Podcast
Questions and Answers
What is the assumption of regression that states that the variance of the residuals should be equal across all levels of the predictor variable?
What is the assumption of regression that states that the variance of the residuals should be equal across all levels of the predictor variable?
Homogenous
What measure of influence is used to detect unusual values on the independent and dependent variables?
What measure of influence is used to detect unusual values on the independent and dependent variables?
Cooks Distance
What is the purpose of using the t-distribution in regression analysis?
What is the purpose of using the t-distribution in regression analysis?
To account for increased error at the top and bottom of the regression line
What does the standardized regression coefficient for each predictor variable in multiple regression analysis provide?
What does the standardized regression coefficient for each predictor variable in multiple regression analysis provide?
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Why might there be a significant association in a Pearson's correlation, but not in multiple regression analysis?
Why might there be a significant association in a Pearson's correlation, but not in multiple regression analysis?
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What is the purpose of maximizing SS Regression in a regression analysis?
What is the purpose of maximizing SS Regression in a regression analysis?
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What does a R2 value of 0 indicate in a regression model?
What does a R2 value of 0 indicate in a regression model?
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What is the difference between unstandardized coefficients and standardized coefficients (Beta) in a regression analysis?
What is the difference between unstandardized coefficients and standardized coefficients (Beta) in a regression analysis?
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What is the purpose of semi-partial correlation (Part) in a regression analysis?
What is the purpose of semi-partial correlation (Part) in a regression analysis?
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What is the purpose of visual inspection of residual plots in regression diagnostics?
What is the purpose of visual inspection of residual plots in regression diagnostics?
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Study Notes
Variance
- Maximise Sum of Squares (SS) Regression: goal of regression analysis
- Minimise SS Error: residual variation not explained by the model
Regression Coefficient R2
- Represents the proportion of variance in the dependent variable explained by independent variables
- Ranges from 0 (no explanation) to 1 (full explanation)
Statistical Control
- Shared variance: not included in the coefficients table
- Unstandardised Coefficients: explain unique contribution of each independent variable
- Standardized coefficients (Beta): allow comparison of different predictors
- Semi-partial correlation (Part): measures unique contribution of a specific independent variable
Identifying Unusual Scores
- Regression diagnostics: identify unusual scores influencing the solution
- Outlier score: unusual on IV, studentised residual, and visual identification
- Cut-offs for identifying outliers: 2.58 (0.01) and 3.29 (0.001)
Measures of Influence
- Cook's Distance: measures influence of a data point on the regression slope
- Leverage: uses distance to measure influence
- Mahalanobis Distance: uses chi-square to measure influence
Assumptions of Regression
- Linearity: relationship between predictors and outcome
- Normally Distributed: residuals should be normally distributed
- Homogenous: equal variances across all levels of predictors
- Independence of observations: cannot be statistically tested
Additional Notes
- Partial correlation: measures relationship between two variables controlling for other variables
- Regression equation: predicts outcome variable based on predictor variables
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Description
Understand the concepts of variance, regression coefficients, and R2 in regression analysis. Learn how to maximize SS Regression and minimize SS Error.
