DA0-002 Data Analysis Practice Question
A data analyst is building a linear regression model to predict sales based on advertising spend. The analyst notices that the residuals are not normally distributed and have a non‑constant variance. Which of the following transformations is most appropriate to apply to the dependent variable?
⚠ Common exam trap
CompTIA often tests the misconception that any scaling technique (standardization or normalization) can fix heteroscedasticity or non‑normality, but these methods only change the range or center of the data, not the shape of the residual distribution or the variance structure.
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
✓
Logarithmic transformation
The logarithmic transformation is the most appropriate choice because it stabilizes non‑constant variance (heteroscedasticity) and helps make the residuals more normally distributed, which are key assumptions for linear regression. By compressing the scale of the dependent variable (sales), it reduces the impact of large values and often linearizes multiplicative relationships, such as diminishing returns from advertising spend.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✗
Standardization (z-score)
Why it's wrong here
Standardization rescales data to mean 0 and std 1 but does not address heteroscedasticity or normality of residuals.
- ✗
Normalization (min-max scaling)
Why it's wrong here
Min-max scaling compresses values into a fixed range; being linear, it leaves skew and heteroscedasticity untouched. It tempts because it is a routine preprocessing step, but it would be correct when features must share a bounded scale, such as neural network inputs, not when residual variance must be stabilised.
- ✓
Logarithmic transformation
Why this is correct
Non-constant variance and non-normal residuals violate linear regression assumptions. A logarithmic transformation of the dependent variable compresses the scale of large values, stabilising variance and pulling the residual distribution towards normality, which is the standard remedy for this pattern of heteroscedasticity.
- ✗
Square root transformation
Why it's wrong here
A square root transformation compresses larger values, which can reduce right skew and stabilise variance, but it is weaker than a log transformation and fails when sales values include zero or negatives. It tempts as a variance-stabilising remedy, yet the log transform is the standard choice for this residual pattern.
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