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Given the following summary information, calculate the value of the coefficient of determination, R?. Enter your answer to three decimal places. ANOVA Source df SS Regression 1 264.7 Error 24 50.1 Total 25

Given the following summary information, calculate the value of the coefficient of determination, R?. Enter your answer to three decimal places. ANOVA Source df SS Regression 1 264.7 Error 24 50.1 Total 25

MATLAB: An Introduction with Applications
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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Given the following summary information, calculate the value of the coefficient of determination, R². Enter your answer to three decimal places. **ANOVA** | Source | df | SS | |-------------|----|------| | Regression | 1 | 264.7| | Error | 24 | 50.1 | | Total | 25 | | --- **Explanation for the Coefficient of Determination (R²):** The coefficient of determination, R², is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable in a regression model. It is calculated as follows: \[ R² = \frac{SS_{\text{Regression}}}{SS_{\text{Total}}} \] From the table: - \( SS_{\text{Regression}} = 264.7 \) - \( SS_{\text{Error}} = 50.1 \) - \( SS_{\text{Total}} = SS_{\text{Regression}} + SS_{\text{Error}} = 264.7 + 50.1 = 314.8 \) Thus, the calculation for R² would be: \[ R² = \frac{264.7}{314.8} \] When you compute this expression, it results in a value that you round to three decimal places.
Transcribed Image Text:Given the following summary information, calculate the value of the coefficient of determination, R². Enter your answer to three decimal places. **ANOVA** | Source | df | SS | |-------------|----|------| | Regression | 1 | 264.7| | Error | 24 | 50.1 | | Total | 25 | | --- **Explanation for the Coefficient of Determination (R²):** The coefficient of determination, R², is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable in a regression model. It is calculated as follows: \[ R² = \frac{SS_{\text{Regression}}}{SS_{\text{Total}}} \] From the table: - \( SS_{\text{Regression}} = 264.7 \) - \( SS_{\text{Error}} = 50.1 \) - \( SS_{\text{Total}} = SS_{\text{Regression}} + SS_{\text{Error}} = 264.7 + 50.1 = 314.8 \) Thus, the calculation for R² would be: \[ R² = \frac{264.7}{314.8} \] When you compute this expression, it results in a value that you round to three decimal places.
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