STA 235 · Week 3 · model diagnostics
What error patterns do to prediction intervals
Every row uses the same fitted linear model. Read the prediction plot alongside the four familiar regression diagnostics: residuals versus fitted, normal Q-Q, a residual histogram, and scale-location.
Structural violation: a nonlinear relationship
The data follow a curve, but the fitted model is forced to use one straight line.
Forced linear prediction versus the true curved mean
forced linear fit95% prediction intervaltrue curved meanmissed future outcome
Residuals vs fitted
Normal Q-Q
Residual histogram
Scale-location
Regular errors: normal and equal spread
The usual prediction interval is calibrated for this data-generating story.
Prediction interval and future outcomes
fitted line95% prediction intervalcovered future outcomemissed future outcome
Residuals vs fitted
Normal Q-Q
Residual histogram
Scale-location
Violation: non-normal, right-skewed errors
Occasional large positive errors make the residual distribution asymmetric.
Prediction interval and future outcomes
fitted line95% prediction intervalcovered future outcomemissed future outcome
Residuals vs fitted
Normal Q-Q
Residual histogram
Scale-location
Violation: unequal variance
Errors are small at low x and grow sharply as x increases.
Prediction interval and future outcomes
fitted line95% prediction intervalcovered future outcomemissed future outcome
Residuals vs fitted
Normal Q-Q
Residual histogram
Scale-location