Question 265 of 986
DA0-002 Data Analysis Practice Question
A data analyst uses linear regression to model the relationship between advertising spend and sales. The residual plot shows a clear U-shaped pattern. What assumption is violated?
⚠ Common exam trap
CompTIA often tests the distinction between residual pattern shapes and their corresponding assumptions, so the trap here is that candidates confuse a curved pattern (nonlinearity) with heteroscedasticity or non-normality, leading them to pick B or C instead of D.
Answer choices
Why each option matters
Answer the question above first, then reveal the full breakdown to understand why each option is right or wrong.
Correct answer & explanation
✓
Linearity
The U-shaped pattern in the residual plot indicates that the relationship between advertising spend and sales is not linear; the model fails to capture the curvature in the data. Linear regression assumes a straight-line relationship between predictors and the response, so a systematic pattern like a U-shape directly violates the linearity assumption. This means the model is misspecified and requires a transformation or a nonlinear modeling approach.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✗
Independence of residuals
Why it's wrong here
Independence violations appear as autocorrelation in time series, not a pattern in residuals vs fitted.
- ✗
Homoscedasticity
Why it's wrong here
Homoscedasticity violations show increasing/decreasing spread, not a U-shape.
- ✗
Normality of residuals
Why it's wrong here
Normality is assessed via histogram or Q-Q plot, not residual vs fitted plot.
- ✓
Linearity
Why this is correct
A U-shaped pattern means the relationship is not linear; the model is missing a nonlinear term.
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Last reviewed: Jun 30, 2026
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