PSYC3010 Lecture 7: Multiple Regression

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Questions and Answers

What is the coefficient of determination (R2) in a bivariate regression model?

SSregression / SSY

1 - r2

SSresidual / SSY

(SSY - SSresidual) / SSY (correct)

In multiple regression, what does the term 'variance accounted for by effect' refer to?

(SSY - SSresidual) / SSY

1 - r2

SSregression / SSY (correct)

SSresidual / SSY

What does the coefficient of determination (R2) in a multiple regression model with uncorrelated predictors indicate?

The shared overlapping variance between predictors.

The importance of the predictors in identifying the variance in the dependent variable.

The overlap of variance between predictors and the dependent variable.

The proportion of variance accounted for by each predictor individually. (correct)

What does it mean when R2 is less than the sum of rY12 and rY22 in a multiple regression model with correlated predictors?

There is an underestimation in the importance of individual predictors. Signup and view all the answers

How is R2 calculated in a multiple regression model with correlated predictors?

(r2Y1 + r2Y2 - 2rY1rY2) Signup and view all the answers

In terms of their contribution to the variance in test scores, what percentage is accounted for by IQ and studying?

< 70% Signup and view all the answers

What does R2 tell us in hierarchical multiple regression?

What is in the full model Signup and view all the answers

Which measure is typically entered at step 2 in a sequential model according to the theory described?

Specific attitudinal measure Signup and view all the answers

What does R2change represent in hierarchical multiple regression?

What has been added at that step Signup and view all the answers

In hierarchical multiple regression, why is R2change for Block 1 identical to R2?

Because it represents the starting point with no prior blocks to add Signup and view all the answers

Which statistic can be reported to show the increment in prediction at each block in hierarchical multiple regression?

$F$-change Signup and view all the answers

When using multiple regression, what does the F test assess?

The strength of the overall relationship between the criterion and set of predictors. Signup and view all the answers

In bivariate regression, what is tested when assessing significance?

Does the predictor account for significant variance in the DV? Signup and view all the answers

What does the multiple correlation (R) indicate in multiple regression analysis?

Relation between the outcome and a set of predictors. Signup and view all the answers

What does the linear composite in the regression equation represent?

A composite score of predictors weighted by their regression coefficients Signup and view all the answers

How does multiple regression differ from bivariate regression?

Multiple regression uses more than one predictor to predict the outcome. Signup and view all the answers

In the regression equation, what does the coefficient represent for each predictor?

The weight or influence of the predictor on the DV Signup and view all the answers

In multiple regression analysis, what do Confidence Intervals [CIs] for parameters indicate?

The range where parameter values are likely to fall. Signup and view all the answers

What is the purpose of regressing the criterion/DV on the linear composite in a regression model?

To predict the DV using multiple predictors Signup and view all the answers

What is tested by the t test in multiple regression analysis?

Significance of individual predictors. Signup and view all the answers

How are actual DV scores compared to predicted scores in a regression analysis?

They are examined for accuracy and variability Signup and view all the answers

What is the role of the constant term in a regression equation?

It acts as a baseline value when all predictors are zero Signup and view all the answers

Why is there always a certain degree of difference between actual DV scores and their predicted scores in regression analysis?

To account for error and uncertainty in predictions Signup and view all the answers

In hierarchical regression, what is the purpose of entering anxiety at step 1?

To control for anxiety while predicting GPA with other variables in later steps. Signup and view all the answers

What does R2change in hierarchical regression indicate?

The change in variance explained when additional predictors are included. Signup and view all the answers

Which statistic is used to test the overall significance of a model in hierarchical regression?

F change Signup and view all the answers

What does the F statistic compare in hierarchical regression?

The fit of the model with and without certain predictors. Signup and view all the answers

In hierarchical regression, why is it important to assess R2 change?

To determine the unique contribution of each predictor to the model. Signup and view all the answers

What does the coefficient beta (β) represent in hierarchical regression?

The slope or change in outcome variable per unit change in predictor variable. Signup and view all the answers

Which step in hierarchical regression involves predicting GPA by motivation and study time above and beyond that explained by anxiety?

Step 2 Signup and view all the answers

'Model Summary' in hierarchical regression provides information about which aspects of the model?

'R2 change' and 'F change'. Signup and view all the answers

'Tests of Coefficients' in hierarchical regression show which specific information about each predictor?

'T-value and P-value'. Signup and view all the answers

'Hierarchy' in hierarchical regression refers to what process?

'Stepwise addition of predictors'. Signup and view all the answers

Study Notes

Hierarchical Multiple Regression

Hierarchical multiple regression is a type of multiple regression that allows researchers to control for the effects of certain variables before examining the relationships between other variables.
In hierarchical multiple regression, variables are entered into the equation in a specific order, with the most important variables entered first.
The order of entry is crucial in hierarchical multiple regression, as it affects the interpretation of the results.

Model Summary

The model summary provides an overview of the regression model, including the R, R2, R2 change, and F statistics.
R is the multiple correlation coefficient, which measures the strength of the relationship between the dependent variable and the set of independent variables.
R2 is the proportion of variance in the dependent variable that is explained by the independent variables.
R2 change is the proportion of variance in the dependent variable that is explained by each additional independent variable.
F is the F-statistic, which tests the significance of the overall regression model.

Testing Coefficients

The coefficients of the independent variables are tested using t-tests, which determine whether each independent variable is significantly related to the dependent variable.
The coefficients are also used to create the regression equation, which predicts the dependent variable based on the independent variables.

Importance of Predictors

The importance of each predictor variable is determined by its unique contribution to the regression model.
The contribution of each predictor variable is measured by the change in R2 (R2 change) when the variable is added to the model.
The F-statistic is used to test the significance of each predictor variable.

Multiple Regression

Multiple regression is a statistical technique that examines the relationship between a dependent variable and multiple independent variables.
Multiple regression is an extension of bivariate regression, which examines the relationship between two variables.
Multiple regression is used to predict the dependent variable based on multiple independent variables.

Assumptions of Multiple Regression

The assumptions of multiple regression include:
- Linearity: The relationship between the dependent variable and the independent variables should be linear.
- Independence: The observations should be independent of each other.
- Homoscedasticity: The variance of the dependent variable should be constant across all levels of the independent variables.
- Normality: The dependent variable should be normally distributed.
- No or little multicollinearity: The independent variables should not be highly correlated with each other.

R2 and R2 Change

R2 is the proportion of variance in the dependent variable that is explained by the independent variables.
R2 change is the proportion of variance in the dependent variable that is explained by each additional independent variable.
R2 and R2 change are used to evaluate the goodness of fit of the regression model.

F-Statistic

The F-statistic is a ratio of two chi-square distributions that tests the overall significance of the regression model.
The F-statistic is used to determine whether the independent variables are jointly significant in explaining the dependent variable.

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Description

This quiz covers the topics discussed in Lecture 7 of PSYC3010, focusing on standard multiple regression, hierarchical multiple regression, bivariate regression, and multiple correlation. Topics include single and multiple predictors, variation as a function of multiple predictors, achieving better predictions, and the relation between the outcome variable and predictors.