ANOVA Regression Residual Total tercept mber of lespersons df Coefficients 77.0 43.0 SS 6,847.3 8,943.3 MS F Significance F Standard Error t Stat 12.613 5.185 P-value
ANOVA Regression Residual Total tercept mber of lespersons df Coefficients 77.0 43.0 SS 6,847.3 8,943.3 MS F Significance F Standard Error t Stat 12.613 5.185 P-value
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Regression Model Analysis
A regression model relating \( x \), the number of salespersons at a branch office, to \( y \), the annual sales at the office (in thousands of dollars), provided the following regression output. The total sample size is \( n_{\text{total}} = 38 \).
#### ANOVA Table
| Source | df | SS | MS | F |
|--------------|-----|--------|--------|-------|
| Regression | | 6,847.3| | |
| Residual | | | | |
| Total | | 8,943.3| | |
#### Coefficients
| | Coefficients | Standard Error | t Stat | P-value |
|-----------------|--------------|----------------|--------|---------|
| Intercept | 77.0 | 12.613 | | |
| Number of Salespersons | 43.0 | 5.185 | 8.29 | < 0.01 |
#### Analysis
a. **Estimated Regression Equation:**
\[
\hat{y} = 77 + 43x
\]
b. **F-Test for Significance (0.05 level):**
- F-value: 27.56
- p-value: less than 0.01
- Conclusion: Reject \( H_0 \)
c. **t-Test for Coefficient Significance (0.05 level):**
- t Stat: 8.29
- p-value: less than 0.01
- Conclusion: Reject \( H_0 : \beta_1 = 0 \)
d. **Prediction for Memphis Branch:**
- Number of salespersons: 13
- Predicted annual sales: $ 636 \text{ thousand}
This analysis demonstrates the statistical significance of the relationship between the number of salespersons and the annual sales, supported by both the F-test and t-test results. The predicted sales for the Memphis branch office, with 13 salespersons, is $636,000, based on the regression model.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbce6a0cf-373b-4a7a-ae65-e94348138195%2F5c49480c-47a5-4a71-a94a-4ab70dbd5f1c%2Fbsxym4bi_processed.png&w=3840&q=75)
Transcribed Image Text:### Regression Model Analysis
A regression model relating \( x \), the number of salespersons at a branch office, to \( y \), the annual sales at the office (in thousands of dollars), provided the following regression output. The total sample size is \( n_{\text{total}} = 38 \).
#### ANOVA Table
| Source | df | SS | MS | F |
|--------------|-----|--------|--------|-------|
| Regression | | 6,847.3| | |
| Residual | | | | |
| Total | | 8,943.3| | |
#### Coefficients
| | Coefficients | Standard Error | t Stat | P-value |
|-----------------|--------------|----------------|--------|---------|
| Intercept | 77.0 | 12.613 | | |
| Number of Salespersons | 43.0 | 5.185 | 8.29 | < 0.01 |
#### Analysis
a. **Estimated Regression Equation:**
\[
\hat{y} = 77 + 43x
\]
b. **F-Test for Significance (0.05 level):**
- F-value: 27.56
- p-value: less than 0.01
- Conclusion: Reject \( H_0 \)
c. **t-Test for Coefficient Significance (0.05 level):**
- t Stat: 8.29
- p-value: less than 0.01
- Conclusion: Reject \( H_0 : \beta_1 = 0 \)
d. **Prediction for Memphis Branch:**
- Number of salespersons: 13
- Predicted annual sales: $ 636 \text{ thousand}
This analysis demonstrates the statistical significance of the relationship between the number of salespersons and the annual sales, supported by both the F-test and t-test results. The predicted sales for the Memphis branch office, with 13 salespersons, is $636,000, based on the regression model.
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