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Completing the ANOVA

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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