The following estimated regression equation is based on 30 observations. The values of SST and SSR are 1,801 and 1,762, respectively. a. Compute R² (to 3 decimals). b. Compute R (to 3 decimals). c. Comment on the goodness of fit. The estimated regression equation provided an excellent fit Hide Feedback Partially Correct Icon Key ŷ 18.1 +3.9x12.1x2 + 7.8x3 +2.8x4 Hint(s) Che Hint(s) Che
The following estimated regression equation is based on 30 observations. The values of SST and SSR are 1,801 and 1,762, respectively. a. Compute R² (to 3 decimals). b. Compute R (to 3 decimals). c. Comment on the goodness of fit. The estimated regression equation provided an excellent fit Hide Feedback Partially Correct Icon Key ŷ 18.1 +3.9x12.1x2 + 7.8x3 +2.8x4 Hint(s) Che Hint(s) Che
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 Analysis Example
**Problem Statement:**
The following estimated regression equation is based on 30 observations.
\[
\hat{y} = 18.1 + 3.9x_1 - 2.1x_2 + 7.8x_3 + 2.8x_4
\]
The values of SST (Total Sum of Squares) and SSR (Sum of Squares for Regression) are 1,801 and 1,762, respectively.
**Tasks:**
a. **Compute \(R^2\) (to 3 decimals).**
b. **Compute \(R^2_{\text{adj}}\) (to 3 decimals).**
c. **Comment on the goodness of fit.**
**Solution:**
a. To compute \(R^2\):
\[
R^2 = \frac{\text{SSR}}{\text{SST}} = \frac{1,762}{1,801} \approx 0.978
\]
Incorrect entry:
\[ \]
b. To compute \(R^2_{\text{adj}}\):
\[
R^2_{\text{adj}} = 1 - \left(\frac{1 - R^2}{n - k - 1} \times (n - 1)\right)
\]
Where:
- \( n \) is the number of observations (30)
- \( k \) is the number of predictors (4)
So,
\[
R^2_{\text{adj}} = 1 - \left(\frac{1 - 0.978}{30 - 4 - 1} \times (30 - 1)\right)
\]
Incorrect entry:
\[ \]
c. Comment on the goodness of fit:
The estimated regression equation provided an excellent fit.
Correct selection:
\[
\boxed{\text{provided an excellent fit}}
\]
Explanation:
- **Hint:** Use the provided results and formulas for calculating the coefficients of determination to evaluate the regression model.
- **Feedback:** Partially correct. Ensure the correct values are entered for theoretical completeness.
**Graph/Diagram Explanation:**
No graphs or diagrams are present in this example.
---
This form of transcription can serve as an understanding aid for students studying regression analysis, helping them to correctly apply and interpret the formulas involved. This example elucidates the process of computing both \(R^2\) and \(R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc3ad949-79b2-4a66-83f9-922936cf2321%2F6f8fa82d-c534-4ae7-a441-223238309eae%2F8ln5y4_processed.png&w=3840&q=75)
Transcribed Image Text:### Regression Analysis Example
**Problem Statement:**
The following estimated regression equation is based on 30 observations.
\[
\hat{y} = 18.1 + 3.9x_1 - 2.1x_2 + 7.8x_3 + 2.8x_4
\]
The values of SST (Total Sum of Squares) and SSR (Sum of Squares for Regression) are 1,801 and 1,762, respectively.
**Tasks:**
a. **Compute \(R^2\) (to 3 decimals).**
b. **Compute \(R^2_{\text{adj}}\) (to 3 decimals).**
c. **Comment on the goodness of fit.**
**Solution:**
a. To compute \(R^2\):
\[
R^2 = \frac{\text{SSR}}{\text{SST}} = \frac{1,762}{1,801} \approx 0.978
\]
Incorrect entry:
\[ \]
b. To compute \(R^2_{\text{adj}}\):
\[
R^2_{\text{adj}} = 1 - \left(\frac{1 - R^2}{n - k - 1} \times (n - 1)\right)
\]
Where:
- \( n \) is the number of observations (30)
- \( k \) is the number of predictors (4)
So,
\[
R^2_{\text{adj}} = 1 - \left(\frac{1 - 0.978}{30 - 4 - 1} \times (30 - 1)\right)
\]
Incorrect entry:
\[ \]
c. Comment on the goodness of fit:
The estimated regression equation provided an excellent fit.
Correct selection:
\[
\boxed{\text{provided an excellent fit}}
\]
Explanation:
- **Hint:** Use the provided results and formulas for calculating the coefficients of determination to evaluate the regression model.
- **Feedback:** Partially correct. Ensure the correct values are entered for theoretical completeness.
**Graph/Diagram Explanation:**
No graphs or diagrams are present in this example.
---
This form of transcription can serve as an understanding aid for students studying regression analysis, helping them to correctly apply and interpret the formulas involved. This example elucidates the process of computing both \(R^2\) and \(R
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