3003PSY Lecture 2

What is the primary purpose of using multiple regression analysis?

• To estimate a single mean response variable.

• To calculate correlation coefficients between variables.

• To predict the value of one dependent variable based on the values of multiple independent variables.

• To predict the value of one dependent variable based on the values of a single independent variable.

Which is NOT an assumption of multiple regression analysis?

• Normal distribution of residuals.

• Constant variance of residuals across predicted values.

• Heteroscedasticity of residuals.

• Linear relationships between variables.

In the context of regression diagnostics, what is the purpose of a residual plot?

• To check for patterns in residuals, ensuring assumptions are met.

• To determine the strength and direction of the relationship between independent and dependent variables.

• To compare the performance of different regression models based on their fit.

• To test for multicollinearity among predictor variables.

Which of the following is an indication of a well-fitting regression model?

• Presence of heteroscedasticity.

• High standard error.

• High R-squared value.

• Presence of multicollinearity.

What is the implication of heteroscedasticity in a regression model?

• Increased R-squared value.

• Reduced multicollinearity among predictors.

• Improved accuracy of the predictions.

• Increased standard errors of the coefficients, leading to less reliable statistical tests.

Why might a researcher decide to apply a transformation to a variable in regression analysis?

• To reduce the computational speed of the analysis.

• To make the data less understandable.

• To make the data distribution more normal or stabilize variance, improving the validity of statistical tests.

• To remove potential outliers which may be impacting the predictive utility of the regression model.

Which of the following transformations could be used to reduce the skew of a positively skewed variable?

• Adding a constant to each data point.

• Multiplying each data point by a constant.

• Squaring each data point.

• Computing the logarithmic value for each data point.

What is Mahalanobis’ distance used for in multiple regression analysis?

• To identify univariate outliers based on their distance from the overall data distribution.

• To identify multivariate outliers based on their distance from the overall data distribution.

• To determine the strength and direction of relationships between variables.

• To check whether residuals in a regression model are normally distributed.

What is a potential issue when applying transformations to correct skewed variables?

• Transformations always eliminate skewness completely, ensuring perfect normality.

• Applying a transformation increases the likelihood of multicollinearity in multiple regression.

• Once a transformation is applied, back-transforming the results is unnecessary for interpretation.

• Transformations can distort the interpretability of the original variable’s scale.

Which of the following statements is correct?

• Univariate outliers should only be removed if removal alters the regression model.

• Multivariate outliers should always be removed.

• Transformed variables should only be used if transformation alters the regression model.

• All of these options are correct.