which of the following residual plots would indicate a good lsrl model?

A good LSRL (least-squares regression line) model is indicated by a residual plot where the points are randomly scattered around the horizontal axis, with no visible pattern or curve.

What a “good” residual plot looks like

For a linear model to be appropriate, the residual plot should show:

• Points scattered randomly above and below 0 (the horizontal axis), with no clear pattern.

• Roughly similar spread of residuals across all x-values (no strong funnel shape narrowing or widening).

• No obvious curvature, clusters, or repeating wave-like shapes.

In many multiple-choice questions, the correct residual plot is the one that looks like a random cloud of points centered around 0.

What indicates a bad LSRL model

If the residual plot shows any of these, the linear model is usually not appropriate:

• A curved pattern (e.g., U-shape or inverted U-shape), suggesting a nonlinear relationship.

• Residuals mostly on one side of the horizontal axis, meaning systematic over- or under-prediction.

• A funnel shape (residuals spread increasing or decreasing with x), indicating non-constant variance (heteroscedasticity).

In an exam question that shows several residual plots, you would choose the one with:

Random scatter of points above and below 0, with no pattern and roughly constant spread across x. ✅

Information gathered from public forums or data available on the internet and portrayed here.