completing the anova from the summary statistics
TRANSCRIPT
Completing the Completing the ANOVAANOVA
From the Summary StatisticsFrom the Summary Statistics
Necessary InformationNecessary Information
It is possible to complete the Analysis It is possible to complete the Analysis of Variance table for simple regression of Variance table for simple regression from the summary statistics.from the summary statistics.
You need the correlation coefficient, You need the correlation coefficient, the sample size, and the sample the sample size, and the sample variance for the response variable, y.variance for the response variable, y.
You do not need any summary statistics You do not need any summary statistics for the predictor variable, x.for the predictor variable, x.
Summary StatisticsSummary Statistics
This explanation will assume the This explanation will assume the following values. following values.
Pearson’s correlation coefficient is Pearson’s correlation coefficient is 0.3140.314
The sample size is 28The sample size is 28 The variance of the response The variance of the response
variable is 20.3401variable is 20.3401
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon
ResiduaResiduall
TotalTotal
Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon 11
ResiduaResiduall
TotalTotal
Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401
The regression df is always 1 for simple
regression
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon 11
ResiduaResiduall
TotalTotal 2727
Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401
The total df is n-1.28 - 1 = 27
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon 11
ResiduaResiduall
2626
TotalTotal 2727
Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401
Use subtraction to find the residual df
27 - 1 = 26
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon 11
ResiduaResiduall
2626
TotalTotal 2727 20.340120.3401
Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401
The total MS is the variance on the
response variable
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon 11
ResiduaResiduall
2626
TotalTotal 549.18549.182727 2727 20.340120.3401
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
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon
54.14754.14722
11
ResiduaResiduall
2626
TotalTotal 549.18549.182727 2727 20.340120.3401
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 549.1827
SS(Reg) = 54.1472
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon
54.14754.14722
11
ResiduaResiduall
495.03495.035555 2626
TotalTotal 549.18549.182727 2727 20.340120.3401
Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401
Use subtraction to findthe residual SS
SS = 549.1827-54.1472SS = 495.0355
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon
54.14754.14722
11 54.147254.1472
ResiduaResiduall
495.03495.035555 2626
TotalTotal 549.18549.182727 2727 20.340120.3401
Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401
Divide SS by df to find MS54.1472 / 1 = 54.1472
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon
54.14754.14722
11 54.147254.1472
ResiduaResiduall
495.03495.035555 2626 19.039819.0398
TotalTotal 549.18549.182727 2727 20.340120.3401
Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401
Divide SS by df to find MS495.0355 / 26 = 19.0398
ANOVAANOVA
SourceSource SSSS dfdf MSMS FF
RegressiRegressionon
54.14754.14722
11 54.147254.1472 2.84392.8439
ResiduaResiduall
495.03495.035555 2626 19.039819.0398
TotalTotal 549.18549.182727 2727 20.340120.3401
Correlation coefficient = 0.314, sample size = 28,variance of response variable = 20.3401
F is found by dividing the two variances
F = 54.1472 / 19.0398F = 2.8439