DA0-002 Data Analysis Practice Question
A data scientist runs a linear regression model to predict customer spending based on income. The R-squared value is 0.45 and the p-value for the slope coefficient is 0.03. At a significance level of α=0.05, which of the following conclusions 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
✓
The slope is statistically significant, and the model explains 45% of the variance.
The p-value (0.03) is less than α (0.05), so the slope is statistically significant. R²=0.45 means the model explains 45% of the variance.
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 slope is not statistically significant, and the model explains 55% of the variance.
Why it's wrong here
Both parts are wrong: p=0.03 is below α=0.05, so the slope is significant, and R-squared 0.45 explains 45%, not 55%. It is tempting because 55% is the complement of R-squared, but that figure represents unexplained variance.
- ✓
The slope is statistically significant, and the model explains 45% of the variance.
Why this is correct
With α=0.05, the slope p-value of 0.03 falls below the threshold, so the slope is statistically significant. R-squared of 0.45 means income explains 45% of the variance in spending. Both conditions in the stem are satisfied simultaneously.
- ✗
The slope is statistically significant, and the model explains 55% of the variance.
Why it's wrong here
The slope conclusion is right, but R-squared of 0.45 means 45% of variance is explained, not 55%. It is tempting because 0.55 is the residual proportion (1−0.45), which describes unexplained variance, not the model's explanatory share.
- ✗
The slope is not statistically significant, and the model explains 45% of the variance.
Why it's wrong here
With p=0.03 below α=0.05, the slope is statistically significant, so this conclusion inverts the decision rule. It is tempting because R-squared genuinely equals 0.45, but that value concerns variance explained, not the significance test on the coefficient.
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