AI0-001 Machine Learning and Deep Learning Practice Question
A company uses linear regression to predict sales based on advertising spend. The model's residuals show a pattern of increasing variance as spend increases. Which assumption of linear regression is violated?
⚠ Common exam trap
CompTIA AI exams often test the distinction between homoscedasticity and normality, trapping candidates who confuse residual variance patterns with residual distribution shape, especially when the question describes a 'fan' or 'cone' shape in the residual plot.
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
✓
Homoscedasticity
The pattern of increasing residual variance with higher advertising spend violates the assumption of homoscedasticity, which requires constant variance of errors across all levels of the independent variable. In linear regression, heteroscedasticity like this can lead to inefficient coefficient estimates and unreliable confidence intervals, often detected via a Breusch-Pagan test or residual plot analysis.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
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Normality
Why it's wrong here
Normality concerns the distribution of residuals at each predictor value, assessed via histograms or Q-Q plots, not how their spread changes. It is tempting because both involve residual shape, but normality would be the answer if residuals were skewed or heavy-tailed rather than heteroscedastic.
- ✓
Homoscedasticity
Why this is correct
Increasing variance in residuals as advertising spend rises directly breaches homoscedasticity, which requires constant error variance across all predictor values. The stem's fan-shaped residual pattern is the textbook signature of heteroscedasticity, so this assumption is the one violated.
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Linearity
Why it's wrong here
Linearity concerns the mean of residuals staying near zero across fitted values; a curved residual pattern indicates it. Here residuals fan outward, which is variance behaviour, not curvature. Linearity would be correct if residuals showed systematic bend rather than widening spread.
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Independence
Why it's wrong here
Independence concerns correlation between successive residuals over time or clustering, not the spread of residuals changing with fitted values. It is tempting because residual patterns suggest structure, but independence would be the answer if residuals were autocorrelated rather than fanning out.
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