Suppose the OLS regression line for average hourly earnings (AHE) on years of education (EDUC) has the following formula:AHE = 4.5 + 2.5*EDUC. Matilda has 5 years of education and earns $22 per hour. The regression residual for Matilda is:

Question

BlackTom AI · Accepted Answer

Residual = actual outcome minus the predicted outcome, so residual = observed AHE − predicted AHE.

1. Relevant concepts:
- The OLS regression line gives predicted values: AHE_pred = intercept + slope × EDUC.
- The residual for an observation measures how far the actual value is above or below the predicted value (in the same units, dollars/hour here). A positive residual means the person earns more than predicted; negative means less.

2. Step-by-step reasoning and calculation:
- Regression formula: AHE = 4.5 + 2.5 × EDUC.
- Matilda’s EDUC = 5 years. Compute the predicted AHE:
  - Multiply slope by education: 2.5 × 5 = 12.5.
  - Add intercept: 4.5 + 12.5 = 17.0.
  - So AHE_pred = $17.00 per hour.
- Matilda’s observed AHE = $22.00 per hour.
- Compute the residual:
  - residual = observed − predicted = 22.0 − 17.0 = 5.0.

3. Intermediate steps shown:
- 2.5 × 5 = 12.5
- 4.5 + 12.5 = 17.0
- 22 − 17 = 5

4. Why the correct answer is correct:
- The residual formula is standard in regression analysis, and the arithmetic above yields a residual of +$5.00, meaning Matilda earns $5/hour more than the regression predicts for someone with 5 years of education.

5. Why the other multiple-choice options are incorrect:
- 18.0 would correspond to misreading or adding observed and predicted (22 − ? or 4?), but it does not match any correct residual calculation.
- 0.0 would imply observed equals predicted (22 = 22), which is false since predicted is $17.
- -8.0 would correspond to predicted being $30 (22 − 30 = −8) or a sign error; neither fits the given regression and data.

6. Conclusion:
The residual for Matilda is 5.0, which matches the provided correct answer.

Suppose the OLS regression line for average hourly earnings (AHE) on years of education (EDUC) has the following formula:AHE = 4.5 + 2.5*EDUC. Matilda has 5 years of education and earns $22 per hour. The regression residual for Matilda is:单项选择题

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