Stat 401 B – Lecture 161Sums of Squares SS(C. Total) = 128647.74 SS(Test 1) =37992.80 Test 1 explains 29.5% SS(Test 2|Test 1) = 9266.54 Test 2 adds 7.2%2Sums of SquaresSS(C. Total) = 128647.74SS(Test 1) = 37992.8029.5%SS(Test 2|Test 1) = 9266.547.2%3Sums of Squares SS(C. Total) = 128647.74 SS(Test 2) =21467.35 Test 2 explains 16.7% SS(Test 1|Test 2) = 25791.99 Test 1 adds 20.0%Stat 401 B – Lecture 164Sums of SquaresSS(C. Total) = 128647.74SS(Test 1|Test 2) = 25791.9920.0%SS(Test 2) = 21467.3516.7%5Sums of SquaresSS(C. Total) = 128647.74SS(Test 1|Test 2) = 25791.9920.0%SS(Test 2|Test 1) = 9266.547.2%SS(shared) = 12200.819.5%6Summary – Test 2 Test 2 is not linearly related to Evaluation. t=2.05, P-value=0.0530 Test 2 does not add significantly to the model that already contains Test 1. t=1.51, P-value=0.1469Stat 401 B – Lecture 167Summary – Test 2 Test 2 does not add significantly to the model that contains both Test 1 and Test 3. t=1.36, P-value=0.1909 Test 2 does add significantly to the model that already contains Test 1, Test 3 and Test 4. t=3.57, P-value=0.00228Possible Models With 4 explanatory variables there are 24– 1 = 15 possible models. 4 – 1 variable models 6 – 2 variable models 4 – 3 variable models 1 – 4 variable model9Which is “best”? A model must be useful. All variables must add significantly to the model. Among models that satisfy the above, choose the model with the highest R2.Stat 401 B – Lecture 16101 – variable models Test 1 – useful, R2= 0.295 Test 2 – not useful Test 3 – not useful Test 4 – useful, R2= 0.343112 – variable models Test 1, Test 2 – useful, no Test 1, Test 3 – useful, yes, R2= 0.480 Test 1, Test 4 – useful, yes, R2= 0.551 Test 2, Test 3 – not useful Test 2, Test 4 – useful, yes, R2= 0.655 Test 3, Test 4 – useful, no123 – variable models Test 1, Test 2, Test 3 – useful, no Test 1, Test 2, Test 4 – useful, yes, R2= 0.739 Test 1, Test 3, Test 4 –useful, yes, R2= 0.663 Test 2, Test 3, Test 4 – useful, noStat 401 B – Lecture 16134 – variable models Test 1, Test 2, Test 3, Test 4 Useful. All variables add significantly. R2= 0.80314Eligible Models Test 1 – R2= 0.295 Test 4 – R2= 0.343 Test 1, Test 3 – R2= 0.480 Test 1, Test 4 – R2= 0.551 Test 2, Test 4 – R2= 0.655 Test 1, Test 2, Test 4 – R2= 0.739 Test 1, Test 3, Test 4 – R2= 0.663 Test 1, Test 2, Test 3, Test 4 – R2= 0.80315The “best” model. The model that is useful, has all variables adding significantly and has the highest R2is the model that contains all four variables – Test 1, Test 2, Test 3, Test
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