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Completing the ANOVA From the Summary Statistics

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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.

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

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ANOVA SourceSSdfMSF Regression Residual Total Correlation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401

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

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ANOVA SourceSSdfMSF Regression1 Residual Total27 Correlation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401 The total df is n-1. 28 - 1 = 27

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ANOVA SourceSSdfMSF Regression1 Residual26 Total27 Correlation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401 Use subtraction to find the residual df 27 - 1 = 26

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ANOVA SourceSSdfMSF Regression1 Residual26 Total2720.3401 Correlation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401 The total MS is the variance on the response variable

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ANOVA SourceSSdfMSF Regression1 Residual26 Total549.18272720.3401 Correlation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401 Find the SS by multiplying the MS by the df 27 x 20.3401 = 549.1827

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ANOVA SourceSSdfMSF Regression54.14721 Residual26 Total549.18272720.3401 Correlation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401 R 2 = SS(Reg) / SS(Total) 0.314 2 = SS(Reg) / 549.1827 SS(Reg) = 0.314 2 x 549.1827 SS(Reg) = 54.1472

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ANOVA SourceSSdfMSF Regression54.14721 Residual495.035526 Total549.18272720.3401 Correlation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401 Use subtraction to find the residual SS SS = 549.1827-54.1472 SS = 495.0355

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ANOVA SourceSSdfMSF Regression54.1472154.1472 Residual495.035526 Total549.18272720.3401 Correlation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401 Divide SS by df to find MS 54.1472 / 1 = 54.1472

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ANOVA SourceSSdfMSF Regression54.1472154.1472 Residual495.03552619.0398 Total549.18272720.3401 Correlation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401 Divide SS by df to find MS 495.0355 / 26 = 19.0398

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ANOVA SourceSSdfMSF Regression54.1472154.14722.8439 Residual495.03552619.0398 Total549.18272720.3401 Correlation coefficient = 0.314, sample size = 28, variance of response variable = 20.3401 F is found by dividing the two variances F = 54.1472 / 19.0398 F = 2.8439

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