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Completing the ANOVA

This guide outlines the process of completing an Analysis of Variance (ANOVA) table for simple regression using summary statistics such as the correlation coefficient, sample size, and variance of the response variable. With a Pearson correlation coefficient of 0.314, a sample size of 28, and a variance of 20.3401, we demonstrate how to calculate degrees of freedom, sums of squares, mean squares, and the F-statistic. This procedure is essential for evaluating the effectiveness of a simple regression model based on summary statistics.

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Completing the ANOVA

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  1. Completing the ANOVA From the Summary Statistics

  2. Necessary Information • It is possible to complete the Analysis of Variance table for simple regression from the summary statistics. • You need the correlation coefficient, the sample size, and the sample variance for the response variable, y. • You do not need any summary statistics for the predictor variable, x.

  3. Summary Statistics • This explanation will assume the following values. • Pearson’s correlation coefficient is 0.314 • The sample size is 28 • The variance of the response variable is 20.3401

  4. ANOVA Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

  5. ANOVA The regression df is always 1 for simple regression Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

  6. ANOVA The total df is n-1.28 - 1 = 27 Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

  7. ANOVA Use subtraction to find the residual df27 - 1 = 26 Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

  8. ANOVA The total MS is the variance on the response variable Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

  9. ANOVA Find the SS by multiplying the MS by the df27 x 20.3401 = 549.1827 Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

  10. ANOVA R2 = SS(Reg) / SS(Total)0.3142 = SS(Reg) / 549.1827SS(Reg) = 0.3142 x 549.1827SS(Reg) = 54.1472 Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

  11. ANOVA Use subtraction to findthe residual SSSS = 549.1827-54.1472SS = 495.0355 Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

  12. ANOVA Divide SS by df to find MS54.1472 / 1 = 54.1472 Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

  13. ANOVA Divide SS by df to find MS495.0355 / 26 = 19.0398 Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

  14. ANOVA F is found by dividing the two variancesF = 54.1472 / 19.0398F = 2.8439 Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401

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