Given the following summary information, calculate the value of the coefficient of determination, R². Enter your answer to three decimal places. = 401.4; Ev – ² = 34.8
Given the following summary information, calculate the value of the coefficient of determination, R². Enter your answer to three decimal places. = 401.4; Ev – ² = 34.8
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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![### Calculating the Coefficient of Determination (R²)
Given the following summary information, calculate the value of the coefficient of determination, R². Enter your answer to three decimal places.
- The total sum of squares (variation of actual values from the mean):
\[
\sum (y - \bar{y})^2 = 401.4
\]
- The residual sum of squares (variation of actual values from the predicted values):
\[
\sum (y - \hat{y})^2 = 34.8
\]
### Explanation:
The coefficient of determination, R², is calculated using the formula:
\[
R^2 = 1 - \frac{\sum (y - \hat{y})^2}{\sum (y - \bar{y})^2}
\]
Plug in the given values to compute R².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8b48535-184f-4977-af2d-d816dbce40fd%2F9a009c0a-418b-47bf-8cb5-19405ceaf137%2Fmf400ds_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Coefficient of Determination (R²)
Given the following summary information, calculate the value of the coefficient of determination, R². Enter your answer to three decimal places.
- The total sum of squares (variation of actual values from the mean):
\[
\sum (y - \bar{y})^2 = 401.4
\]
- The residual sum of squares (variation of actual values from the predicted values):
\[
\sum (y - \hat{y})^2 = 34.8
\]
### Explanation:
The coefficient of determination, R², is calculated using the formula:
\[
R^2 = 1 - \frac{\sum (y - \hat{y})^2}{\sum (y - \bar{y})^2}
\]
Plug in the given values to compute R².
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