Question

topic: model selection on applied linear regression

Exercise 5.5.10 Perform model selection for the blood pressure data in Table 3.1 using Ri and stepwise selection algorithm. Compare the results with all possible subsets regression. 47 3.8 Exercises Age Weight Pulse Blood pressure 21 7 88 24 56 70 25 65 72 28 53 60 32 67 60 35 80 70 7 57 68 38 58 64 39 68 75 160 135 140 118 134 60 67 1 64 8 42 68 78 43 54 60 5 6 56 47 55 64 54 87 92 62 52 74 68 85 88 73 49 70 79 56 69 124 144 112 138 128 118 134 116 123 161 112 129 Table 3.1 Blood pressure data.

Answer 1

Solution: Using Minitab: Stat> Regression Stepwise MIB> Stepwise pressure' 'Age' weight pulse'; SUBC Enter 'Age' weight pulse'; SUBC AEnter 0.15 SUBC ARemove 0.15; SUBC+ Constant Stepwise Regression: pressure versus Age, weight, pulse Alpha-to-Enter: 0.15 Alpha-to-Remove: 0.15 Response is pressure on 3 predictors, with N-20 Step 1 23 Constant 47.05 52.00 46.77 Age-0.13 0.11 T-Value I 0.94 -0.81 P-Value 0.363 0.427
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weight 1.23 135 1.36 Value 4.43 6.83 6.95 P-Value 0000 0,000 0.000 pulse 0.19 T-Value 0.63 P-Value 0.539 9.47 9.30 9.21 R-Sq74.49 73.86 72.85 R-Sa(adj) 69.71 70.79 71.34 Ср 4.0 24 10 Here we have three models 1) Pressure- 47.05-0.13*Age 1.23*weight+0.19"pulse 2) Pressure -52-0.11*Age 1.35*weight 3) Pressure- 46.77+1.36*weight From the above three models, The R-sq (ad) vałue is large for third model and is 71.34, mean square value is less, and also mallows cp value is also small as compare to other models therefore third only Conclusion: model is adequate. Therefore we conclude that Pressure depends on weight