4.1 Answer each of the following: a. Suppose that a simple regression has quantities N = 20, Ey=7825.94, y = 19.21, and SSR = 375.47, find R². b. Suppose that a simple regression has quantities R² = 0.7911, SST = 725.94, and N = 20, find ². c. Suppose that a simple regression has quantities Σ(y₁ - y)² = 631.63 and E= 182.85, find R². 4.2 Consider the following estimated regression equation (standard errors in parentheses): y = 64.29 +0.99x R² = 0.379 (se) (2.42) (0.18) Rewrite the estimated equation, including coefficients, standard errors, and R², that would result if a. All values of x were divided by 10 before estimation. b. All values of y were divided by 10 before estimation. c. All values of y and x were divided by 10 before estimation. 4.3 We have five observations on
4.1 Answer each of the following: a. Suppose that a simple regression has quantities N = 20, Ey=7825.94, y = 19.21, and SSR = 375.47, find R². b. Suppose that a simple regression has quantities R² = 0.7911, SST = 725.94, and N = 20, find ². c. Suppose that a simple regression has quantities Σ(y₁ - y)² = 631.63 and E= 182.85, find R². 4.2 Consider the following estimated regression equation (standard errors in parentheses): y = 64.29 +0.99x R² = 0.379 (se) (2.42) (0.18) Rewrite the estimated equation, including coefficients, standard errors, and R², that would result if a. All values of x were divided by 10 before estimation. b. All values of y were divided by 10 before estimation. c. All values of y and x were divided by 10 before estimation. 4.3 We have five observations on
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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Please answer 4.1 and 4.2, thanks!
![# 4.7 Exercises
## 4.7.1 Problems
### 4.1 Answer each of the following:
a. Suppose that a simple regression has quantities \( N = 20 \), \( \sum y_i^2 = 7825.94 \), \( \bar{y} = 19.21 \), and \( SSR = 375.47 \). Calculate \( R^2 \).
b. Suppose that a simple regression has quantities \( R^2 = 0.7911 \), \( SST = 725.94 \), and \( N = 20 \). Find \( \hat{\sigma}^2 \).
c. Suppose that a simple regression has quantities \( \sum (y_i - \bar{y})^2 = 631.63 \) and \( \sum \hat{e}_i^2 = 182.85 \). Find \( R^2 \).
### 4.2 Consider the following estimated regression equation (standard errors in parentheses):
\[ \hat{y} = 64.29 + 0.99x \quad R^2 = 0.379 \]
\[ (se) \quad (2.42)\, (0.18) \]
Rewrite the estimated equation, including coefficients, standard errors, and \( R^2 \), that would result if:
a. All values of \( y \) were divided by 10 before estimation.
b. All values of \( y \) were divided by 10 before estimation.
c. All values of \( y \) and \( x \) were divided by 10 before estimation.
### 4.3 We have the observations on \( x \) and \( y \). They are \( x_i = 3, 2, 1, -1, 0 \) with corresponding \( y \) values \( y_i = 4, 2, 3, 1, 0 \). The fitted least squares line is \( \hat{y}_i = 1.2 + 0.8x_i \). The sum of squared least squares residuals is \( \sum_{i=1}^5 \hat{e}_i^2 = 3.6 \), \( \sum_{i=1}^5 (x_i - \bar{x})^2 = 10 \), and \( \sum_{i=1}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1ec9e1-71c5-41a7-88e5-1ec0b0e62692%2F6bca573e-40ed-484b-b131-db3f82a78d8c%2Fgtvht6f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# 4.7 Exercises
## 4.7.1 Problems
### 4.1 Answer each of the following:
a. Suppose that a simple regression has quantities \( N = 20 \), \( \sum y_i^2 = 7825.94 \), \( \bar{y} = 19.21 \), and \( SSR = 375.47 \). Calculate \( R^2 \).
b. Suppose that a simple regression has quantities \( R^2 = 0.7911 \), \( SST = 725.94 \), and \( N = 20 \). Find \( \hat{\sigma}^2 \).
c. Suppose that a simple regression has quantities \( \sum (y_i - \bar{y})^2 = 631.63 \) and \( \sum \hat{e}_i^2 = 182.85 \). Find \( R^2 \).
### 4.2 Consider the following estimated regression equation (standard errors in parentheses):
\[ \hat{y} = 64.29 + 0.99x \quad R^2 = 0.379 \]
\[ (se) \quad (2.42)\, (0.18) \]
Rewrite the estimated equation, including coefficients, standard errors, and \( R^2 \), that would result if:
a. All values of \( y \) were divided by 10 before estimation.
b. All values of \( y \) were divided by 10 before estimation.
c. All values of \( y \) and \( x \) were divided by 10 before estimation.
### 4.3 We have the observations on \( x \) and \( y \). They are \( x_i = 3, 2, 1, -1, 0 \) with corresponding \( y \) values \( y_i = 4, 2, 3, 1, 0 \). The fitted least squares line is \( \hat{y}_i = 1.2 + 0.8x_i \). The sum of squared least squares residuals is \( \sum_{i=1}^5 \hat{e}_i^2 = 3.6 \), \( \sum_{i=1}^5 (x_i - \bar{x})^2 = 10 \), and \( \sum_{i=1}
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