Stat 401 B – Lecture 141Sums of Squares The effects of adding variables to a model can be seen in the changes in the sums of squares given in the ANalysis Of VAriance(ANOVA) table.2RSquareRSquare AdjRoot Mean Square ErrorMean of ResponseObservations (or Sum Wgts)0.2953240.26176865.70313444.478323Summary of FitModelErrorC. TotalSource12122DF37992.8090654.94128647.74Sum ofSquares37992.84316.9Mean Square8.8009F Ratio0.0074*Prob > FAnalysis of VarianceInterceptTest1Term329.22621.4243941Estimate41.194250.480137Std Error7.992.97t Ratio<.0001*0.0074*Prob>|t|Parameter EstimatesTest1Source1Nparm1DF37992.802Sum ofSquares8.8009F Ratio0.0074*Prob > FEffect TestsResponse EVAL3RSquareRSquare AdjRoot Mean Square ErrorMean of ResponseObservations (or Sum Wgts)0.3673550.3040963.79201444.478323Summary of FitModelErrorC. TotalSource22022DF47259.3481388.40128647.74Sum ofSquares23629.74069.4Mean Square5.8066F Ratio0.0103*Prob > FAnalysis of VarianceInterceptTest1Test2Term129.376391.22146251.5114559Estimate138.34520.4851811.00162Std Error0.942.521.51t Ratio0.36090.0205*0.1469Prob>|t|Parameter EstimatesTest1Test2Source11Nparm11DF25791.9949266.538Sum ofSquares6.33802.2771F Ratio0.0205*0.1469Prob > FEffect TestsResponse EVALStat 401 B – Lecture 144Model with only Test 1128647.7422C. Total90654.9421Error37992.801ModelSum of SquaresdfSource5Model with Test 1, Test 2128647.7422C. Total81388.4020Error47259.342ModelSum of SquaresdfSource6Effects of adding Test 2 The C. Total Sum of Squares does not change. The Model Sum of Squares has increased by 9266.54. The Error Sum of Squares has decreased by 9266.54.Stat 401 B – Lecture 147Effects of adding Test 2 The C. Total degrees of freedom does not change. The Model degrees of freedom increase by 1. The Error degrees of freedom decrease by 1.8Effects of adding Test 2 When Test 2 is added to the model that contains Test 1, 9266.54 and 1 df move from what was Error (unexplained variation) to Model (explained variation).9Effects of adding Test 2 This change shows up under Effects Test as the Sum of Squares associated with Test 2. Remember that this is the amount of variation that is explained by adding Test 2 to Test 1.Stat 401 B – Lecture 1410Effects of adding a variable Whenever you add a variable to a model, sum of squares and 1 df move from what was Error (unexplained variation) to Model (explained variation). This shows up under Effect Tests as the Sum of Squares.11Effect Tests9266.541Test225791.991Test1Sum of SquaresdfSource12Effects of adding Test 1 When Test 1 is added to a model that contains Test 2, 25791.99 and 1 df move from what was Error (unexplained variation) to Model (explained variation).Stat 401 B – Lecture 1413Model with Test 1, Test 2128647.7422C. Total81388.4020Error47259.342ModelSum of SquaresdfSource14Model with only Test 2128647.7422C. Total107180.3921Error21467.351ModelSum of SquaresdfSource15RSquareRSquare AdjRoot Mean Square ErrorMean of ResponseObservations (or Sum Wgts)0.1668690.12719671.44108444.478323Summary of FitModelErrorC. TotalSource12122DF21467.35107180.39128647.74Sum ofSquares21467.35103.8Mean Square4.2061F Ratio0.0530Prob > FAnalysis of VarianceInterceptTest2Term128.201122.2103841Estimate154.93281.077771Std Error0.832.05t Ratio0.41730.0530Prob>|t|Parameter EstimatesTest2Source1Nparm1DF21467.347Sum ofSquares4.2061F Ratio0.0530Prob > FEffect TestsResponse
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