Completing the ANOVA From the Summary Statistics.

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Presentation transcript:

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. 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 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. You do not need any summary statistics for the predictor variable, x.

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

ANOVA SourceSSdfMSF Regression Residual Total Correlation coefficient = 0.314, sample size = 28, variance of response variable =

ANOVA SourceSSdfMSF Regression1 Residual Total The regression df is always 1 for simple regression

ANOVA SourceSSdfMSF Regression1 Residual Total27 Correlation coefficient = 0.314, sample size = 28, variance of response variable = The total df is n = 27

ANOVA SourceSSdfMSF Regression1 Residual26 Total27 Correlation coefficient = 0.314, sample size = 28, variance of response variable = Use subtraction to find the residual df = 26

ANOVA SourceSSdfMSF Regression1 Residual26 Total Correlation coefficient = 0.314, sample size = 28, variance of response variable = The total MS is the variance on the response variable

ANOVA SourceSSdfMSF Regression1 Residual26 Total Correlation coefficient = 0.314, sample size = 28, variance of response variable = Find the SS by multiplying the MS by the df 27 x =

ANOVA SourceSSdfMSF Regression Residual26 Total Correlation coefficient = 0.314, sample size = 28, variance of response variable = R 2 = SS(Reg) / SS(Total) = SS(Reg) / SS(Reg) = x SS(Reg) =

ANOVA SourceSSdfMSF Regression Residual Total Correlation coefficient = 0.314, sample size = 28, variance of response variable = Use subtraction to find the residual SS SS = SS =

ANOVA SourceSSdfMSF Regression Residual Total Correlation coefficient = 0.314, sample size = 28, variance of response variable = Divide SS by df to find MS / 1 =

ANOVA SourceSSdfMSF Regression Residual Total Correlation coefficient = 0.314, sample size = 28, variance of response variable = Divide SS by df to find MS / 26 =

ANOVA SourceSSdfMSF Regression Residual Total Correlation coefficient = 0.314, sample size = 28, variance of response variable = F is found by dividing the two variances F = / F =