The following estimated regression equation relating sales to inventory investment and advertising expenditures was given. ý - 22 + 15x, + 9x2 The data used to develop the model came from a survey of 10 stores; for those data, SSyy (Total Sum of Squares) - 19,000 and SSR (Regression Sum of Squares) - 14,250. (a) For the estimated regression equation given, compute R2.(Round your answer to two decimal places.) R2 = (b) Compute the adjusted r-square, R2. (Round your answer to two decimal places.) R- (c) Does the model appear to explain a large amount of variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to the nearest integer.) The adjusted coefficient of determination shows that % of the variability has been explained by the two independent variables; thus, we conclude that the model -Select-v explain a large amount variability.
The following estimated regression equation relating sales to inventory investment and advertising expenditures was given. ý - 22 + 15x, + 9x2 The data used to develop the model came from a survey of 10 stores; for those data, SSyy (Total Sum of Squares) - 19,000 and SSR (Regression Sum of Squares) - 14,250. (a) For the estimated regression equation given, compute R2.(Round your answer to two decimal places.) R2 = (b) Compute the adjusted r-square, R2. (Round your answer to two decimal places.) R- (c) Does the model appear to explain a large amount of variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to the nearest integer.) The adjusted coefficient of determination shows that % of the variability has been explained by the two independent variables; thus, we conclude that the model -Select-v explain a large amount variability.
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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![**Estimated Regression Equation and Analysis**
The following estimated regression equation relates sales to inventory investment and advertising expenditures:
\( \hat{y} = 22 + 15x_1 + 9x_2 \)
The data to develop the model was obtained from a survey of 10 stores. The calculations for those data include:
- SSyy (Total Sum of Squares) = 19,000
- SSR (Regression Sum of Squares) = 14,250
**Tasks:**
(a) **Compute \( R^2 \) for the Estimated Regression Equation**
To calculate \( R^2 \), use the formula:
\[ R^2 = \frac{\text{SSR}}{\text{SSyy}} \]
Round your answer to two decimal places.
**\( R^2 = \_\_\_\_ \)**
(b) **Compute the Adjusted \( R^2 \), \( R^2_a \)**
Use the adjusted \( R^2 \) formula:
\[ R^2_a = 1 - \left(\frac{(1 - R^2)(n - 1)}{n - p - 1}\right) \]
Where \( n \) is the number of observations, and \( p \) is the number of independent variables.
Round your answer to two decimal places.
**\( R^2_a = \_\_\_\_ \)**
(c) **Model Variability Explanation**
Determine if the model explains a large amount of variability.
Consider the variability explanation significant if it is at least 55%. Round your answer to the nearest integer.
**Conclusion:**
The adjusted coefficient of determination shows that \_\_\_\_ % of the variability has been explained by the two independent variables. Therefore, we conclude that the model \_\_\_ explain a large amount of variability.
---
This text is designed as an educational guide for understanding and computing the components of a regression analysis, emphasizing practical application and interpretation of \( R^2 \) and adjusted \( R^2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9aee9d7-69b3-43e2-b021-7b6cf1d794ed%2F78961f82-31bc-4b65-9dbd-3c85f870a998%2F2q1w9ef_processed.png&w=3840&q=75)
Transcribed Image Text:**Estimated Regression Equation and Analysis**
The following estimated regression equation relates sales to inventory investment and advertising expenditures:
\( \hat{y} = 22 + 15x_1 + 9x_2 \)
The data to develop the model was obtained from a survey of 10 stores. The calculations for those data include:
- SSyy (Total Sum of Squares) = 19,000
- SSR (Regression Sum of Squares) = 14,250
**Tasks:**
(a) **Compute \( R^2 \) for the Estimated Regression Equation**
To calculate \( R^2 \), use the formula:
\[ R^2 = \frac{\text{SSR}}{\text{SSyy}} \]
Round your answer to two decimal places.
**\( R^2 = \_\_\_\_ \)**
(b) **Compute the Adjusted \( R^2 \), \( R^2_a \)**
Use the adjusted \( R^2 \) formula:
\[ R^2_a = 1 - \left(\frac{(1 - R^2)(n - 1)}{n - p - 1}\right) \]
Where \( n \) is the number of observations, and \( p \) is the number of independent variables.
Round your answer to two decimal places.
**\( R^2_a = \_\_\_\_ \)**
(c) **Model Variability Explanation**
Determine if the model explains a large amount of variability.
Consider the variability explanation significant if it is at least 55%. Round your answer to the nearest integer.
**Conclusion:**
The adjusted coefficient of determination shows that \_\_\_\_ % of the variability has been explained by the two independent variables. Therefore, we conclude that the model \_\_\_ explain a large amount of variability.
---
This text is designed as an educational guide for understanding and computing the components of a regression analysis, emphasizing practical application and interpretation of \( R^2 \) and adjusted \( R^2 \).
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