SAT Math · Two-variable data: models and scatterplots · medium
A researcher fits a linear model to a data set. When the residuals are plotted against the x-values, they show a clear curved (U-shaped)…
A researcher fits a linear model to a data set. When the residuals are plotted against the x-values, they show a clear curved (U-shaped) pattern instead of being randomly scattered. What does this pattern suggest?
Answer and explanation
Answer: C: A linear model may not be the best fit for this data; a nonlinear model might fit better.
When a linear model fits well, the residuals scatter randomly around zero with no pattern. A clear U-shape in the residual plot means the model overpredicts in some regions and underpredicts in others in a systematic way, which signals curvature in the real relationship. A nonlinear model, such as a quadratic, might fit better. That is choice C. Choice A is the opposite of what the pattern shows. Choice B overstates the problem, since a relationship exists but is curved. Choice D is unsupported, because the residual pattern says nothing directly about sample size.
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