When more than 5% of observations have standardized residuals with an absolute value greater than 1.96, this suggests ...

• A. The residuals are homoscedastic.
• B. The sample size is insufficient to assess fit.
• C. The model is perfectly specified.
• D. The model is a poor representation of the actual data.

Answer: (D)

When you look at standardized residuals, you’re checking whether the model’s errors behave like random noise with a normal distribution. The cutoff 1.96 corresponds to the 97.5th percentile of a standard normal, so about 5% of observations are expected to have an absolute standardized residual greater than 1.96 just by chance if the model is appropriate. If more than 5% fall beyond this threshold, the residuals aren’t matching the assumed normal error behavior, signaling that the model isn’t capturing the data well. This points to the model not being a good representation of the actual data, which could be due to nonlinearity, missing important predictors, incorrect error structure, or outliers influencing the fit.