Which plot is commonly used to assess homoscedasticity in regression?

Which plot is commonly used to assess homoscedasticity in regression?

• A. QQ plot.
• B. Residuals vs fitted values plot.
• C. Histogram of the dependent variable.
• D. Scatterplot of X versus Y.

Answer: (B)

Homoscedasticity means the residuals have constant variance across the range of predicted values from the model. The residuals vs fitted values plot directly shows this: plot residuals (y-axis) against fitted values (x-axis). If the spread of the residuals is roughly the same everywhere, the assumption is met. If you see the spread widening or narrowing as fitted values increase (a funnel or cone shape), that indicates heteroscedasticity, meaning the variance of the errors changes with the level of the prediction and standard errors may be biased. This plot is favored for this assessment because it visualizes the pattern of residual dispersion across the entire range of predictions, making it easy to detect non-constant variance, outliers, or potential model misspecification. In contrast, a QQ plot checks whether residuals are normally distributed, a histogram shows the distribution of the dependent variable rather than the residuals’ variance, and a scatterplot of X versus Y shows the relationship between variables but not the behavior of residual variance across predictions.

Homoscedasticity means the residuals have constant variance across the range of predicted values from the model. The residuals vs fitted values plot directly shows this: plot residuals (y-axis) against fitted values (x-axis). If the spread of the residuals is roughly the same everywhere, the assumption is met. If you see the spread widening or narrowing as fitted values increase (a funnel or cone shape), that indicates heteroscedasticity, meaning the variance of the errors changes with the level of the prediction and standard errors may be biased.

This plot is favored for this assessment because it visualizes the pattern of residual dispersion across the entire range of predictions, making it easy to detect non-constant variance, outliers, or potential model misspecification. In contrast, a QQ plot checks whether residuals are normally distributed, a histogram shows the distribution of the dependent variable rather than the residuals’ variance, and a scatterplot of X versus Y shows the relationship between variables but not the behavior of residual variance across predictions.