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The ANOVA summary table to the right is for a multiple regression model with six independent variables. Complete parts (a) through (e). d. Compute the coefficient of multiple determination, r², and interpret its meaning. 2 = (Round to four decimal places as needed.) Interpret the meaning of the coefficient of multiple determination. The coefficient of multiple determination indicates that% of the variation in the variables. (Round to two decimal places as needed.) e. Compute the adjusted r². (Round to four decimal places as needed.) Source Regression Error Total Degrees of Sum of Freedom Squares 240 190 430 6 26 32 variable can be explained by the variation in the

The ANOVA summary table to the right is for a multiple regression model with six independent variables. Complete parts (a) through (e). d. Compute the coefficient of multiple determination, r², and interpret its meaning. 2 = (Round to four decimal places as needed.) Interpret the meaning of the coefficient of multiple determination. The coefficient of multiple determination indicates that% of the variation in the variables. (Round to two decimal places as needed.) e. Compute the adjusted r². (Round to four decimal places as needed.) Source Regression Error Total Degrees of Sum of Freedom Squares 240 190 430 6 26 32 variable can be explained by the variation in the

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
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The ANOVA summary table on the right is for a multiple regression model with six independent variables. Complete parts (a) through (e). | Source | Degrees of Freedom | Sum of Squares | |-------------|--------------------|----------------| | Regression | 6 | 240 | | Error | 26 | 190 | | Total | 32 | 430 | --- **Draw a conclusion. Choose the correct answer below.** - **A.** There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is less than the critical value. - **B.** There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the p-value is less than the level of significance. - **C.** There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the level of significance. - **D.** There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the critical value.
Transcribed Image Text:The ANOVA summary table on the right is for a multiple regression model with six independent variables. Complete parts (a) through (e). | Source | Degrees of Freedom | Sum of Squares | |-------------|--------------------|----------------| | Regression | 6 | 240 | | Error | 26 | 190 | | Total | 32 | 430 | --- **Draw a conclusion. Choose the correct answer below.** - **A.** There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is less than the critical value. - **B.** There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the p-value is less than the level of significance. - **C.** There is sufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the level of significance. - **D.** There is insufficient evidence of a significant linear relationship with at least one of the independent variables because the test statistic is greater than the critical value.
**ANOVA Summary Table and Calculation of Coefficient of Determination** The ANOVA summary table provided is for a multiple regression model with six independent variables. Here are the parts requiring completion: **ANOVA Summary Table:** - **Source:** - Regression - Error - Total - **Degrees of Freedom:** - Regression: 6 - Error: 26 - Total: 32 - **Sum of Squares:** - Regression: 240 - Error: 190 - Total: 430 **Task (d): Compute the coefficient of multiple determination, \( r^2 \), and interpret its meaning.** - Formula to compute \( r^2 \): \[ r^2 = \frac{\text{Sum of Squares for Regression}}{\text{Total Sum of Squares}} \] - Interpretation: - The coefficient of multiple determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variables. - Boxes to complete: - \( r^2 = \text{[ ] (Round to four decimal places as needed.)} \) - The coefficient of multiple determination indicates that [ ]% of the variation in the [dependent variable] can be explained by the variation in the [independent variables]. - (Round to two decimal places as needed.) **Task (e): Compute the adjusted \( r^2 \).** - Adjusted \( r^2 \) formula takes into account the number of predictors in the model and the number of data points: \[ r^2_{adj} = 1 - \left(\frac{(1 - r^2)(\text{Total Degrees of Freedom})}{\text{Total Degrees of Freedom} - \text{Number of Predictors} - 1}\right) \] - Box to complete: - \( r^2_{adj} = \text{[ ] (Round to four decimal places as needed.)} \) Understanding and computing \( r^2 \) and adjusted \( r^2 \) provides insight into the effectiveness of the regression model in explaining the variability of the response data.
Transcribed Image Text:**ANOVA Summary Table and Calculation of Coefficient of Determination** The ANOVA summary table provided is for a multiple regression model with six independent variables. Here are the parts requiring completion: **ANOVA Summary Table:** - **Source:** - Regression - Error - Total - **Degrees of Freedom:** - Regression: 6 - Error: 26 - Total: 32 - **Sum of Squares:** - Regression: 240 - Error: 190 - Total: 430 **Task (d): Compute the coefficient of multiple determination, \( r^2 \), and interpret its meaning.** - Formula to compute \( r^2 \): \[ r^2 = \frac{\text{Sum of Squares for Regression}}{\text{Total Sum of Squares}} \] - Interpretation: - The coefficient of multiple determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variables. - Boxes to complete: - \( r^2 = \text{[ ] (Round to four decimal places as needed.)} \) - The coefficient of multiple determination indicates that [ ]% of the variation in the [dependent variable] can be explained by the variation in the [independent variables]. - (Round to two decimal places as needed.) **Task (e): Compute the adjusted \( r^2 \).** - Adjusted \( r^2 \) formula takes into account the number of predictors in the model and the number of data points: \[ r^2_{adj} = 1 - \left(\frac{(1 - r^2)(\text{Total Degrees of Freedom})}{\text{Total Degrees of Freedom} - \text{Number of Predictors} - 1}\right) \] - Box to complete: - \( r^2_{adj} = \text{[ ] (Round to four decimal places as needed.)} \) Understanding and computing \( r^2 \) and adjusted \( r^2 \) provides insight into the effectiveness of the regression model in explaining the variability of the response data.
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