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Answer: 3.5.
## Explanation The standard error of the estimate (SEE) in regression analysis is calculated as: $$\text{SEE} = \sqrt{\text{Mean Square Error}}$$ From the ANOVA table: - **Error Sum of Squares** = 48 - **Degrees of Freedom for Error** = 4 - **Mean Square Error** = 12 (calculated as Error Sum of Squares ÷ Degrees of Freedom = 48 ÷ 4 = 12) Therefore: $$\text{SEE} = \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \approx 3.464$$ Rounding to one decimal place gives 3.5. **Key Points:** 1. The Mean Square Error (MSE) is the variance of the residuals 2. The standard error of the estimate is the square root of MSE 3. This measures the typical distance between the observed values and the regression line 4. In the ANOVA table, Mean Square Error is found in the "Error" row under "Mean Square" Thus, the correct answer is **A. 3.5.**
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An analyst computes the following analysis of variance (ANOVA) table for a simple linear regression:
| Source | Sum of Squares | Degrees of Freedom | Mean Square |
|---|---|---|---|
| Regression | 144 | 1 | 144 |
| Error | 48 | 4 | 12 |
| Total | 192 | 5 | --- |
The standard error of the estimate for the regression is closest to:
A
3.5.
B
6.9.
C
12.0.
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