During a model-design iteration of a multiple linear regression that predicts daily building energy consumption, you review the four standard diagnostic plots. The Normal Q-Q plot of standardized residuals is nearly linear, but the Scale-Location (spread-location) plot displays a pronounced fan shape in which the spread of residuals widens as the fitted values increase. Based on this evidence, which action should you prioritize in the next model iteration?
Refit the model using a variance-stabilizing transformation (such as a log or Box-Cox) or weighted least squares to make the residual variance approximately constant.
Standard-scale all predictor variables to zero mean and unit variance and then refit the ordinary least-squares model.
Introduce higher-order polynomial terms for each predictor to capture possible non-linear relationships.
Remove observations with large Cook's distance values to reduce leverage effects before refitting the same model.
A fan-shaped Scale-Location plot indicates heteroscedasticity-error variance grows with the predicted value. The most direct way to remove this violation of the homoscedasticity assumption is to transform the response with a variance-stabilizing transformation (for example, a log or Box-Cox power transform) or to refit the model with weighted least squares so that observations with larger error variance receive less influence. Adding polynomial terms targets non-linearity rather than unequal variance, deleting high-leverage points deals with influence not heteroscedasticity, and merely standardizing predictors leaves the residual variance pattern unchanged. Therefore, the transformation or heteroscedasticity-aware re-estimation is the correct next step.
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What is heteroscedasticity in regression analysis?
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How does a variance-stabilizing transformation like a log or Box-Cox work?
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What is weighted least squares (WLS) and how does it address heteroscedasticity?