DA0-002 Data Analysis Practice Question
In a simple linear regression model y = 2.5 + 1.2x, what is the predicted value of y when x = 10?
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
✓
14.5
Plug x=10: y = 2.5 + 1.2*10 = 2.5 + 12 = 14.5.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✗
12.0
Why it's wrong here
This applies the slope alone (1.2 × 10 = 12.0) and omits the intercept of 2.5, giving 12.0 instead of 14.5. Dropping the intercept is tempting when the slope term dominates, but the model's baseline value must always be added.
- ✗
13.7
Why it's wrong here
Substituting x = 10 gives 2.5 + 12.0 = 14.5, not 13.7. The value 13.7 tempts anyone who multiplies 1.2 by 10 and then adds only 1.2, or who misreads the intercept as 1.7, but the intercept is fixed at 2.5.
- ✓
14.5
Why this is correct
Substituting x = 10 into the fitted equation gives y = 2.5 + 1.2(10) = 2.5 + 12 = 14.5. The slope of 1.2 contributes twelve units across the ten-unit increase, and the intercept of 2.5 adds the baseline, yielding the predicted response.
- ✗
10.0
Why it's wrong here
Returning 10.0 simply echoes the input x rather than evaluating the model, ignoring both the slope of 1.2 and the intercept of 2.5. The correct prediction is 14.5; 10.0 would only arise if the regression line were the identity y = x.
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