Multiple regression analysis allows researchers to examine the relationship between one dependent or outcome variable and two or more independent or predictor variables. It extends simple linear regression to model more complex relationships. Stepwise regression is a technique that automates the process of building regression models by sequentially adding or removing variables based on statistical criteria. It begins with no variables in the model and adds variables one at a time based on their contribution to the model until none improve it significantly.
this ppt gives you adequate information about Karl Pearsonscoefficient correlation and its calculation. its the widely used to calculate a relationship between two variables. The correlation shows a specific value of the degree of a linear relationship between the X and Y variables. it is also called as The Karl Pearson‘s product-moment correlation coefficient. the value of r is alwys lies between -1 to +1. + 0.1 shows Lower degree of +ve correlation, +0.8 shows Higher degree of +ve correlation.-0.1 shows Lower degree of -ve correlation. -0.8 shows Higher degree of -ve correlation.
this ppt gives you adequate information about Karl Pearsonscoefficient correlation and its calculation. its the widely used to calculate a relationship between two variables. The correlation shows a specific value of the degree of a linear relationship between the X and Y variables. it is also called as The Karl Pearson‘s product-moment correlation coefficient. the value of r is alwys lies between -1 to +1. + 0.1 shows Lower degree of +ve correlation, +0.8 shows Higher degree of +ve correlation.-0.1 shows Lower degree of -ve correlation. -0.8 shows Higher degree of -ve correlation.
Today’s overwhelming number of techniques applicable to data analysis makes it extremely difficult to define the most beneficial approach while considering all the significant variables.
The analysis of variance has been studied from several approaches, the most common of which uses a linear model that relates the response to the treatments and blocks. Note that the model is linear in parameters but may be nonlinear across factor levels. Interpretation is easy when data is balanced across factors but much deeper understanding is needed for unbalanced data.
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.
Sir Ronald Fisher pioneered the development of ANOVA for analyzing results of agricultural experiments.1 Today, ANOVA is included in almost every statistical package, which makes it accessible to investigators in all experimental sciences. It is easy to input a data set and run a simple ANOVA, but it is challenging to choose the appropriate ANOVA for different experimental designs, to examine whether data adhere to the modeling assumptions, and to interpret the results correctly. The purpose of this report, together with the next 2 articles in the Statistical Primer for Cardiovascular Research series, is to enhance understanding of ANVOA and to promote its successful use in experimental cardiovascular research. My colleagues and I attempt to accomplish those goals through examples and explanation, while keeping within reason the burden of notation, technical jargon, and mathematical equations.
Brief description of the concepts related to correlation analysis. Problem Sums related to Karl Pearson's Correlation, Spearman's Rank Correlation, Coefficient of Concurrent Deviation, Correlation of a grouped data.
Multiple regression analysis is a powerful technique used for predicting the unknown value of a variable from the known value of two or more variables.
Correlation and regression.
It shows different aspects of Correlation and regression.
A small comparison of these two is also listed in this presentation.
Today’s overwhelming number of techniques applicable to data analysis makes it extremely difficult to define the most beneficial approach while considering all the significant variables.
The analysis of variance has been studied from several approaches, the most common of which uses a linear model that relates the response to the treatments and blocks. Note that the model is linear in parameters but may be nonlinear across factor levels. Interpretation is easy when data is balanced across factors but much deeper understanding is needed for unbalanced data.
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.Analysis of variance (ANOVA) is an analysis tool used in statistics that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.
Sir Ronald Fisher pioneered the development of ANOVA for analyzing results of agricultural experiments.1 Today, ANOVA is included in almost every statistical package, which makes it accessible to investigators in all experimental sciences. It is easy to input a data set and run a simple ANOVA, but it is challenging to choose the appropriate ANOVA for different experimental designs, to examine whether data adhere to the modeling assumptions, and to interpret the results correctly. The purpose of this report, together with the next 2 articles in the Statistical Primer for Cardiovascular Research series, is to enhance understanding of ANVOA and to promote its successful use in experimental cardiovascular research. My colleagues and I attempt to accomplish those goals through examples and explanation, while keeping within reason the burden of notation, technical jargon, and mathematical equations.
Brief description of the concepts related to correlation analysis. Problem Sums related to Karl Pearson's Correlation, Spearman's Rank Correlation, Coefficient of Concurrent Deviation, Correlation of a grouped data.
Multiple regression analysis is a powerful technique used for predicting the unknown value of a variable from the known value of two or more variables.
Correlation and regression.
It shows different aspects of Correlation and regression.
A small comparison of these two is also listed in this presentation.
To get a copy of the slides for free Email me at: japhethmuthama@gmail.com
You can also support my PhD studies by donating a 1 dollar to my PayPal.
PayPal ID is japhethmuthama@gmail.com
To get a copy of the slides for free Email me at: japhethmuthama@gmail.com
You can also support my PhD studies by donating a 1 dollar to my PayPal.
PayPal ID is japhethmuthama@gmail.com
Regression analysis mathematically and statistically describes the relationship between a set of independent variables and a dependent variable. This presentation describes the concept of regression and its types with suitable illustrations. This presentation also explains the regression analysis spss path and its interpretations.
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
Topic: Regression
Student Name: Nayab
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
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• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
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The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
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Bob Boule
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Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
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Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
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1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
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Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
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Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
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Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
2. History:
The earliest form of regression was
the method of least squares, which was
published by Legendre in 1805, and by Gauss in
1809.
The term "regression" was used by British
biometrician sir Francis Galton in the (1822-
1911), to describe a biological phenomenon.
Sir Galton's work on inherited characteristics
of sweet peas led to the initial conception of
linear regression.
3. Introduction:
Regression is a statistical technique for investigating
and modeling the relationship between variables.
Applications of regression are numerous and occur
in almost every field, including engineering, the
physical and the social sciences, and the biological
sciences.
Usually, the investigator seeks to ascertain the causal
effect of one variable upon another—the effect of a
price increase upon demand, for example, or the effect
of changes in the money supply upon the inflation rate.
4. Definition:
Regression is the measure of the average
relationship between two or more variables in terms of
the original units of the data. It is unquestionably the
most widely used statistical technique in social
sciences. It is also widely used in biological and
physical science.
Regression equation is (y) =a + b x
Slope (b) = (NΣXY-(ΣX)( ΣY)) / (NΣX2 – (ΣX)2)
Intercept (a) = (ΣY-b(ΣX)) / N
5. Review of Simple linear regression.
A simple linear regression is carried out to
estimate the relationship between a dependent variable, Y
and a single explanatory variable, x given a set of data
that includes observations for both of these variables for a
particular population.
•For ex: A real estate agent wishes to examine the
relationship between the selling price of a home and its size
(measured in square feet)
•A random sample of 10 houses is selected
Dependent variable (Y) = house price
Independent variable (X) = square feet
6. Simple Linear Regression Model
ii10i
εXββY
Linear component
Population
Y intercept
Population
Slope
Coefficient
Random
Error
term
Dependent
Variable
Independen
t Variable
Random Error
component
7. i10i
XbbYˆ
The simple linear regression equation provides
an estimate of the population regression line
Estimate of
the regression
intercept
Estimate of the
regression slope
Estimated
(or predicted)
Y value for
observation i
Value of X for
observation i
The individual random error terms ei have a mean of zero
Prediction equation is given by:
9. Measures of Variation
Total variation is made up of two parts:
SSESSRSST
Total Sum of
Squares
Regression Sum
of Squares
Error Sum of
Squares
2
i
)YY(SST 2
ii
)YˆY(SSE
2
i
)YYˆ(SSR
where:
= Average value of the dependent variable
Yi = Observed values of the dependent variable
i = Predicted value of Y for the given Xi valueYˆ
Y
11. Coefficient of Determination, r2
• The coefficient of determination is the
portion of the total variation in the
dependent variable that is explained by
variation in the independent variable
• The coefficient of determination is also
called r-squared and is denoted as r2
1r0
2note:
squaresofsum
squaresofregression2
total
sum
SST
SSR
r
12. Multiple linear regression
Introduction:
The general purpose of multiple regression (the
term was first used by Pearson, 1908) is to learn more
about the relationship between several independent or
predictor variables and a dependent or criterion
variables.
13. Definition:
A regression model that involves the relationship
between two or more explanatory variables and a response
variable by fitting a linear equation to observed data (more
than one regressor variable) is called a multiple regression
model. Every value of the independent variable x is
associated with a value of the dependent variable y.
Suppose that the yield in the pounds of conversation in a
chemical process depends on temperature and the catalyst
concentration. A multiple regression model that might
describe the relationship is
14. y=β0+β1x1+β2x2+ε
where y denotes the yield,x1denotes the temperature,x2
denotes the catalyst concentration. This is multiple linear
regression model with two regressor variables.
The term linear is used because equation is a linear function
of the known parameters β0,β1& β2 and ε is error term.
The parameter β1 indicates that the expected
change in response (y) per unit change in x1 when x2 is held
constant. Similarly β2 measures the expected change in (y)
per unit change in x2 when x1 held constant.
In general, the response y may be related to k regressor (or)
predictor variables. The model
y= β0+β1x1+β2x2+……………+ βkxk+ε
15. is a multiple linear regression with k regressors. The parameters
βj, j=0,1,…….k. are called regression coefficients.
The parameter βj represents the expected change in the response (y)
per unit change in xj when all of the remaining regressor variables xi
(i≠j) are held constant. For this reason the parameters βj, j=1,…….k are
often called partial regression coefficients.
16.
17. Assumptions of Regression
• For any given set of values of x1, x2, … , xk, the random
error has a probability distribution with the following
properties:
• 1. Mean equal to 0
• 2. Variance equal to 2
• 3. Normal distribution
• 4. Random errors are independent
18. Regression Analysis: Model Building
• General Linear Model
• Determining When to Add or Delete Variables
• Analysis of a Larger Problem
• Multiple Regression Approach
to Analysis of Variance
19. General Linear Model
Models in which the parameters (β0, β1, . . . , βp)
all have exponents of one are called linear
models.
• First-Order Model with One Predictor
Variable
y x0 1 1
y x0 1 1
20. Variable Selection Procedures
• Stepwise Regression
• Forward Selection
• Backward Elimination
Iterative; one
independent
variable at a time
is added or
deleted
Based on
the F statistic
21. Variable Selection Procedures
• F Test
• To test whether the addition of x2 to a model
involving x1 (or the deletion of x2 from a model
involving x1and x2) is statistically significant
F0=MSR/MSRes
(MSR=SSR/K)
The p-value corresponding to the F statistic is the
criterion used to determine if a variable should be added or
deleted
(SSE(reduced)-SSE(full))/number of extra terms
MSE(full)
F
22. Forward Selection
• This procedure is similar to stepwise-
regression, but does not permit a variable to
be deleted.
• This forward-selection procedure starts with
no independent variables.
• It adds variables one at a time as long as a
significant reduction in the error sum of
squares (SSE) can be achieved.
23. Backward Elimination
• This procedure begins with a model that
includes all the independent variables the
modeler wants considered.
• It then attempts to delete one variable at a
time by determining whether the least
significant variable currently in the model
can be removed because its p-value is less
than the user-specified or default value.
• Once a variable has been removed from the
model it cannot re enter at a subsequent step.
24. Stepwise regression:
Procedure of simultaneous forward and backward
selection also available
In a stepwise regression, predictor variables are
entered into the regression equation one at a time
based upon statistical criteria.
At each step in the analysis the predictor variable that
contributes the most to the prediction equation in
terms of increasing the multiple correlation, R, is
entered first. This process is continued only if
additional variables add anything statistically to the
regression equation.
25. The choosing is done according to following
manner
i.e.) delete x.i if ^i
2 E( 2 )(Z1
lZl)-1
ii<Fout=F1,n-r-1
pout
enter x.j if (n-r-2)cjq
2 (cjjcqq-cjq
2) > Fin=F1,n-r-2
pin
here either pin or pout are specify the stepwise
procedure is terminated when either of the two
following points happens
26. We can’t enter or delete the variables according to the above criteria
i.e.) this includes the case where enter all regressor & can’t delete any.
The processor dictates that the same regressor be enter and deleted in
successive operations the stepwise selection procedure is an attempt to
achieve to insert variables in terms until the regression equation is
satisfactory.
When additional predictor variables add anything statistically
meaningful to the regression equation, the analysis stops. Thus, not all
predictor variables may enter the equation in stepwise regression.
There are a number of multiple regression variants. Stepwise is usually
a good choice though one can enter all variables simultaneously as an
alternative. Similarly, one can enter all of the variables simultaneously
and gradually eliminate predictors one by one if elimination does little to
change the overall prediction.
Stepwise regression procedure is the best procedure when
compared to the all procedures we have see earlier.
27. Uses of Regression Analysis:
1.Regression analysis helps in establishing a functional
Relationship between two or more variables.
2. Since most of the problems of economic analysis are based
on cause and effect relationships, the regression analysis is a
highly valuable tool in economic and business research.
3. Regression analysis predicts the values of dependent
variables from the values of independent variables.
4. We can calculate coefficient of correlation (r) and
coefficient of determination (R2) with the help of regression
coefficients.
28.
29.
30.
31.
32.
33. ANOVA TABLE:
Source Degrees of freedom Sum of squares Mean Square F
Regression 2 5550.8166 2775.4083 4.7*10-16
Residual 22 233.7260 10.6239
Total 24 5784.5426
R2 = 0.9596 Adjusted R2 = 0.9559
Scatter plot for cases and
distance