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STA5168_HW3 - Jaime Frade STA6168 Dr Niu HW3 1 a The...

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Jaime Frade STA6168 Dr. Niu: HW3 1. a) The estimated probability is always less than the intercept, 0.7578, and decreases by 0.0694 every decade from 0.6884 ( = 0.7578 - 0.0694) at the first decade, 1900 to 0.1332 in 1990. I reran using simple linear regression and obtained the following model: Pi_hat2 = 0.7565 – 0.6957x Using SAS, I also reran the example, using the number of total fames =100.
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Jaime Frade STA6168 Dr. Niu: HW3 b) x y Pi_hat Residual Pi_hat2 Residual 0 0.727 0.7578 -0.0308 0.7565 -0.0295 1 0.634 0.6884 -0.0544 0.686933 -0.05293 2 0.5 0.619 -0.119 0.617367 -0.11737 3 0.443 0.5496 -0.1066 0.5478 -0.1048 4 0.416 0.4802 -0.0642 0.478233 -0.06223 5 0.328 0.4108 -0.0828 0.408667 -0.08067 6 0.272 0.3414 -0.0694 0.3391 -0.0671 7 0.225 0.272 -0.047 0.269533 -0.04453 8 0.133 0.2026 -0.0696 0.199967 -0.06697 9 0.1332 0.1304 10 0.0638 0.060833 11 -0.0056 -0.00873 12 -0.075 -0.0783 When x>10, the estimated probabilities are less than zero. These predictions are not plausible because the linear function which is valid over the entire real line, whereas Pi_hat can only take on values [0,1] c) x y Pi_hat (part c) Residual 0 0.727 0.759218549 -0.03222 1 0.634 0.69698889 -0.06299 2 0.5 0.626679981 -0.12668 3 0.443 0.550576435 -0.10758 4 0.416 0.472029233 -0.05603 5 0.328 0.394842931 -0.06684 6 0.272 0.322566954 -0.05057 7 0.225 0.257883176 -0.03288 8 0.133 0.202296909 -0.0693 9 0.156170777 -0.15617 10 0.118993095 -0.11899 11 0.089724781 -0.08972 12 0.067107135 -0.06711
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Jaime Frade STA6168 Dr. Niu: HW3 Checking the rules of probability From above the model for part c, can only take on values from [0,1]. Predictions are more plausible because they fall into this range of probability. [0, 1]. CODE options linesize= 80 ; options pagesize= 200 ; options missing= 'M' ; title '4.2: Regression Models with baseball Data: Data Analysis' ; data base; input year comp total; datalines ; 1 72.7 100 2 63.4 100 3 50 100 4 44.3 100 5 41.6 100 6 32.8 100 7 27.2 100 8 22.5 100 9 13.3 100 ; /* * HTML code */ Filename GSASFile Dummy ; GOptions Device =PDF FText =Helvetica FTitle =Helvetica; Options TopMargin= 1 BottomMargin= 1 LeftMargin= 1.0 RightMargin= 1.0 ; ODS PDF File = "STA5168-hw3-prob4-2a.pdf" ; /**/ proc genmod data =base; model comp/total = year / dist =bin link =identity; run ; proc genmod data =base; model comp/total = year / dist =bin link =logit; run ; proc genmod data =base; model comp/total = year / dist =bin link =probit; run ; ODS HTML Close ;
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Jaime Frade STA6168 Dr. Niu: HW3 ODS Listing ;
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Jaime Frade STA6168 Dr. Niu: HW3 4.4 a) Model : In this example, the y-intercept cannot be interpreted because it falls outside of the range of probability values, [0,1]. The estimated probability increases by 0.32270 At weight = 5.2, the predicted probability = 1.53. Comment. This is much higher than the upper bound of 1 for probability. b) ??
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Jaime Frade STA6168 Dr. Niu: HW3
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Jaime Frade STA6168 Dr. Niu: HW3 c) Comments: At weight = 5.2, the predicted logit = 5.74. and log(0.9968/(1-0.9968)) = 5.74
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Jaime Frade STA6168 Dr. Niu: HW3
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Jaime Frade STA6168 Dr. Niu: HW3 d) Comments: At weight = 5.2,
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Jaime Frade STA6168 Dr. Niu: HW3 CODE options linesize= 80 ; options pagesize= 200 ; options missing= 'M' ; title '4.4: Regression Models with Crab Data of Table 4.3: Data Analysis' ; data crab; input color
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