DA0-002 Data Analysis Practice Question
A simple linear regression model predicts sales (y) from advertising spend (x). The equation is y = 2.5x + 10, and R² = 0.81. Which interpretation is correct?
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
✓
81% of the variation in sales is explained by advertising spend.
Slope indicates that each unit increase in x increases y by 2.5 units. R² of 0.81 means 81% of variance in y is explained by x.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✗
The correlation between sales and advertising is 0.81.
Why it's wrong here
R² of 0.81 means 81% of variance in sales is explained by advertising spend; correlation is the square root, about 0.90, with sign matching the positive slope. Reporting 0.81 as the correlation understates the linear relationship. The 0.81 figure would correctly describe the coefficient of determination, not r.
- ✗
When advertising is $0, sales are $2.5.
Why it's wrong here
The intercept is 10, so at zero advertising spend predicted sales equal $10; 2.5 is the slope, the change per unit of x. Confusing intercept with slope is the trap, though reading the intercept is valid when x=0 is meaningful.
- ✓
81% of the variation in sales is explained by advertising spend.
Why this is correct
R-squared is the coefficient of determination: 0.81 means 81% of the variance in the dependent variable (sales) is accounted for by the independent variable (advertising spend). The remaining 19% is unexplained by the model, so this interpretation matches the statistic precisely.
- ✗
For every $1 increase in advertising, sales increase by $10 on average.
Why it's wrong here
The intercept of 10 is the predicted sales when advertising spend is zero, not a per-dollar rate; the slope of 2.5 governs that change. Confusing intercept with slope is tempting because both are constants in the equation, yet the intercept describes the baseline only, and would be the correct focus if the question asked for predicted sales at zero spend.
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