Completing the ANOVAFrom the Summary Statistics

Necessary InformationIt 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.

Summary StatisticsThis explanation will assume the following values. Pearsons correlation coefficient is 0.314The sample size is 28The variance of the response variable is 20.3401

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

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

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

ANOVACorrelation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401Use subtraction to find the residual df 27 - 1 = 26

ANOVACorrelation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401The total MS is the variance on the response variable

ANOVACorrelation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401Find the SS by multiplying the MS by the df 27 x 20.3401 = 549.1827

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

ANOVACorrelation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401Use subtraction to find the residual SS SS = 549.1827-54.1472 SS = 495.0355

ANOVACorrelation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401Divide SS by df to find MS 54.1472 / 1 = 54.1472

ANOVACorrelation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401Divide SS by df to find MS 495.0355 / 26 = 19.0398

ANOVACorrelation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401F is found by dividing the two variances F = 54.1472 / 19.0398 F = 2.8439