Judging a linear sales model from its residual plot

A residual is actual value minus predicted value. If a linear model suits the data, the residuals should look like random scatter around 0, with no shape to them.

These residuals do have a shape. They start well below 0, climb above 0 through the middle, and fall back below 0 at the end, tracing an upside-down U. That curve says the data bend in a way the line cannot follow: the line overestimates early and late and underestimates in the middle. A curved model, such as a quadratic, would capture that bend.

So the linear model is not appropriate, and the reason is the clear pattern in the residuals. That is choice A.

Each choice

• A (correct). The residuals form a clear arch, so the line is missing curvature in the data and is not a good model.
• B. The verdict is right but the reason is not. Having more positive than negative residuals does not on its own rule out a line. What matters is that the residuals follow a pattern rather than scattering randomly.
• C. This reverses the meaning of a pattern. A clear shape in the residuals is evidence against the model; a good fit leaves residuals with no pattern.
• D. Matching the biggest positive and negative residuals says nothing about whether a line fits. The arch shape is the key feature, and it shows the line is the wrong kind of model here.