12
7
3
__
14
Allentown
8
7
15
16
14
__
The e.
State Two ways in which Neanderthals and Cro-Magnons differed. .docxrafaelaj1
State Two ways in which Neanderthals and Cro-Magnons differed.
List an important achievement for each of these scientist. Aristarchus, Euclid, Archimedes, and Herophilus
"Civilizations" is defined as the stage of development in which people have developed :
1. large, permanet communites.
2. a system of writing
3. divirsion
4. trade
5. a srtong central goverment
.
STAT 3300 Homework #6Due Thursday, 03282019Note Answe.docxrafaelaj1
This document outlines a homework assignment for a statistics course. It provides details on a multiple regression analysis examining the relationship between average student debt and various college metrics like admission rates, graduation rates, and in-state costs. The assignment asks students to conduct the multiple regression, analyze residuals, test hypotheses, and determine which variables are significant predictors of debt. It also provides learning objectives for a chapter on juvenile justice treatment and prevention programs.
State Standard by Content AreaLiteracy State Standard to Integra.docxrafaelaj1
State Standard by Content Area
Literacy State Standard to Integrate into Another Content Area
Use a different literacy standard for each content standard.
Standards-based Learning Objective
Aligned to content standards
Instructional Strategy to Integrate Literacy
Resources
Provide links to websites, PDFs, and any other documents used or referenced for strategy
Rationale
How the strategy will promote balanced literacy curriculum
State Content Standard 1:
State Content Standard 2:
State Content Standard 3:
.
STAT200: Assignment #2 - Descriptive Statistics Analysis and Writeup - Instructions
Page 1 of 3
STAT200 Introduction to Statistics
Assignment #2: Descriptive Statistics Analysis and Writeup
Assignment #2: Descriptive Statistics Analysis and Writeup
In the first assignment (Assignment #1: Descriptive Statistics Analysis Data Plan), you developed a
scenario about annual household expenditures and a plan for analyzing the data using descriptive
statistic methods. The purpose of this assignment is to carry out the descriptive statistics analysis plan
and write up the results. The expected outcome of this assignment is a two to three page write-up of
the findings from your analysis as well as a recommendation.
Assignment Steps:
Step #1: Review Feedback from Your Instructor
Before performing any analysis, please make sure to review your instructor’s feedback on Assignment
#1: Descriptive Statistics Data Analysis Plan. Based on the feedback, modify variables, tables, and
selected statistics, graphs, and tables, if needed.
Step #2: Perform Descriptive Statistic Analysis
Task 1: Look at the dataset.
• (Re)Familiarize yourself with the variables. Review Table 1: Variables Selected for the
Analysis you generated for the first assignment as well as your instructor’s feedback. In
addition, look at the data dictionary contained in the data set for information about the
variables.
• Select the variables you need for the analysis.
Task 2: Complete your data analysis, as outlined in your first assignment, with any needed
modifications, based on your instructor’s feedback.
• Calculate Measures of Central Tendency and Variability. Use the information from
Assignment #1 - Table 2. Numerical Summaries of the Selected Variables. Here again,
be sure to see your instructor’s feedback and incorporate into the analysis.
• Prepare Graphs and/or Tables. Use the information from Assignment #1 - Table 3.
Type of Graphs and/or Tables for Selected Variables. Here again, be sure to see your
instructor’s feedback and incorporate into the analysis.
STAT200: Assignment #2 - Descriptive Statistics Analysis and Writeup - Instructions
Page 2 of 3
Step #3: Write-up findings using the Provided Template
For this part of the assignment, write a short 2-3 page write-up of the process you followed and the
findings from your analysis. You will describe, in words, the statistical analysis used and present the
results in both statistical/text and graphic formats.
Here are the main sections for this assignment:
✓ Identifying Information. Fill in information on name, class, instructor, and date.
✓ Introduction. For this section, use the same scenario you submitted for the first assignment and
modified using your instructor’s feedback, if needed. Include Table 1 (Table 1: Variables
Selected for the Analysis) you used in Assignment #1 to show the variables you selected for the
analysis.
✓ Data .
STAT200: Assignment #2 - Descriptive Statistics Analysis Writeup - Template
Page 3 of 3
University of Maryland University College
STAT200 - Assignment #2: Descriptive Statistics Analysis and Writeup
Identifying Information
Student (Full Name):
Class:
Instructor:
Date:
Introduction:
Use the same scenario you submitted for the first assignment with modifications using your instructor’s feedback, if needed. Include Table 1: Variables Selected for the Analysis you used in Assignment #1 to show the variables you selected for analysis.
Table 1. Variables Selected for the Analysis
Variable Name in data set
Description
Type of Variable (Qualitative or Quantitative)
Variable 1: “Income”
Annual household income in USD.
Quantitative
Variable 2:
Variable 3:
Variable 4:
Variable 5:
Data Set Description and Method Used for Analysis:
Results:
Variable 1: Income
Numerical Summary.
Table 2. Descriptive Analysis for Variable 1
Variable
n
Measure(s) of Central Tendency
Measure(s) of Dispersion
Variable: Income
Median=
SD =
Graph and/or Table: Histogram of Income
(Place Histogram here)
Description of Findings.
Variable 2: (Fill in name of variable)
Numerical Summary.
Table 3. Descriptive Analysis for Variable 2
Variable
n
Measure(s) of Central Tendency
Measure(s) of Dispersion
Variable:
Graph and/or Table.
(Place Graph or Table Here)
Description of Findings.
Variable 3: (Fill in name of variable)
Numerical Summary.
Table 4. Descriptive Analysis for Variable 3
Variable
n
Measure(s) of Central Tendency
Measure(s) of Dispersion
Variable:
Graph and/or Table.
(Place Graph or Table Here)
Description of Findings.
Variable 4: (Fill in name of variable)
Numerical Summary.
Table 5. Descriptive Analysis for Variable 4
Variable
N
Mean/Median
St. Dev.
Variable 4:
Graph and/or Table.
(Place Graph or Table Here)
Description of Findings.
Variable 5: (Fill in name of variable)
Numerical Summary.
Table 6. Descriptive Analysis for Variable 5
Variable
n
Measure(s) of Central Tendency
Measure(s) of Dispersion
Variable:
Graph and/or Table.
(Place Graph or Table Here)
Description of Findings.
Discussion and Conclusion.
Briefly discuss each variable in the same sequence as presented in the results. What has the highest expenditure? What variable has the lowest expenditure? If you were to recommend a place to save money, which expenditure would it be and why? Note: The section should be no more than 2 paragraphs.
STAT200 Introduction to Statistics
Dataset for Written Assignments
Description of Dataset:
The data is a random sample from the US Department of Labor’s 2016 Consumer Expenditure Surveys (CE) and provides information about the composition of households and their annual expenditures (https://www.bls.gov/cex/). It contains information from 30 households, where a survey responder provided the requested information; it is all self-reported information. This dataset contains four socioeconomic variables (whose names.
State legislatures continue to advance policy proposals to address c.docxrafaelaj1
The document discusses a 2-page paper assignment on failed cybersecurity policy amendments proposed by the Kentucky legislature in 2019. Students are asked to answer two questions: 1) provide a brief background on a proposed amendment that failed and speculate on why it failed, and 2) propose an amendment for the legislature to pass in 2020. The assignment requires citing sources and original work, and is due by the specified date. It also provides background on one failed proposed amendment related to protecting personal information.
State FLORIDAInstructionsThis written assignment requ.docxrafaelaj1
State: FLORIDA
Instructions
This written assignment requires the student to investigate his/her local, state and federal legislators and explore their assigned committees and legislative commitments. The student is expected to investigate current and actual legislative initiatives that have either passed or pending approval by the house, senate or Governor’s office. The student will draft a letter to a specific legislator and offer support or constructive argument against pending policy or legislation. The letter must be supported with a minimum of 3 evidence based primary citations. (See Rubric)
Submission Details:
Support your responses with examples.
Cite any sources in APA format.
Submit your document to the
Submissions Area
by
the due date assigned.
.
State of the Science Quality ImprovementNameInst.docxrafaelaj1
State of the Science Quality ImprovementNameInstitutionsDate
Abstract
The condition of chronic heart failure sometimes is referred to as congestive heart failure (CHF), which is recognized as an acute life-threatening disease that majorly affects millions of American citizens annually. The condition of the chronic heart failure results when the heart is incapable of sufficient pump the blood throughout the body tissues due to the weak heart muscles (January et al., 2019). Certain conditions, such as narrowed arteries in the heart (CAD) or high blood pressure, gradually leave the heart too weak or stiff to fill and pump efficiently. Moreover, there are some of the several conditions such as coronary artery diseases and hypertension that leads to acute and chronic heart failure in the body system. More importantly, to avoid the possibility of this dangerous condition as well as the ever-increasing of the re-admitted hospital continue, collectively, the patient must be able to control the earlier stated conditions along with diabetes as well as obesity at home-based care and with their primary healthcare providers as well. According to Santesmases-Masana et al. (2019), "Primary health care planned care has been shown to reduce heart failure re-hospitalizations and maintain the patient quality of life." With this known knowledge, it is important to continue care at home and with their primary care provider to monitor and detect worsening of their condition sooner rather than later with evidence-based treatment practices. There are many evidence-based treatments for chronic heart failure that includes monitoring of vital signs, weight, and diet along with medications. In this paper, chronic heart failure, problem discussion, PICO question, and theoretical framework will be presented.
Problem Discussion
Chronic heart failure is a chief public health care concern linked with the high degree of mortality and morbidity in the U.S. Heart failure usually results in adverse outcomes, and the most costly is the issues of hospital readmissions. Currently, the heart failure management clinical procedures and pieces of evidence emphasizes the significance and the function of the care interventions a mid preventing the heart failure readmissions in the hospital set up. The current literature review is meant to evaluate and assess the effectiveness of transitional care interventions that intend to minimize hospital readmissions. Increase hospital readmission and worsening chronic heart failure complications are due to lack of following of a primary care provider and home monitoring of vital signs, weight, diet, energy level, and breathing patterns by the patient. There are many evidence-based practices and comprehensive guidelines for chronic heart failure treatment with side effects of some medications about individual races. For instance, losartan has little to adverse impact on blacks. Furthermore, according to Hadidi et al. (2018), "It has been.
State Data_1986-2015YearGross state product per capitaEducation sp.docxrafaelaj1
The document provides data on various metrics for a U.S. state from 1986 to 2016 including gross state product per capita, education spending per student, unemployment rates, and high school graduation rates. It shows trends over time, with generally increasing economic output and education spending, and decreasing unemployment and increasing graduation rates. The data could help inform policymaking and planning.
State and major urban area fusion centers serve as focal points wi.docxrafaelaj1
State and major urban area fusion centers serve as focal points within the state and local environment for the receipt, analysis, gathering, and sharing of threat-related information between the federal government and state, local, tribal, territorial (SLTT), and private sector partners.
There are issues and concerns related to intelligence collection methods at some of the country's local law enforcement agencies, joint terrorism task groups, and fusion centers. The first issue relates to constitutional limitations. Constitutional limitations restrict the government’s ability to access private information. The Fourth Amendment to the U.S. Constitution is particularly relevant. To the extent that government activity burdens individuals’ freedom of speech and related rights, the First Amendment may also play a role. Another issue is related to the process of collecting and sharing the information, which in many cases is not standardized, creating potential holes in the way officials exchange information on terror threats.
1. Briefly describe the six-step intelligence cycle.
2. What are some potential problems with collecting intelligence within the United States?
3. Give some examples of fusion centers and how these centers fuse intelligence at the local, state, and federal levels.
1. What is DHS’s Intelligence role in Homeland Security?
2. What are the roles of the National Counterterrorism Center (NCTC) and FBI for national intelligence? How do these roles benefit DHS?
.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
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For more information about PECB:
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Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
1. Statistica Sinica 16(2006), 847-860
PSEUDO-R
2
IN LOGISTIC REGRESSION MODEL
Bo Hu, Jun Shao and Mari Palta
University of Wisconsin-Madison
Abstract: Logistic regression with binary and multinomial
outcomes is commonly
used, and researchers have long searched for an interpretable
measure of the strength
of a particular logistic model. This article describes the large
sample properties
of some pseudo-R2 statistics for assessing the predictive
strength of the logistic
regression model. We present theoretical results regarding the
convergence and
asymptotic normality of pseudo-R2s. Simulation results and an
example are also
presented. The behavior of the pseudo-R2s is investigated
numerically across a
2. range of conditions to aid in practical interpretation.
Key words and phrases: Entropy, logistic regression, pseudo-R2
1. Introduction
Logistic regression for binary and multinomial outcomes is
commonly used
in health research. Researchers often desire a statistic ranging
from zero to one
to summarize the overall strength of a given model, with zero
indicating a model
with no predictive value and one indicating a perfect fit. The
coefficient of deter-
mination R2 for the linear regression model serves as a standard
for such measures
(Draper and Smith (1998)). Statisticians have searched for a
corresponding in-
dicator for models with binary/multinomial outcome. Many
different R2 statis-
tics have been proposed in the past three decades (see, e.g.,
McFadden (1973),
McKelvey and Zavoina (1975), Maddala (1983), Agresti (1986),
Nagelkerke
(1991), Cox and Wermuch (1992), Ash and Shwartz (1999),
Zheng and Agresti
3. (2000)). These statistics, which are usually identical to the
standard R2 when
applied to a linear model, generally fall into categories of
entropy-based and
variance-based (Mittlböck and Schemper (1996)). Entropy-
based R2 statistics,
also called pseudo-R2s, have gained some popularity in the
social sciences (Mad-
dala (1983), Laitila (1993) and Long (1997)). McKelvey and
Zavoina (1975)
proposed a pseudo-R2 based on a latent model structure, where
the binary/
multinomial outcome results from discretizing a continuous
latent variable that
is related to the predictors through a linear model. Their
pseudo-R2 is defined
as the proportion of the variance of the latent variable that is
explained by the
848 BO HU, JUN SHAO AND MARI PALTA
covariate. McFadden (1973) suggested an alternative, known as
“likelihood-
ratio index”, comparing a model without any predictor to a
model including all
4. predictors. It is defined as one minus the ratio of the log
likelihood with inter-
cepts only, and the log likelihood with all predictors. If the
slope parameters
are all 0, McFadden’s R2 is 0, but it is never 1. Maddala (1983)
developed
another pseudo-R2 that can be applied to any model estimated
by the maximum
likelihood method. This popular and widely used measure is
expressed as
R2M = 1 −
(
L(θ̃)
L(θ̂)
)
2
n
, (1)
where L(θ̃) is the maximized likelihood for the model without
any predictor and
L(θ̂) is the maximized likelihood for the model with all
predictors. In terms of
5. the likelihood ratio statistic λ = −2 log(L(θ̃)/L(θ̂)), R2M = 1 −
e−λ/n. Maddala
proved that R2M has an upper bound of 1 − (L(θ̃))2/n and, thus,
suggested a
normed measure based on a general principle of Cragg and
Uhler (1970):
R2N =
1 −
(
L(θ̃)
L(θ̂)
)
2
n
1 − (L(θ̃))
2
n
. (2)
While the statistics in (1) and (2) are widely used, their
statistical properties
have not been fully investigated. Mittlböck and Schemper
(1996) reviewed R2M
and R2N along with other measures, but their results are mainly
empirical and
6. numerical. The R2 for the linear model is interpreted as the
proportion of the
variation in the response that can explained by the regressors.
However, there is
no clear interpretation of the pseudo-R2s in terms of variance of
the outcome in
logistic regression. Note that both R2M and R
2
N are statistics and thus random.
In linear regression, the standard R2 converges almost surely to
the ratio of the
variability due to the covariates over the total variability as the
sample size in-
creases to infinity. Once we know the limiting values of R2M
and R
2
N , these limits
can be similarly used to understand how the pseudo-R2s capture
the predictive
strength of the model. The pseudo-R2s for a given data set are
point estimators
for the limiting values that are unknown. To account for the
variability in esti-
mation, it is desirable to study the asymptotic sampling
distributions of R2M and
7. R2N , which can be used to obtain asymptotic confidence
intervals for the limiting
values of pseudo-R2s. Helland (1987) studied the sampling
distributions of R2
statistics in linear regression.
In this article we study the behavior of R2M and R
2
N under the logistic re-
gression model. In Section 2, we derive the limits of R2M and R
2
N and provide
PSEUDO-R2 IN LOGISTIC REGRESSION MODEL 849
interpretations of them. We also present some graphs describing
the behavior of
R2N across a range of practical situations. The asymptotic
distributions of R
2
M
and R2N are derived in Section 3 and some simulation results
are presented. An
example is given in Section 4.
2. What Does Pseudo-R2 Measure
In this section we explore the issue of what R2M in (1) and R
8. 2
N in (2) measure
in the setting of binary or multinomial outcomes.
2.1. Limits of pseudo-R2s
Consider a study of n subjects whose outcomes fall in one of m
categories.
Let Yi = (Yi1, . . . , Yim)
′ be the outcome vector associated with the ith subject,
where Yij = 1 if the outcome falls in the jth category, and Yij =
0 otherwise.
We assume that Y1, . . . , Yn are independent and that Yi is
associated with a p-
dimensional vector Xi of predictors (covariates) through the
multinomial logit
model
Pij = E(Yij|Xi) =
exp(αj + X
′
iβj )
∑m
k=1 exp(αk + X
′
iβk)
9. , j = 1, . . . , m, (3)
where αm = βm = 0, α1, . . . , αm−1 are unknown scalar
parameters, and β1, . . .,
βm−1 are unknown p-vectors of parameters. Let θ be the (p +
1)(m − 1) dimen-
sional parameter (α1, β
′
1, . . . , αm−1, β
′
m−1). Then the likelihood function under
the multinomial logit model can be written as
L(θ) =
n
∏
i=1
P
Yi1
i1 P
Yi2
i2 · · · P
Yim
im . (4)
Procedures for obtaining the maximum likelihood estimator θ̂ of
10. θ are available
in most statistical software packages. The following theorem
provides the asymp-
totic limits of the pseudo-R2s defined in (1) and (2). Its proof is
given in the
Appendix.
Theorem 1. Assume that covariates Xi, i = 1, . . . , n, are
independent and
identically distributed random p-vectors with finite second
moment. If
H1 = −
m
∑
j=1
E(Pij ) log E(Pij ), (5)
H2 = −
m
∑
j=1
E(Pij log Pij ), (6)
850 BO HU, JUN SHAO AND MARI PALTA
11. then, as n → ∞, R2M →p 1−e2(H2−H1) and R2N →p (1 −
e2(H2−H1))/(1 − e−2H1 ),
where →p denotes convergence in probability.
2.2. Interpretation of the limits of pseudo-R2s
It is useful to consider whether the limits of pseudo-R2 can be
interpreted
much as R2 can be for linear regression analysis.
Theorem 1 reveals that both R2M and R
2
N converge to limits that can be
described in terms of entropy. If the covariates Xis are i.i.d., Yi
= (Yi1, . . . , Yim)
′,
i = 1, . . . , n, are also i.i.d. multinomial distributed with
probability vector (E(Pi1),
. . . , E(Pim)) where the expectation is taken over Xi. Then H1
given in (5) is
exactly the entropy measuring the marginal variation of Yi.
Similarly, −
∑m
j=1 Pij
log Pij corresponds to the conditional entropy measuring the
variation of Yi given
Xi and H2 can be considered as the average conditional entropy.
Therefore
12. H1 − H2 measures the difference in entropy explained by the
covariate X, which
is always greater than 0 by Jensen’s inequality, and is 0 if and
only if the covariates
and outcomes are independent. For example, when (Xi, Yi) is
bivariate normal,
H1 − H2 = log(
√
1 − ρ2)−1 where ρ is the correlation coefficient, and the limit
of R2M is ρ
2.
The limit of R2M is 1 − e−2(H1−H2) monotone in increasing
H1 − H2. Then
we can write the limit of R2N as the limit of R
2
M divided by its upper bound:
R2N →p
1 − e−2(H1−H2)
1 − e−2H1
=
e2H1 − e2H2
e2H1 − 1
.
When both H1 and H2 are small, 1 − e−2(H1−H2) ≈ 2(H1 −
H2), 1 − e−2H1 ≈ 2H1
13. and the limit of R2N is approximately (H1 − H2)/H1, the
entropy explained by
the covariates relative to the marginal entropy H1.
2.3. Limits of R2
M
and R2
N
relative to model parameters
For illustration, we examine the magnitude of the limits of RM
and RN
under different parameter settings when the Xis are i.i.d.
standard normal and
the outcome is binary. Figures 1 and 2 show the relationship
between the limits
of R2M and R
2
N and the parameters α and β. In these figures, profile lines of
the
limits are given for different levels of the response probability
eα/(1 + eα) at the
mean of Xi and odds ratio e
β per standard deviation of the covariate. The limits
tend to increase as the absolute value of β increases with other
parameters fixed,
which is consistent with the behavior of the usual R2 in linear
regression models.
14. However, we note that the limits tend to be low, even in models
where the
parameters indicate a rather strong association with the
outcome. For example,
PSEUDO-R2 IN LOGISTIC REGRESSION MODEL 851
a moderate size odds ratio of 2 per standard deviation of Xi is
associated with
the limit of R2N at most 0.10. As the pseudo-R
2 measures do not correspond
in magnitude to what is familiar from R2 for ordinary
regression, judgments
about the strength of the logistic model should refer to profiles
such as those
provided in Figures 1 and 2. Knowing what odds ratio for a
single predictor
model produces the same pseudo-R2 as a given multiple
predictor model greatly
facilitates subject matter relevance assessment.
PSfrag replacements
0
2
15. 4
6
0.0
0.2 0.4 0.6 0.8
e
α
β
e
α
1+eα
e
β
Figure 1. Contour plot of limits of R2M against e
α/(1 + eα) and odds ratio eβ .
852 BO HU, JUN SHAO AND MARI PALTA
PSfrag replacements
0
2
4
6
0.0
16. 0.2 0.4 0.6 0.8
e
α
β
e
α
1+eα
e
β
Figure 2. Contour plot of limits of R2N against e
α/(1 + eα) and odds ratio eβ.
It may be noted that neither R2N nor R
2
M can equal 1, except in degenerate
models. This property is a logical consequence of the nature of
binary outcomes.
The denominator, 1 − (L(θ̃))2/n, equals the numerator when
L(θ̂) equals 1, which
occurs only for a degenerate outcome that is always 0 or 1. In
fact, any perfectly
fitting model for binary data would predict probabilities that are
only 0 or 1. This
constitutes a degenerate logistic model, which cannot be fit. In
17. comparison to
PSEUDO-R2 IN LOGISTIC REGRESSION MODEL 853
the R2 for a linear model, R2 of 1 implies residual variance of
0. As the variance
and entropy of binomial and multinomial data depend on the
mean, this again
can occur only when the predicted probabilities are 0 and 1. The
mean-entropy
dependence influences the size of the pseudo-R2s and tends to
keep them away
from 1 even when the mean probabilities are strongly dependent
on the covariate.
For ease of model interpretation, investigators often categorize
a continuous
variable, which leads to a loss of information. Consider a
standard normally
distributed covariate. We calculate the limit of R2N when
cutting the normal
covariate into two, three, five or six categories. The threshold
points we choose
are 0 for two categories, ±1 for three categories, ±0.5, ±1 for
five categories, and
0, ±0.5, ±1 for six categories. In Figures 3 and 4, we plot the
18. corresponding limits
of R2N against e
α/(1 + eα) by fixing β at 1, and against eβ by setting α = 1. The
fewer the number of categories we use for the covariate, the
more information we
lose, i.e., the smaller the limit of R2N . In this example, we
note that using five or
six categories retains most of the information provided by the
original continuous
covariate.
PSfrag replacements
0
2
4
6
0.0
0.2
0.4
0.6
0.8
e
α
23. into K categories
against odds ratio eβ , K = 2, 3, 5, 6
3. Sampling Distributions of Pseudo-R2s
The result in the previous section indicates that the limit of a
pseudo-R2 is
a measure of the predictive strength of a model relating the
logistic responses to
some predictors (covariates). The quantities R2M and R
2
N are statistics and are
random. They should be treated as estimators of their limiting
values in assessing
the model strength. In this section, we derive the asymptotic
distributions of R2M
and R2N that are useful for deriving large sample confidence
intervals.
3.1. Asymptotic distributions of pseudo-R2s
Theorem 2. Under the conditions of Theorem 1,
√
n
[
R2M − (1 − e2(H2−H1))
]
→d N (0, σ21 ) (7)
24. √
n
[
R2N −
1 − e2(H2−H1)
1 − e−2H1
]
→d N (0, σ22 ), (8)
PSEUDO-R2 IN LOGISTIC REGRESSION MODEL 855
where H1 and H2 are given by (5) and (6), σ
2
1 = g
′
1Σg1 and σ
2
2 = g
′
2Σg2 with
g1 = −2e2(H2−H1) (1 + log γ1, . . . , 1 + log γm, −1) , (9)
g2 =
25. e−2H1 (1 − e2H2 )
(1 − e−2H1 )2
(
1 + log γ1, . . . , 1 + log γm, e
2H2
1 − e2H1
1 − e2H2
)
, (10)
Σ =
(
Cov(Yi) η
η′ �
)
. (11)
Here γj = Ex(Pij ), j = 1, . . . , m, is the expected probability
that the outcome
falls in jth category, the jth element of η is ηj = Ex(Pij log Pij )
+ γj H2, and
� =
∑m
26. j=1 Ex
(
Pij (log Pij )
2
)
− H22 .
When all the slope parameters βj are 0 (i.e., Xi and Yi are
uncorrelated),
both σ21 and σ
2
2 are zero. g1, g2 and Σ can be estimated by replacing the un-
known quantities, which are related to the covariate
distribution, with consistent
estimators. For example, γ can be estimated by (
∑
P̂ i1/n, . . . ,
∑
P̂ im/n)
′.
Suppose gk, k = 1, 2, and Σ are estimated by ĝk and Σ̂,
respectively. Theorem
2 leads to the following asymptotic 100(1 − α)% confidence
interval for the limit
of R2M :
(
27. R2M − Z α
2
ĝ′1Σ̂ĝ1, R
2
M + Z α
2
ĝ′1Σ̂ĝ1
)
, (12)
where Zα is the 1 − α quantile of the standard normal
distribution. A confidence
interval for the limit of R2N can be obtained by replacing R
2
M and ĝ1 in (12) with
R2N and ĝ2, respectively. If the resulting lower limit of the
confidence interval is
below 0 or the upper limit is above 1, it is conventional to use
the margin value
of 0 or 1.
3.2. Simulation results
In this section, we examine by simulation the finite sample
performance of
the confidence intervals based on the asymptotic results derived
in Section 3.1.
28. Our simulation experiments consider the logistic regression
model with binary
outcome and a single normal covariate with mean 0 and
standard deviation 1.
All the simulations were run with 3,000 replications of an
artificially gener-
ated data set. In each replication, we simulated a sample of size
200 or 1,000
from the standard normal distribution as covariate vectors X ,
and simulated
200 or 1,000 binary outcomes according to success probability
exp(α + βX)/(1+
exp(α + βX)). Tables 1 and 2 show the results for different
values of α and β.
In all the simulations with sample size 1,000, the estimated
confidence inter-
vals derived by Theorem 2 displayed coverage probability close
to the expected
level of 0.95. Coverage probability is less satisfactory with
sample size 200 when
the model is weak.
856 BO HU, JUN SHAO AND MARI PALTA
30. 0 0.5 0.056 (0.055) (0.030,0.083) (0.938) 0.075 (0.074)
(0.039,0.111) (0.938)
1 0.171 (0.171) (0.133,0.210) (0.931) 0.229 (0.228)
(0.177,0.281) (0.933)
2 0.371 (0.370) (0.332,0.409) (0.925) 0.490 (0.494)
(0.443,0.546) (0.929)
∗ The relative frequency with which the intervals contain the
true limit
Table 2. Simulation average of pseudo-R2s and 95% confidence
intervals in
the logit model with normal covariate (sample size=200).
α β R2M (limit) CI (coverage) R
2
N (limit) CI (coverage)
2 0.5 0.031 (0.027) (0, 0.074) (0.912) 0.058 (0.050) (0, 0.138)
(0.922)
1 0.107 (0.103) (0.0310, 0.182) (0.918) 0.185 (0.178) (0.0580,
0.312) (0.920)
2 0.299 (0.298) (0.2110, 0.387) (0.910) 0.458 (0.454) (0.3290,
0.588) (0.913)
1 0.5 0.050 (0.046) (0, 0.105) (0.915) 0.073 (0.066) (0, 0.151)
(0.914)
1 0.152 (0.150) (0.0680, 0.235) (0.928) 0.215 (0.213) (0.0980,
0.332) (0.925)
2 0.351 (0.350) (0.2650, 0.437) (0.930) 0.484 (0.483) (0.3660,
31. 0.601) (0.932)
0.5 0.5 0.058 (0.053) (0, 0.116) (0.919) 0.078 (0.072) (0, 0.157)
(0.920)
1 0.168 (0.166) (0.0820, 0.253) (0.927) 0.227 (0.226) (0.1120,
0.343) (0.930)
2 0.367 (0.365) (0.2820, 0.452) (0.925) 0.494 (0.491) (0.3790,
0.608) (0.925)
0 0.5 0.059 (0.055) (0.0010, 0.118) (0.911) 0.079 (0.074)
(0.0010, 0.158) (0.912)
1 0.174 (0.171) (0.0880, 0.260) (0.928) 0.233 (0.228) (0.1180,
0.347) (0.930)
2 0.372 (0.370) (0.2870, 0.457) (0.925) 0.496 (0.494) (0.3830,
0.610) (0.922)
4. Example
We now turn to an example of logistic regression from Fox’s
(2001) text on
fitting generalized linear models. This example draws on data
from the 1976 U.S.
Panel Study of Income Dynamics. There are 753 families in the
data set with
8 variables. The variables are defined in Table 3. The logarithm
of the wife’s
estimated wage rate is based on her actual earnings if she is in
the labor force;
32. otherwise this variable is imputed from other predictors. The
definition of other
variables is straightforward.
PSEUDO-R2 IN LOGISTIC REGRESSION MODEL 857
Table 3. Variables in the women labor force dataset.
Variable Description Remarks
lfp wife’s labor-force participation factor: no,yes
k5 number of children ages 5 and younger 0-3, few 3’s
k618 number of children ages 6 to 18 0-8, few > 5
age wife’s age in years 30-60, single years
wc wife’s college attendance factor: no,yes
hc husband’s college attendance factor: no,yes
lwg log of wife’s estimated wage rate see text
inc family income excluding wife’s income $1, 000s
We assume a binary logit model with no labor force
participation as the
baseline category. Other variables are treated as predictors in
the model. The
estimated model with all the predictors has the following form:
log
33. P
1−P
=
3.18−1.47k5−0.07k618−0.06age+0.81wc+0.11hc+0.61lwg−0.03i
nc,
where P is the probability that the wife in the family is in the
labor force. The
variables k618 and hc are not statistically significant based on
the likelihood-ratio
test. Table 4 shows the values of R2M and R
2
N , as well as 95% confidence intervals
of limits of R2M and R
2
N , for the model containg all the predictors, and models
excluding certain predictors.
Table 4. R2M and R
2
N with 95% confidence intervals of models for women
labor force data.
Model R2M (95% CI.) R
2
N (95% CI.)
Use all predictors 0.152 ( 0.109, 0.195) 0.205 ( 0.147, 0.262)
Exclude k5 0.074 ( 0.040, 0.108) 0.100 ( 0.054, 0.145)
34. Exclude age 0.123 ( 0.083, 0.164) 0.165 ( 0.111, 0.219)
Exclude wc 0.138 ( 0.096, 0.180) 0.185 ( 0.129, 0.241)
Exclude lwg 0.133 ( 0.092, 0.174) 0.179 ( 0.123, 0.234)
Exclude inc 0.130 ( 0.087, 0.172) 0.175 ( 0.119, 0.230)
Exclude k618 0.151 ( 0.108, 0.194) 0.203 ( 0.145, 0.261)
Exclude hc 0.152 ( 0.109, 0.195) 0.204 ( 0.146, 0.262)
Use k618, hc only 0.003 (-0.005, 0.010) 0.004 (-0.006, 0.013)
For the model with all the covariates, R2M and R
2
N are around 0.15 and 0.20,
respectively. The results imply a moderately strong model when
referencing the
odds ratio scale equivalents in Figure 1. Dropping a significant
covariate results
in a notable decrease in the values of pseudo-R2s, while no
significant change
occurs if we drop the insignificant covariates. R2M and R
2
N are near zero when we
858 BO HU, JUN SHAO AND MARI PALTA
exclude all the significant covariates. However, model selection
35. procedures using
pseudo-R2 need further research.
Acknowledgements
The research work is supported by Grant CA-53786 from the
National Cancer
Institute. The authors thank the referees and an editor for
helpful comments.
Appendix
For the proof of results in Section 3, we begin with a lemma and
then sketch
the main steps for Theorem 1 and 2.
Lemma 1. Assume that covariates Xi, i = 1, . . . , n, are i.i.d.
random p-vectors
with finite second moment, then (log L(θ̂) − log L(θ))/
√
n →p 0, where θ̂ is the
maximum likelihood estimator of θ.
Proof of Lemma 1. We first prove that ∂2 log L(θ)/∂θ∂θ
′
= Op(n). The score
function is
∂ log L(θ)
36. ∂θ
=
(
n
∑
i=1
(Yi1 − Pi1),
n
∑
i=1
(Yi1 − Pi1)X′i, . . . ,
n
∑
i=1
(Yim − Pim)X′i
)
′
.
Let ηk = (αk, β
′
k)
′ ∈ Rp+1 for k = 1, . . . , m, and Ui = (1, X′i )′. Then
37. ∂2 log L(θ)
∂ηk∂η
′
k
= −
n
∑
i=1
Pik(1 − Pik)UiU ′i , k = 1, 2, . . . , m,
∂2 log L(θ)
∂ηk∂η
′
l
= −
n
∑
i=1
PikPilUiU
′
i , k 6= l.
Since UiU
′
38. i =
(
1 X′i
Xi XiX
′
i
)
, each element in the second derivative matrix
∂2 log L(θ)/∂θ∂θ
′
is Op(n) by assumption. For simplicity, we write this as
∂2 log L(θ)/∂θ∂θ
′
= Op(n). Let Sn(θ) = ∂ log L(θ)/∂θ, Jn(θ) =−∂2 log L(θ)/∂θ∂θ
′
and In(θ) = E(Jn(θ)), where the expectation is taken over
covariates. It follows
that the cumulative information matrix In(θ) = Op(n). By a
second-order Taylor
expansion,
log L(θ̂) − log L(θ)√
39. n
=
Sn(θ̂)√
n
′
(θ̂ − θ) −
1
2
√
n
(θ̂ − θ)′Jn(θ∗)(θ̂ − θ)
= (θ̂ − θ)′In(θ)
1
2 In(θ)
−
1
2
√
n
Jn(θ
∗ )
2n
3
40. 2
√
nIn(θ)
−
1
2 In(θ)
1
2 (θ̂ − θ),
PSEUDO-R2 IN LOGISTIC REGRESSION MODEL 859
where θ∗ is a vector between θ and θ̂. The asymptotic normality
results of the
MLE gives In(θ)
1/2(θ̂ −θ) → N (0, 1). The lemma then follows from the fact that
In(θ)
−1/2
√
n = Op(1) and Jn(θ
∗ )/n = Op(1).
Proof of Theorem 1. Let f (x) = log(1 − x)/2, then
f (R2) =
1
41. n
log L(θ̃) − 1
n
log L(θ̂)
=
m
∑
j=1
nj
n
log(
nj
n
) − 1
n
log L(θ) +
1
n
(
log L(θ) − log L(θ̂)
)
.
The convergence of
42. ∑m
j=1(nj /n) log(nj/n) and log L(θ)/n come from the Law
of Large Numbers. The results of the theorem follow from the
lemma and the
Continuous Mapping Theorem.
Proof of Theorem 2. Let S2M = 1 − (L(θ̃)/L(θ))2/n and S2N =
(1−
(L(θ̃)/L(θ))2/n)/(1 − (L(θ̃))2/n). It follows from the lemma that
S2M and S2N
have the same asymptotic distribution as R2M and R
2
N , respectively, in the sense
that
√
n(S2M − R2M ) →p 0 and
√
n(S2N − R2N ) →p 0.
Define Zi = (Yi1, . . . , Yim, Wi) where Wi =
∑m
j=1 Yij log Pij . Then Zi’s form
a i.i.d. random sequence with µ = E(Zi) = (γ
′,
∑m
j=1 E(P1j log P1j )) = (γ
′, −E2),
43. Cov (Zi) = Σ, γ and Σ as defined in Section 3. By the
Multidimensional Central
Limit Theorem,
√
n
(
Z
̄ − µ
)
→ N (0, Σ). (13)
Let φ1(x1, . . . , xm) = 1 − e2(
∑
m
j=1
xj log xj−xm+1) and φ2(x1, . . . , xm) = (1−
e2(
∑
m
j=1
xj log xj −xm+1))/(1 − e2
∑
m
j=1
xj log xj ). Applying the delta-method with φ1
and φ2 to (13), respectively, leads to the asymptotic normality
44. results in
Theorem 2.
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model. Statist. Medicine 19, 1771-1781.
Department of Statistics, University of Wisconsin-Madison,
Madison, WI, 53706, U.S.A.
E-mail: [email protected]
Department of Statistics, University of Wisconsin-Madison,
Madison, WI, 53706, U.S.A.
E-mail: [email protected]
Department of Population Health Sciences, University of
Wisconsin-Madison, Madison, WI,
53706, U.S.A.
E-mail: [email protected]
(Received August 2004; accepted July 2005)
1. Introduction2. What Does Pseudo-R2 Measure2.1. Limits of
pseudo-R2s2.2. Interpretation of the limits of pseudo2.3. Limits
of R2M and R2N relative to model parameters3. Sampling
Distributions of Pseudo-R2s3.1. Asymptotic distributions of
pseudo3.2. Simulation results4. …
A note about the References tool in Word
47. On a PC/Windows system (based on Office 2010)
When you need to create a citation (giving credit for work that
you are referencing), you
click on References, then on Insert Citation. The next step is to
add a new source.
When you get to the "Create Source" window, it is suggested
that you click on the
"Show All Bibliography Fields." Here is a sample Source
screen.
Once you have entered all the source information, click on
Bibliography and then Insert
Bibliography.
This is the citation:
(Joseph, 2000)
This is how the source is entered into the References list:
Joseph, J. (2000, October). Ethics in the Workplace. Retrieved
August 3, 2015, from asae-The
Center for Association Leadership:
http://www.asaecenter.org/Resources/articledetail.cfm?ItemNum
ber=13073
Other fields on the source page would be used for a journal
article or an article from a
periodical.
48. On a Mac/OS system (based on Office 2013)
From the MAC Help files:
To add a citation, a works cited list, or a bibliography to your
document, you first
add a list of the sources that you used.
Add a source by using the Source Manager
The Source Manager lists every source ever entered on your
computer so that
you can reuse them in any other document. This is useful, for
example, if you
write research papers that use many of the same sources. If you
open a
document that includes citations, the sources for those citations
appear under
Current list. All the sources that you have cited, either in
previous documents or
in the current document, appear under Master list.
1. Open up your Word document.
2. On the Document Elements tab , under References ,
click Manage.
3. At the bottom of the Citations tool, click , and then click
Citation Source Manager .
49. 1 2
3
4
1 2
3
4
4. Click New.
5. On the Type of Source pop-up menu, select a source type.
6. Complete as many of the fields as you want. The required
fields are
marked with an asterisk (*). These fields provide the minimum
information
that you must have for a citation.
7.
Note You can insert citations even when you do not have all
the publishing details.
If publishing details are omitted, citations are inserted as
numbered placeholders.
Then you can edit the sources later. You must enter all the
required information for a
50. source before you can create a bibliography.
8. When you are finished, click OK.The source information that
you entered
appears in the Current list and Master list of the Source
Manager.
9. To add additional sources, repeat steps 3 through 6.
10. Click Close.The source information that you entered appears
in the
Citations List in the Citations tool.
Edit a source in the Citations tool
You can edit a source directly in the document or in the
Citations tool. When you
change the source, the changes apply to all instances of that
citation throughout
the document. However, if you make a manual change to a
particular citation
within the document, those changes apply only to that particular
citation. Also,
that particular citation is not updated or overridden when you
update the citations
and bibliography.
1. On the Document Elements tab, under References, click
Manage.
2. In the Citations List, select the citation that you want to edit.
3. At the bottom of the Citations tool, click , and then click Edit
Source.
51. 4. Make the changes that you want, and then click OK. If you
see a message
that asks whether you want to save changes in both the Master
list and the
Current list, click No to change only the current document, or
click Yes to
apply changes to the source of the citation and use it in other
documents.
Remove a source from the Citations List
Before you can remove a source from the Citations List, you
must delete all
related citations.
1. In the document, delete all the citations associated with the
source that
you want to remove.
2. Tip You can use the search field to locate citations. In the
search field , enter part of the citation.
3. On the Document Elements tab, under References, click
Manage.
4. At the bottom of the Citations tool, click , and then click
Citation Source
Manager.
5. In the Current list, select the source that you want to remove,
and then
click Delete. The source now appears only in the Master list.
52. 6.
Note If the Delete button is unavailable, or if you see a check
mark next to the source in the list, there is still at least one
related citation in the document. Delete all remaining related
citations in the document, and then try deleting
the source again.
7. Click Close. The source that you removed no longer
appears in the Citations
List.
Step 2. Insert, edit, or delete a citation (optional)
Insert a citation
1. In your document, click where you want to insert the citation.
2. On the Document Elements tab, under References, click
Manage.
3. In the Citations List, double-click the source that you want to
cite. The
citation appears in the document.
Add page numbers or suppress author, year, or title for a
specific citation
Use this option to make custom changes to a citation and keep
the ability to
update the citation automatically.
53. Note The changes that you make by using this method apply
only to this citation.
1. Click anywhere between the parentheses of the citation. A
frame appears
around the citation.
2. Click the arrow on the frame, and then click Edit this
Citation.
3. Add page numbers, or select the Author, Year, or Title check
box to keep that
information from showing in the citation.
Make manual changes to a specific citation
If you want to change a specific citation manually, you can
make the citation text
static and edit the citation in any way that you want. After you
make the text
static, the citation will no longer update automatically. If you
want to make
changes later, you must make the changes manually.
1. Click anywhere between the parentheses of the citation. A
frame appears
around the citation.
2. Click the arrow on the frame, and then click Convert Citation
to Static Text.
54. 3. In the document, make the changes to the citation.
Delete a single citation from the document
1. In the document, find the citation that you want to delete.
2.
Tip You can use the search field to locate citations. In the
search field , enter part of the citation.
3. Select the whole citation, including the parentheses, and then
press DELETE.
Step 3. Insert or edit a works cited list or a bibliography
A works cited list is a list of all works you referred to (or
"cited") in your
document, and is typically used when you cite sources using the
MLA style. A
works cited list differs from a bibliography, which is a list of
all works that you
consulted when your researched and wrote your document.
Insert a works cited list or a bibliography
1. In your document, click where you want the works cited list
or bibliography to
appear (usually at the very end of the document, following a
page break).
2. On the Document Elements tab, under References, click
Bibliography, and
55. then click Bibliography or Works Cited.
Change a works cited list or a bibliography style
You can change the style of all the citations contained in a
document's works
cited list or bibliography without manually editing the style of
the citations
themselves. For example, you can change the citations from the
APA style to the
MLA style.
1. On the View menu, click Draft or Print Layout.
2. On the Document Elements tab, under References, click the
Bibliography
Style pop-up menu, and then click the style that you want to
change the
bibliography's references to. All
references in your document's bibliography change to the new
style.
Update a works cited list or a bibliography
If you add new sources to the document after you inserted the
works cited list or
bibliography, you can update the works cited list or
bibliography to include the
new sources.
1. Click the works cited list or bibliography. A frame appears
around it.
2. Click the arrow on the frame, and then click Update Citations
56. and
Bibliography.
Research Paper Using Word
This assignment has two goals: 1) have students, via research,
increase their understanding of impacts of information
technology on current world issues, and 2) learn to correctly use
the tools and techniques within Word to format a research
paper, including use of available References and citation tools.
These skills will be valuable throughout a student’s
academic career.
The paper will require a title page, NO abstract, three to five
full pages of content with incorporation of a minimum of 3
external resources from credible sources and a Works
Cited/References page. Wikipedia and similar general
information
sites, blogs or discussion groups are not considered creditable
sources for a research project. No more than 10% of the
paper may be in the form of a direct citation from an external
source. Choose your topic from the list of topics that follow
these organization steps.
Paper organization
Open Word and save a blank document with the following
name:
57. “Student’s LastNameFirstInitial Research Paper”
The paper should be organized in the following way:
1. Title page:
a. Center in the middle of the page (horizontally and vertically)
the title (subject) of the paper and below that
your name
2. Body of the paper:
a. Use 12-point Arial font
b. Set the margins at 1”
c. Entire paper should be double-spaced
d. Length – 3-5 full pages, not counting the title page or the
References page.
e. Include a minimum of 3 APA-formatted citations and related
References page. Every reference must be cited
at least once, and every citation have an entry in the References
list. If you are not familiar with APA format,
it is recommended that you use the References feature in Word
for your citations and Reference List or refer
to the "Citing and Writing" option under the
Resources/Library/Get Help area in the LEO classroom. It is
important to review the final format for APA-style correctness
even if generated by Word.
f. Include at least two (2) informational footnotes. Footnotes are
not used to list a reference! Footnotes contain
information about the topic to which the footnote has been
attached.
g. Place the references on a separate page following the body of
the paper. Note: Use a hard return (CTRL
Enter) after the end of your paper body and the start of the
58. References page.
3. Organization of the content of the paper:
Include the following sections in the paper (include, in bold,
the headings identified here):
a. Introduction - Identify the issue or idea. Explain why the
topic was selected and what you are trying to
achieve (what is your end goal). The introduction should not be
more than half a page; details will be
discussed in the follow-on areas.
b. Areas of interest, activity or issue – Define the issue or idea
in greater detail. Define the specific problem
or problems or new idea. Identify other underlining or related
issues as well as dependencies. Explain what
impacts will result if not addressed.
c. Research Findings – Summarize your research findings and
what they contribute to the study of the issue
or idea. You must identify (cite) the sources of the research or
class material related to your topic that you
include in the findings.
d. Proposed solution(s), idea(s), courses of action(s). List
solutions, ideas or courses of action with an
analysis of its effectiveness (how will your suggestions affect
or change the current situation). If more than
one idea is suggested, provide an analysis that covers all
proposed suggestions.
e. Conclusion – Summarize the conclusions of your paper.
59. A list of topics from which students can choose is provided
here:
Topics for Research Paper
The focus of the paper should be on one of the following:
1. How has information technology led to the struggle between
online and brick-and-mortar stores? What do the
next 5-10 years look like?
2. How has information technology opened up the potential for
5G networks? Are there any downsides to
the implementation of this technology?
3. How has information technology impacted the use of robots
in your local stores?
4. How has information technology supported the development
of monopolies – Amazon, Microsoft, telecom
companies? Will these monopolies survive?
5. How has information technology supported the development
of facial recognition software and the current issues
related to its use?
6. How has information technology led to the use of biometrics
and the potential for rise of an International “Big
Brother”?
7. How has information technology led to the development of
the Internet of Things and the concern about the
impact of privacy laws (or lack thereof) on the IOT?
60. 8. How has information technology supported the development
of Facebook and other social media sites? Should
social media sites be regulated?
9. Who/what is Huawei and what are the issues the U.S. and
other countries are having with Huawei?
10. How has information technology changed the political
process within the past 5 years?
Writing Quality for the Research Paper
• All Grammar, Verb Tenses, Pronouns, Spelling, Punctuation,
and Writing Competency should be without error.
• Be particularly careful about mis-matching a noun and
pronoun. For example, if you say "A person does this…" then
do
not use "their" or "they" when referring to that person. "Person"
is singular; "their" or "they" is plural.
• Remember: there is not their, your is not you're, its is not it's,
too is not to or two, site is not cite, and who should be
used after an individual, not that. For example, "the person
WHO made the speech" not "the person THAT made the
speech."
• in the previous sentence. It is more business-like to say "In a
professional paper one should not use contractions,"
rather than saying, "In a professional paper you don't use
contractions."
• In a professional paper one does not use contractions (doesn't,
don't, etc.) and one
61. does not use the personal I, you or your. Use the impersonal as
in the previous
sentence. It is more business-like to say "In a professional paper
one should not use
contractions," rather than saying, "In a professional paper you
don't use contractions."
• Remember: spell-check, then proofread. Better yet, have a
friend or colleague read it before submitting it. Read it out
loud to yourself. Read it as if you are submitting it to your boss.
Grading Criteria
Paper Mechanics
Format- title pg,
font, margins, paper
length
0.5 Title page included: Arial 12-point font used; margins set at
1";
body of the paper is 3-5 pages, double spaced. The title page
and References page are not counted as part of the 3-5 pages of
text.
APA work -
citations and
references
0.5 A minimum of 3 correctly formatted citations matched to
62. references; both citations and references in APA format.
Footnotes 0.5 A minimum of 2 footnotes that contain additional
information
but are NOT references.
Mechanics-
grammar, spelling,
etc.
1.5 Grammar, spellings, and punctuation correct throughout the
paper.
Content
Introduction 2 This is a summary of the topic. Simply identify
the issue
without going into great detail, explain why was the topic
selected and what the you are trying to achieve (what is your
end goal). The introduction should not be more than half a
page; details will be discussed in the follow-on areas.
Issue 2.0 Define the issue or idea. Define the specific problem
or
problems or new idea. Identify other underlying or related
issues as well as dependencies. Explain what impacts will
result if not addressed.
Findings 2.0 Identify research or class material related to your
topic.
63. Summarize your findings and what they contribute to the
study of the issue or idea. Sources must be identified in
citations and the related References list.
Solution
s/actions 3.0 List solution, idea or courses of action with an
analysis of its
effectiveness (how will your suggestions affect or change the
current situation). If more than one idea is suggested,
provide an analysis that covers all proposed suggestions.
Conclusion 2 Summarize the conclusions of your paper. In a
paragraph
briefly identify the issue, the findings, your proposed
solution/actions. However, do not simply repeat the words in
the previous sections.
You can find instructions on how to use the References tool in
Word on a PC or on a Mac in a file included in the
Assignment link.