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Based on the ANOVA table given, is there enough evidence at the 0.01 level of significance to conclude that the linear relationship between the independent variables and the dependent variable is statistically significant? ANOVA Source df MS F Significance F Regression 975.230086 487.615043 6.928784 0.009990 Residual 12 844.503247 70.375271 Total 14 1819.733333 Copy Data O Tables I Keypad Answer Keyboard Shortcuts O Yes O No

Based on the ANOVA table given, is there enough evidence at the 0.01 level of significance to conclude that the linear relationship between the independent variables and the dependent variable is statistically significant? ANOVA Source df MS F Significance F Regression 975.230086 487.615043 6.928784 0.009990 Residual 12 844.503247 70.375271 Total 14 1819.733333 Copy Data O Tables I Keypad Answer Keyboard Shortcuts O Yes O No

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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**ANOVA Analysis** **Question:** Based on the ANOVA table given, is there enough evidence at the 0.01 level of significance to conclude that the linear relationship between the independent variables and the dependent variable is statistically significant? **ANOVA Table:** | Source | df | SS | MS | F | Significance F | |------------|----|-------------|------------|----------|----------------| | Regression | 2 | 975.230086 | 487.615043 | 6.928784 | 0.009990 | | Residual | 12 | 844.503247 | 70.375271 | | | | Total | 14 | 1819.733333 | | | | **Explanation:** - **Source**: This refers to the components of the model – 'Regression' for the explained variance and 'Residual' for the unexplained variance. 'Total' combines both. - **df (Degrees of Freedom)**: Represents the number of values in the final calculation of a statistic that are free to vary. - **SS (Sum of Squares)**: Measures the variability. Here, 975.230086 is for regression, 844.503247 is residual, and 1819.733333 is the total. - **MS (Mean Square)**: SS divided by their respective df. It is 487.615043 for regression and 70.375271 for residual. - **F**: The F-statistic is used to determine if the variances between the populations’ means are significantly different. - **Significance F**: The probability that the observed F-statistic would occur if the null hypothesis were true. A value of 0.009990 indicates significance at the 0.01 level. **Answer:** O Yes O No The F-statistic with a Significance F value of 0.009990 is below the 0.01 significance level, suggesting strong evidence against the null hypothesis. Therefore, choose "Yes" to indicate that there is enough evidence to conclude a statistically significant relationship at the 0.01 level.
Transcribed Image Text:**ANOVA Analysis** **Question:** Based on the ANOVA table given, is there enough evidence at the 0.01 level of significance to conclude that the linear relationship between the independent variables and the dependent variable is statistically significant? **ANOVA Table:** | Source | df | SS | MS | F | Significance F | |------------|----|-------------|------------|----------|----------------| | Regression | 2 | 975.230086 | 487.615043 | 6.928784 | 0.009990 | | Residual | 12 | 844.503247 | 70.375271 | | | | Total | 14 | 1819.733333 | | | | **Explanation:** - **Source**: This refers to the components of the model – 'Regression' for the explained variance and 'Residual' for the unexplained variance. 'Total' combines both. - **df (Degrees of Freedom)**: Represents the number of values in the final calculation of a statistic that are free to vary. - **SS (Sum of Squares)**: Measures the variability. Here, 975.230086 is for regression, 844.503247 is residual, and 1819.733333 is the total. - **MS (Mean Square)**: SS divided by their respective df. It is 487.615043 for regression and 70.375271 for residual. - **F**: The F-statistic is used to determine if the variances between the populations’ means are significantly different. - **Significance F**: The probability that the observed F-statistic would occur if the null hypothesis were true. A value of 0.009990 indicates significance at the 0.01 level. **Answer:** O Yes O No The F-statistic with a Significance F value of 0.009990 is below the 0.01 significance level, suggesting strong evidence against the null hypothesis. Therefore, choose "Yes" to indicate that there is enough evidence to conclude a statistically significant relationship at the 0.01 level.
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