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Completing the ANOVA - PowerPoint PPT Presentation

Completing the ANOVA. From the Summary Statistics. 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.

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Completing the ANOVA

From the Summary Statistics

• 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.

• 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

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

The regression df is always 1 for simple regression

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

The total df is n-1.28 - 1 = 27

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

Use subtraction to find the residual df27 - 1 = 26

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

The total MS is the variance on the response variable

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

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

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

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

Divide SS by df to find MS54.1472 / 1 = 54.1472

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

Divide SS by df to find MS495.0355 / 26 = 19.0398

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

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