Statistical Analysis, Pre-processing, Exploratory Analysis, Pivot Tables, charts and graphical representation of Information to improve business decision making.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Cobb Douglas production function in excel
Yi=a X1i^b1 X2i^b2 X3i^b3 e^ui
Where,
Y= dependent variable
X=explanatory(independent)variable
a=intercept
bi are regression coefficients
e=2.718………….
u=error term Follows N(0,constant variance)
This function is non linear in parameters so to make it linear in parameters apply ln both sides then equation looks like
lnYi=lna+ b1lnX1i +b2lnX2i +b3lnX3i+ui
Steps
1. Open Excel, Give Variable Names and Provide Data
2. Apply Logarithmic Transformation to the Data
3. Go to Data analysis
4. Get Output
This document provides instructions for estimating a Cobb-Douglas production function using SPSS. It explains that taking the natural logarithm of both sides of the production function makes it linear in parameters. It then outlines the 5 steps to perform this analysis in SPSS: 1) Go to the variable view, 2) View the data, 3) Apply a logarithmic transformation to the variables, 4) Go to the analyze menu, and 5) Obtain the output, which will provide estimates of the intercept, coefficients, and estimated production function in log-linear form.
Linear Regression and Logistic Regression in MLKumud Arora
Linear regression and logistic regression are statistical modeling techniques. Linear regression predicts continuous dependent variables using independent variables, while logistic regression predicts binary dependent variables. Both aim to model relationships between variables by estimating coefficients. Logistic regression models the log odds of the dependent variable rather than the variable directly. Key evaluation metrics for regression include accuracy, precision, recall, and F1 score, which are calculated using a confusion matrix.
Application of Graphic LASSO in Portfolio Optimization_Yixuan Chen & Mengxi J...Mengxi Jiang
- The document describes using graphical lasso to estimate the precision matrix of stock returns and apply portfolio optimization.
- Graphical lasso estimates the precision matrix instead of the covariance matrix to allow for sparsity. This makes the estimation more efficient for large datasets.
- The study uses 8 different models to simulate stock return data and compares the performance of graphical lasso, sample covariance, and shrinkage estimators on portfolio optimization of in-sample and out-of-sample test data. Graphical lasso performed best on out-of-sample test data, showing it can generate portfolios that generalize well.
Linear Regression vs Logistic Regression | EdurekaEdureka!
YouTube: https://youtu.be/OCwZyYH14uw
** Data Science Certification using R: https://www.edureka.co/data-science **
This Edureka PPT on Linear Regression Vs Logistic Regression covers the basic concepts of linear and logistic models. The following topics are covered in this session:
Types of Machine Learning
Regression Vs Classification
What is Linear Regression?
What is Logistic Regression?
Linear Regression Use Case
Logistic Regression Use Case
Linear Regression Vs Logistic Regression
Blog Series: http://bit.ly/data-science-blogs
Data Science Training Playlist: http://bit.ly/data-science-playlist
Follow us to never miss an update in the future.
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Transportation Problem with Pentagonal Intuitionistic Fuzzy Numbers Solved Us...IJERA Editor
This paper presents a solution methodology for transportation problem in an intuitionistic fuzzy environment in
which cost are represented by pentagonal intuitionistic fuzzy numbers. Transportation problem is a particular
class of linear programming, which is associated with day to day activities in our real life. It helps in solving
problems on distribution and transportation of resources from one place to another. The objective is to satisfy
the demand at destination from the supply constraints at the minimum transportation cost possible. The problem
is solved using a ranking technique called Accuracy function for pentagonal intuitionistic fuzzy numbers and
Russell’s Method
Polynomial regression model of making cost prediction in mixed cost analysisAlexander Decker
This document presents a study comparing different regression models for predicting costs based on production levels. It finds that a cubic polynomial regression model provides a better fit than linear regression or the high-low method. The study uses cost and production data from a company to build linear, quadratic, and cubic regression models. It finds the cubic polynomial regression has the highest R-squared value and lowest p-value, indicating it is the best-fitting model. The study concludes that polynomial regression generally provides a better approach for cost prediction than conventional linear regression or the high-low method.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Cobb Douglas production function in excel
Yi=a X1i^b1 X2i^b2 X3i^b3 e^ui
Where,
Y= dependent variable
X=explanatory(independent)variable
a=intercept
bi are regression coefficients
e=2.718………….
u=error term Follows N(0,constant variance)
This function is non linear in parameters so to make it linear in parameters apply ln both sides then equation looks like
lnYi=lna+ b1lnX1i +b2lnX2i +b3lnX3i+ui
Steps
1. Open Excel, Give Variable Names and Provide Data
2. Apply Logarithmic Transformation to the Data
3. Go to Data analysis
4. Get Output
This document provides instructions for estimating a Cobb-Douglas production function using SPSS. It explains that taking the natural logarithm of both sides of the production function makes it linear in parameters. It then outlines the 5 steps to perform this analysis in SPSS: 1) Go to the variable view, 2) View the data, 3) Apply a logarithmic transformation to the variables, 4) Go to the analyze menu, and 5) Obtain the output, which will provide estimates of the intercept, coefficients, and estimated production function in log-linear form.
Linear Regression and Logistic Regression in MLKumud Arora
Linear regression and logistic regression are statistical modeling techniques. Linear regression predicts continuous dependent variables using independent variables, while logistic regression predicts binary dependent variables. Both aim to model relationships between variables by estimating coefficients. Logistic regression models the log odds of the dependent variable rather than the variable directly. Key evaluation metrics for regression include accuracy, precision, recall, and F1 score, which are calculated using a confusion matrix.
Application of Graphic LASSO in Portfolio Optimization_Yixuan Chen & Mengxi J...Mengxi Jiang
- The document describes using graphical lasso to estimate the precision matrix of stock returns and apply portfolio optimization.
- Graphical lasso estimates the precision matrix instead of the covariance matrix to allow for sparsity. This makes the estimation more efficient for large datasets.
- The study uses 8 different models to simulate stock return data and compares the performance of graphical lasso, sample covariance, and shrinkage estimators on portfolio optimization of in-sample and out-of-sample test data. Graphical lasso performed best on out-of-sample test data, showing it can generate portfolios that generalize well.
Linear Regression vs Logistic Regression | EdurekaEdureka!
YouTube: https://youtu.be/OCwZyYH14uw
** Data Science Certification using R: https://www.edureka.co/data-science **
This Edureka PPT on Linear Regression Vs Logistic Regression covers the basic concepts of linear and logistic models. The following topics are covered in this session:
Types of Machine Learning
Regression Vs Classification
What is Linear Regression?
What is Logistic Regression?
Linear Regression Use Case
Logistic Regression Use Case
Linear Regression Vs Logistic Regression
Blog Series: http://bit.ly/data-science-blogs
Data Science Training Playlist: http://bit.ly/data-science-playlist
Follow us to never miss an update in the future.
YouTube: https://www.youtube.com/user/edurekaIN
Instagram: https://www.instagram.com/edureka_learning/
Facebook: https://www.facebook.com/edurekaIN/
Twitter: https://twitter.com/edurekain
LinkedIn: https://www.linkedin.com/company/edureka
Transportation Problem with Pentagonal Intuitionistic Fuzzy Numbers Solved Us...IJERA Editor
This paper presents a solution methodology for transportation problem in an intuitionistic fuzzy environment in
which cost are represented by pentagonal intuitionistic fuzzy numbers. Transportation problem is a particular
class of linear programming, which is associated with day to day activities in our real life. It helps in solving
problems on distribution and transportation of resources from one place to another. The objective is to satisfy
the demand at destination from the supply constraints at the minimum transportation cost possible. The problem
is solved using a ranking technique called Accuracy function for pentagonal intuitionistic fuzzy numbers and
Russell’s Method
Polynomial regression model of making cost prediction in mixed cost analysisAlexander Decker
This document presents a study comparing different regression models for predicting costs based on production levels. It finds that a cubic polynomial regression model provides a better fit than linear regression or the high-low method. The study uses cost and production data from a company to build linear, quadratic, and cubic regression models. It finds the cubic polynomial regression has the highest R-squared value and lowest p-value, indicating it is the best-fitting model. The study concludes that polynomial regression generally provides a better approach for cost prediction than conventional linear regression or the high-low method.
11.polynomial regression model of making cost prediction in mixed cost analysisAlexander Decker
This document presents a study comparing different regression models for predicting costs based on production levels. It finds that a cubic polynomial regression model provides a better fit than linear regression or the high-low method. The study uses cost and production data from a company to build linear, quadratic, and cubic regression models. It finds the cubic polynomial regression has the highest R-squared value and lowest p-value, indicating it is best able to model the cost patterns in the data. The document concludes the cubic polynomial regression provides a better approach for cost prediction than traditional linear regression or high-low methods.
This document summarizes a student project on building machine learning models to recognize handwritten digits. The project involved collecting handwritten digit data, preprocessing the data, implementing logistic regression with gradient descent, evaluating performance on test data, and achieving over 90% accuracy on the test set. The models have applications in areas like banking, postal services, and document digitization.
This document discusses advanced functions and subroutines in Visual Basic, including:
- The difference between iteration and recursion
- Passing parameters by reference and arrays as parameters
- Optional parameters and overloading functions
- Calling one function from another function
It provides examples of writing recursive functions to calculate sums, factorials, and Fibonacci sequences. It also demonstrates overloading functions and using optional parameters.
1) The document discusses using machine learning techniques like logistic regression, random forest, and K-means clustering to develop a credit scoring model based on financial ratios to predict a company's probability of default.
2) Random forest performed the best with an AUC of 0.87 and high precision and recall, while logistic regression had a AUC of 0.75 but issues with type II errors.
3) K-means clustering had a lower precision predicting defaults but an acceptable F1-score and AUC of 0.80.
This document provides an overview of linear and logistic regression models. It discusses that linear regression is used for numeric prediction problems while logistic regression is used for classification problems with categorical outputs. It then covers the key aspects of each model, including defining the hypothesis function, cost function, and using gradient descent to minimize the cost function and fit the model parameters. For linear regression, it discusses calculating the regression line to best fit the data. For logistic regression, it discusses modeling the probability of class membership using a sigmoid function and interpreting the odds ratios from the model coefficients.
This document discusses various types of regression modeling and linear regression. It provides examples of linear regression analysis on fraud data and discusses assessing goodness of fit. It also briefly covers non-linear regression, problem areas like heteroskedasticity and collinearity, and model selection methods. Linear regression is presented geometrically and the assumptions and computations of ordinary least squares regression are explained.
Linear algebra application in linear programming Lahiru Dilshan
Linear programming is used to maximize or minimize quantities subject to constraints. It can be applied to problems with any number of variables and constraints, as long as the relationships are linear. Key aspects include defining an objective function to optimize, determining the feasible region where all constraints are satisfied, and finding extreme points where the objective function may be maximized or minimized. An example problem involves determining how to allocate candy mixtures to maximize revenue given constraints on available ingredients. The optimal solution is found at an extreme point within the bounded feasible region.
Bayesian analysis of shape parameter of Lomax distribution using different lo...Premier Publishers
The Lomax distribution also known as Pareto distribution of the second kind or Pearson Type VI distribution has been used in the analysis of income data, and business failure data. It may describe the lifetime of a decreasing failure rate component as a heavy tailed alternative to the exponential distribution. In this paper we consider the estimation of the parameter of Lomax distribution. Baye’s estimator is obtained by using Jeffery’s and extension of Jeffery’s prior by using squared error loss function, Al-Bayyati’s loss function and Precautionary loss function. Maximum likelihood estimation is also discussed. These methods are compared by using mean square error through simulation study with varying sample sizes. The study aims to find out a suitable estimator of the parameter of the distribution. Finally, we analyze one data set for illustration.
The document discusses post-optimal analysis in linear optimization problems. It describes how changes can affect feasibility or optimality, including changes to right-hand sides, adding new constraints, or changing objective coefficients. It also discusses adding a new activity/variable and using the dual simplex method to find the new optimal solution.
The document discusses models of computation and their uses. It provides examples of how a mathematical function takes an input and produces an output based on the model. Models describe how computation, memory, and communication are organized. The complexity of an algorithm can be measured given a model of computation, which allows studying performance independently of specific implementations. It also discusses how variables in a model require declaration and reservation of space in memory, with examples of space needed for different variable types.
This document provides an overview of recommender systems including background information, implementation details, and a demonstration. It discusses machine learning applications like unsupervised learning, linear regression, and gradient descent algorithms. It covers content-based filtering using known product features and collaborative filtering to identify unknown product features. Examples are given on using linear regression and gradient descent to make predictions for skills data and handle unknown values.
The document discusses the K-nearest neighbors (KNN) algorithm, a supervised machine learning classification method. KNN classifies new data based on the labels of the k nearest training samples in feature space. It can be used for both classification and regression problems, though it is mainly used for classification. The algorithm works by finding the k closest samples in the training data to the new sample and predicting the label based on a majority vote of the k neighbors' labels.
This document discusses simple and multiple regression analysis. Simple regression considers the relationship between one explanatory variable and one response variable, while multiple regression considers the relationship between one dependent variable and multiple independent variables. The document provides the formulas for simple and multiple linear regression. It also presents an example using SPSS to analyze the relationship between firm size, age, and performance. The SPSS output includes measures of model fit like R, R-squared, adjusted R-squared, ANOVA, regression coefficients, and diagnostics for assumptions. Hypothesis testing is conducted on the regression coefficients.
This document describes a parallel implementation of the Apriori algorithm for frequent itemset mining using MapReduce. The key steps are: (1) The Apriori algorithm is broken down into independent mapping tasks to count candidate itemset occurrences in parallel; (2) A MapReduce job is used for each iteration where the map function counts occurrences and the reduce function sums the counts; (3) Experimental results on real datasets show the approach achieves good speedup, scaleup, and can efficiently process large datasets in a distributed manner.
This document discusses multiple regression analysis. It begins by introducing multiple regression as an extension of simple linear regression that allows for modeling relationships between a response variable and multiple explanatory variables. It then covers topics such as examining variable distributions, building regression models, estimating model parameters, and assessing overall model fit and significance of individual predictors. An example demonstrates using multiple regression to build a model for predicting cable television subscribers based on advertising rates, station power, number of local families, and number of competing stations.
Linear regression and logistic regression are two machine learning algorithms that can be implemented in Python. Linear regression is used for predictive analysis to find relationships between variables, while logistic regression is used for classification with binary dependent variables. Support vector machines (SVMs) are another algorithm that finds the optimal hyperplane to separate data points and maximize the margin between the classes. Key terms discussed include cost functions, gradient descent, confusion matrices, and ROC curves. Code examples are provided to demonstrate implementing linear regression, logistic regression, and SVM in Python using scikit-learn.
The document discusses multiple regression models and their use in predicting a dependent variable from several independent variables. It defines a general multiple regression model and describes how regression coefficients are estimated using the least squares method. It also discusses assessing the significance and utility of regression models through measures like the F-test and R-squared value. An example is provided of researchers using multiple regression to predict lung capacity based on variables like height, age, gender and activity level.
The document discusses linear regression analysis and its applications. It provides examples of using regression to predict house prices based on house characteristics, economic forecasts based on economic indicators, and determining optimal advertising levels based on past sales data. It also explains key concepts in regression including the least squares method, the regression line, R-squared, and the assumptions of the linear regression model.
This document discusses shrinkage methods in linear regression, specifically Lasso and Ridge regression. Ridge regression aims to minimize coefficients by adding a penalty term that is the sum of the squared coefficients to the ordinary least squares objective function. Lasso regression is similar but uses the sum of the absolute values of coefficients as the penalty term. This causes Lasso to tend to set more coefficients exactly to zero, making it more suitable for feature selection. Gradient descent can be used to optimize Ridge regression, while coordinate descent is better for optimizing Lasso due to its non-differentiability at zero.
Business Analytics Foundation with R tools - Part 2Beamsync
Beamsync is providing analytics training courses in Bangalore. If you are looking business analytics training in Bangalore, then consult Beamsync.
For upcoming training schedules visit: http://beamsync.com/business-analytics-training-bangalore/
11.polynomial regression model of making cost prediction in mixed cost analysisAlexander Decker
This document presents a study comparing different regression models for predicting costs based on production levels. It finds that a cubic polynomial regression model provides a better fit than linear regression or the high-low method. The study uses cost and production data from a company to build linear, quadratic, and cubic regression models. It finds the cubic polynomial regression has the highest R-squared value and lowest p-value, indicating it is best able to model the cost patterns in the data. The document concludes the cubic polynomial regression provides a better approach for cost prediction than traditional linear regression or high-low methods.
This document summarizes a student project on building machine learning models to recognize handwritten digits. The project involved collecting handwritten digit data, preprocessing the data, implementing logistic regression with gradient descent, evaluating performance on test data, and achieving over 90% accuracy on the test set. The models have applications in areas like banking, postal services, and document digitization.
This document discusses advanced functions and subroutines in Visual Basic, including:
- The difference between iteration and recursion
- Passing parameters by reference and arrays as parameters
- Optional parameters and overloading functions
- Calling one function from another function
It provides examples of writing recursive functions to calculate sums, factorials, and Fibonacci sequences. It also demonstrates overloading functions and using optional parameters.
1) The document discusses using machine learning techniques like logistic regression, random forest, and K-means clustering to develop a credit scoring model based on financial ratios to predict a company's probability of default.
2) Random forest performed the best with an AUC of 0.87 and high precision and recall, while logistic regression had a AUC of 0.75 but issues with type II errors.
3) K-means clustering had a lower precision predicting defaults but an acceptable F1-score and AUC of 0.80.
This document provides an overview of linear and logistic regression models. It discusses that linear regression is used for numeric prediction problems while logistic regression is used for classification problems with categorical outputs. It then covers the key aspects of each model, including defining the hypothesis function, cost function, and using gradient descent to minimize the cost function and fit the model parameters. For linear regression, it discusses calculating the regression line to best fit the data. For logistic regression, it discusses modeling the probability of class membership using a sigmoid function and interpreting the odds ratios from the model coefficients.
This document discusses various types of regression modeling and linear regression. It provides examples of linear regression analysis on fraud data and discusses assessing goodness of fit. It also briefly covers non-linear regression, problem areas like heteroskedasticity and collinearity, and model selection methods. Linear regression is presented geometrically and the assumptions and computations of ordinary least squares regression are explained.
Linear algebra application in linear programming Lahiru Dilshan
Linear programming is used to maximize or minimize quantities subject to constraints. It can be applied to problems with any number of variables and constraints, as long as the relationships are linear. Key aspects include defining an objective function to optimize, determining the feasible region where all constraints are satisfied, and finding extreme points where the objective function may be maximized or minimized. An example problem involves determining how to allocate candy mixtures to maximize revenue given constraints on available ingredients. The optimal solution is found at an extreme point within the bounded feasible region.
Bayesian analysis of shape parameter of Lomax distribution using different lo...Premier Publishers
The Lomax distribution also known as Pareto distribution of the second kind or Pearson Type VI distribution has been used in the analysis of income data, and business failure data. It may describe the lifetime of a decreasing failure rate component as a heavy tailed alternative to the exponential distribution. In this paper we consider the estimation of the parameter of Lomax distribution. Baye’s estimator is obtained by using Jeffery’s and extension of Jeffery’s prior by using squared error loss function, Al-Bayyati’s loss function and Precautionary loss function. Maximum likelihood estimation is also discussed. These methods are compared by using mean square error through simulation study with varying sample sizes. The study aims to find out a suitable estimator of the parameter of the distribution. Finally, we analyze one data set for illustration.
The document discusses post-optimal analysis in linear optimization problems. It describes how changes can affect feasibility or optimality, including changes to right-hand sides, adding new constraints, or changing objective coefficients. It also discusses adding a new activity/variable and using the dual simplex method to find the new optimal solution.
The document discusses models of computation and their uses. It provides examples of how a mathematical function takes an input and produces an output based on the model. Models describe how computation, memory, and communication are organized. The complexity of an algorithm can be measured given a model of computation, which allows studying performance independently of specific implementations. It also discusses how variables in a model require declaration and reservation of space in memory, with examples of space needed for different variable types.
This document provides an overview of recommender systems including background information, implementation details, and a demonstration. It discusses machine learning applications like unsupervised learning, linear regression, and gradient descent algorithms. It covers content-based filtering using known product features and collaborative filtering to identify unknown product features. Examples are given on using linear regression and gradient descent to make predictions for skills data and handle unknown values.
The document discusses the K-nearest neighbors (KNN) algorithm, a supervised machine learning classification method. KNN classifies new data based on the labels of the k nearest training samples in feature space. It can be used for both classification and regression problems, though it is mainly used for classification. The algorithm works by finding the k closest samples in the training data to the new sample and predicting the label based on a majority vote of the k neighbors' labels.
This document discusses simple and multiple regression analysis. Simple regression considers the relationship between one explanatory variable and one response variable, while multiple regression considers the relationship between one dependent variable and multiple independent variables. The document provides the formulas for simple and multiple linear regression. It also presents an example using SPSS to analyze the relationship between firm size, age, and performance. The SPSS output includes measures of model fit like R, R-squared, adjusted R-squared, ANOVA, regression coefficients, and diagnostics for assumptions. Hypothesis testing is conducted on the regression coefficients.
This document describes a parallel implementation of the Apriori algorithm for frequent itemset mining using MapReduce. The key steps are: (1) The Apriori algorithm is broken down into independent mapping tasks to count candidate itemset occurrences in parallel; (2) A MapReduce job is used for each iteration where the map function counts occurrences and the reduce function sums the counts; (3) Experimental results on real datasets show the approach achieves good speedup, scaleup, and can efficiently process large datasets in a distributed manner.
This document discusses multiple regression analysis. It begins by introducing multiple regression as an extension of simple linear regression that allows for modeling relationships between a response variable and multiple explanatory variables. It then covers topics such as examining variable distributions, building regression models, estimating model parameters, and assessing overall model fit and significance of individual predictors. An example demonstrates using multiple regression to build a model for predicting cable television subscribers based on advertising rates, station power, number of local families, and number of competing stations.
Linear regression and logistic regression are two machine learning algorithms that can be implemented in Python. Linear regression is used for predictive analysis to find relationships between variables, while logistic regression is used for classification with binary dependent variables. Support vector machines (SVMs) are another algorithm that finds the optimal hyperplane to separate data points and maximize the margin between the classes. Key terms discussed include cost functions, gradient descent, confusion matrices, and ROC curves. Code examples are provided to demonstrate implementing linear regression, logistic regression, and SVM in Python using scikit-learn.
The document discusses multiple regression models and their use in predicting a dependent variable from several independent variables. It defines a general multiple regression model and describes how regression coefficients are estimated using the least squares method. It also discusses assessing the significance and utility of regression models through measures like the F-test and R-squared value. An example is provided of researchers using multiple regression to predict lung capacity based on variables like height, age, gender and activity level.
The document discusses linear regression analysis and its applications. It provides examples of using regression to predict house prices based on house characteristics, economic forecasts based on economic indicators, and determining optimal advertising levels based on past sales data. It also explains key concepts in regression including the least squares method, the regression line, R-squared, and the assumptions of the linear regression model.
This document discusses shrinkage methods in linear regression, specifically Lasso and Ridge regression. Ridge regression aims to minimize coefficients by adding a penalty term that is the sum of the squared coefficients to the ordinary least squares objective function. Lasso regression is similar but uses the sum of the absolute values of coefficients as the penalty term. This causes Lasso to tend to set more coefficients exactly to zero, making it more suitable for feature selection. Gradient descent can be used to optimize Ridge regression, while coordinate descent is better for optimizing Lasso due to its non-differentiability at zero.
Business Analytics Foundation with R tools - Part 2Beamsync
Beamsync is providing analytics training courses in Bangalore. If you are looking business analytics training in Bangalore, then consult Beamsync.
For upcoming training schedules visit: http://beamsync.com/business-analytics-training-bangalore/
This document provides guidance on performing and interpreting logistic regression analyses in SPSS. It discusses selecting appropriate statistical tests based on variable types and study objectives. It covers assumptions of logistic regression like linear relationships between predictors and the logit of the outcome. It also explains maximum likelihood estimation, interpreting coefficients, and evaluating model fit and accuracy. Guidelines are provided on reporting logistic regression results from SPSS outputs.
very detailed illustration of Log of Odds, Logit/ logistic regression and their types from binary logit, ordered logit to multinomial logit and also with their assumptions.
Thanks, for your time, if you enjoyed this short article there are tons of topics in advanced analytics, data science, and machine learning available in my medium repo. https://medium.com/@bobrupakroy
Suggest one psychological research question that could be answered.docxpicklesvalery
Suggest one psychological research question that could be answered by each of the following types of statistical tests:
z test
t test for independent samples, and
t test for dependent samples
FINAL EXAM
STAT 5201
Fall 2016
Due on the class Moodle site or in Room 313 Ford Hall
on Tuesday, December 20 at 11:00 AM
In the second case please deliver to the office staff
of the School of Statistics
READ BEFORE STARTING
You must work alone and may discuss these questions only with the TA or Glen Meeden. You
may use the class notes, the text and any other sources of printed material.
Put each answer on a single sheet of paper. You may use both sides and additional sheets if
needed. Number the question and put your name on each sheet.
If I discover a misprint or error in a question I will post a correction on the class web page. In
case you think you have found an error you should check the class home page before contacting us.
1
1. Find a recent survey reported in a newspaper, magazine or on the web. Briefly describe
the survey. What are the target population and sampled population? What conclusions are drawn
from the survey in the article. Do you think these conclusions are justified? What are the possible
sources of bias in the survey? Please be brief.
2. In a small country a governmental department is interested in getting a sample of school
children from grades three through six. Because of a shortage of buildings many of the schools had
two shifts. That is one group of students came in the morning and a different group came in the
afternoon. The department has a list of all the schools in the country and knows which schools
have two shifts of students and which do not. Devise a sampling plan for selecting the students to
appear in the sample.
3. For some population of size N and some fixed sampling design let π1 be the inclusion
probability for unit i. Assume a sample of size n was used to select a sample.
i) If unit i appears in the sample what is the weight we associate with it?
ii) Suppose the population can be partitioned into four disjoint groups or categories. Let Nj be
the size of the j’th category. For this part of the problem we assume that the Nj’s are not known.
Assume that for units in category j there is a constant probability, say γi that they will respond if
selected in the sample. These γj’s are unknown. Suppose in our sample we see nj units in category
j and 0 < rj ≤ nj respond. Note n1 + n2 + n3 + n4 = n. In this case how much weight should be
assigned to a responder in category j.
iii) Answer the same question in part ii) but now assume that the Nj’s are known.
iv) Instead of categories suppose that there is a real valued auxiliary variable, say age, attached
to each unit and it is known that the probability of response depends on age. That is units of
a similar age have a similar probability of responding when selected in the sample. Very briefly
explain how you would assign adjusted weights o ...
International Journal of Engineering Research and Development (IJERD)IJERD Editor
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journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
Nonlinear regression functions allow the regression model to be nonlinear in one or more independent variables. There are two main approaches to modeling nonlinear relationships: polynomials and logarithmic transformations. Polynomials approximate the relationship with higher-order terms of the independent variable, such as quadratic or cubic terms. Logarithmic transformations model relationships in percentage terms by taking logarithms of variables. Both approaches can be estimated using ordinary least squares regression.
This document proposes using machine learning techniques to predict COVID-19 infections based on chest x-ray images. Specifically, it involves using discrete wavelet transform to extract space-frequency features from chest x-rays, reducing the dimensionality of features using Shannon entropy, and then training standard machine learning classifiers like logistic regression, support vector machine, decision tree, and convolutional neural network on the extracted features to classify images as COVID-19 positive or negative. The document provides background on the proposed techniques of discrete wavelet transform, entropy, and various machine learning models.
Exploring Support Vector Regression - Signals and Systems ProjectSurya Chandra
Our team competed in a Kaggle competition to predict the bike share use as a part of their capital bike share program in Washington DC using a powerful function approximation technique called support vector regression.
This document summarizes an analysis of using Support Vector Regression (SVR) to predict bike rental data from a bike sharing program in Washington D.C. It begins with an introduction to SVR and the bike rental prediction competition. It then shows that linear regression performs poorly on this non-linear problem. The document explains how SVR maps data into higher dimensions using kernel functions to allow for non-linear fits. It concludes by outlining the derivation of the SVR method using kernel functions to simplify calculations for the regression.
This document presents a comparison of dimension reduction techniques for survival analysis, including principal component analysis (PCA), partial least squares (PLS), and random matrix approaches. Simulation data with 100 observations and 1000 covariates was generated to test the ability of each method to minimize bias and mean squared error in estimating survival functions. PCA and PLS were able to capture 50% of the variance by reducing the dimensions to 37. The estimated survival functions were compared to the true function over 5000 iterations. PLS had the lowest bias and mean squared error, followed by PCA, with the random matrix approaches performing worse.
This document provides an overview of linear regression and logistic regression concepts. It begins with an introduction to linear regression, discussing finding the best fit line to training data. It then covers the loss function and gradient descent optimization algorithm used to minimize loss and fit the model parameters. Next, it discusses logistic regression for classification problems, covering the sigmoid function for hypothesis representation and interpreting probabilities. It concludes by discussing feature scaling techniques like normalization and standardization to prepare data for modeling.
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Lab 10 covers hypothesis testing for two population means and linear regression analysis.
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Churn Prediction on customer data
1. Problem
´ Explore the dataset to determine its quality and specify data quality issues
identified. Apply the pre-processing and visualisation techniques used in
completing the Day 2 Group work.
´ Describe how you dealt with the data quality issues encountered
´ Modify the R code provided to fit a logistic regression model to predict
churn
´ Identify the variables that contribute most to predicting churn
´ What business insights can be derived from the analysis?
2. Preprocessing Data
Data cleaning:
´ Dropped four unwanted columns .
´ Changed categorical variables to Numerical variables.
´ No NULL records found
Exploratory Data Analysis:
´ Graphs for numerical values show normal Distribution
3. ´Gender count comparison
for churn – 0 and 1, shows
Male-Female count was very
high at around 2500 for churn-
0 compared to Male-female
count of < 1000 for churn-1, this
shows gender can be a good
predictor variable for
predicting churn.
Gender count churn-0 Vs churn-1
0
500
1000
1500
2000
2500
3000
0 1
Fema
le
Male
8. Payment Method and PaperlessBilling
count
0
200
400
600
800
1000
1200
1400
0 1
Bank transfer (automatic)
Credit card (automatic)
Electronic check
Mailed check
0
500
1000
1500
2000
2500
3000
0 1
No
Yes
9. Contract & StreamingMovie Count
0
500
1000
1500
2000
2500
0 1
Month-to-month
One year
Two year
0
500
1000
1500
2000
2500
0 1
No
No internet service
Yes
10. StreamingTV & TechSupport Count
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 1
No
No internet service
Yes
0
500
1000
1500
2000
2500
0 1
No
No internet service
Yes
11. Logistic Regression Model
´ Binary LR model works on categorical dependent variables or qualitative
variables that can take 2 values, ex: Yes/No,
´ Multinomial LR models can work for three possible categories.
´ LR models estimates probability of occurrence of event using logarithmic
likelihood function and not least minimum square method used by
regression models.
´ Binary logistic regression model estimates probability of occurrence of
dependent variable Y, which present itself in dichotomous form(0/1).
´ 𝑧 = 𝛼 + 𝛽1𝑋1 + 𝛽2𝑋2 + ⋯ + 𝛽𝑛𝑋𝑛
´ Z is known as logit., a,B1,B2,..Bk are the estimated parameters for
explanatory variables X1,X2,…Xk
12. LR model
´ Binary logistic regression defines Z logit as natural logarithm of odds, such
that:
´ Type equation here.
´ ℓ𝓃(pi/(1-pi))=zi
´ pi=1/(1+e-zi) or p=f(Z)
´ Substitute Categorical variables with dummy
Variables, then maximize the logarithmic
Likelihood function given by (yi).ln(pi)+(1-yi).ln(1-pi).
Keeping 𝛼1=𝛽1= 𝛽 2= 𝛽3=..= 𝛽n=0, calculate zi , pi, lli .
13. Logistic Regression
´ M3, M5,M7,M9 cells contain respective estimation parameters, use solver to
calculate z, pi, lli ,maximizing the sum of Lli using the data file.
´ There is no percentage of variance w.r.t predicting variables or R^2 as in
traditional regression models estimated by least minimum square., More
adequate criteria to choose best model is ROC curve(receiver operating
characteristic)
´ X2 test is used to verify the model significance , since its null hypothesis are
´ H0: =B2=B2=…=Bk=0
´ H1: there is atleast one Bi !=0
14. Logistic Regression
´ Confusion Matrix based on cutoff = 0.5, representing number of FP, TP, FN,
TN
´ OME- Overall model efficiency = (TP+ TN)/Total events
´ Sensitivity= % of hits, for a determined cutoff considering observations that
are in-fact events
´ Specificity = % of hits, for a determined cutoff considering observations that
are not events.