Actual Minus Predicted, in That Order

You'll learnthe residual as actual minus predicted and what its sign means, how to read one in context, what a residual plot is for, why random scatter is the good case, and how a curve in the residuals overrules any correlation.

A residual is what the model missed for one individual, and it is computed in one order: actual minus predicted. Reverse the subtraction and every sign flips, so over-prediction and under-prediction trade places — this page draws both plots side by side and checks that each pair is an exact negation. Collected against x, the residuals answer a question the scatterplot answers less sharply and the correlation cannot answer at all: is a straight line the right shape. A cloud built from a curve still earns r = 0.925 here, and its residuals arch 8.9 points from ends to middle. The residual plot wins that argument, every time.

8 STEPS · 6 QUICK CHECKS · THE ORDER · THE SIGN · THE PLOT · PATTERNS · v1

actual minus predicted · the residuals total exactly 0 · a curve gives r = 0.925 and an 8.9-point arch

Before you start

What you're looking at

The eight students and their fitted line, and then the same eight numbers with the line subtracted out — which is all a residual plot is.

The question

The scatterplot and the correlation both say the fit is good. What is the residual plot able to see that neither of them can?

Watch for

Which side of zero each point lands on, and whether the points hold a shape. In a residual plot, a shape is the finding and no shape is the good news.

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