Question

We can use residual plots to gauge changing variability. The residuals are generally plotted against each predictor variable xj Which of the following indicates there is no violation?

A. There is no way to indicate no violation
B. The predictor variable is randomly dispersed across the residuals
C. The residuals are randomly dispersed across the values of xj
D. The residuals are NOT randomly dispersed across the values of xj

Answer 1

To use residual plots for checking changing variability, we should look for the residuals to be randomly dispersed across the values of the predictor variable, indicating no violation of the homoscedasticity assumption in linear regression.

Step-by-step explanation:

The question asks how we can use residual plots to check for changing variability and what indicates there is no violation of the assumptions of homoscedasticity (constant variance across values of predictor variables). The correct answer is that the residuals are randomly dispersed across the values of xj, which means there is no apparent pattern to the residuals as the predictor variable changes. This randomness suggests that the variability of the residual values does not change with the values of xj and that the assumption of equal variance is likely being met.

In linear regression, it is crucial to check that the residuals, or differences between observed and predicted values, are distributed randomly around the zero line with no clear pattern when plotted against each predictor variable. If this assumption holds, it suggests that the predictors are suitable for the regression model and that the predictions are reliable. A lack of pattern also indicates the residuals are independent, another critical assumption in regression analysis.