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
A U-shaped residual pattern indicates non-linearity, meaning the linear functional form is misspecified; independence concerns correlation between successive errors, not curvature. Independence is tempting because it is a core regression assumption, and it would be the correct answer if residuals showed clustering by time or group rather than a systematic curve.
- ✗
Homoscedasticity
Why it's wrong here
Homoscedasticity concerns constant residual variance; a U-shaped pattern shows systematic curvature, meaning the linear form misfits the data. It is tempting because homoscedasticity genuinely fails when residual spread fans out or narrows across fitted values.
- ✗
Normality of residuals
Why it's wrong here
A U-shaped residual pattern indicates systematic curvature, meaning the linearity assumption is violated; the model needs polynomial or transformed predictors. Normality concerns the distribution of residuals, assessed via Q-Q plots or histograms, and would be the correct diagnosis if residuals were skewed or heavy-tailed rather than patterned.
- ✓
Linearity
Why this is correct
A U-shaped residual pattern means the model systematically under- and over-predicts across the predictor range, indicating the true relationship is curved rather than straight. The linearity assumption, that predictors relate to the outcome additively in a straight line, is therefore violated.
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