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732G21/732G28/732A35 Lecture 9

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25 computer programmers with different experience have performed a test. For each programmer we have recorded whether he or she passed the test (Y = 1) or not (Y = 0). 2 Months of experience (X) Task success (Y) 140 290 60 251.... 81

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Binary Logistic Regression: Task success (Y) versus Months of experi Link Function: Logit Response Information Variable Value Count Task success (Y) 1 11 (Event) 0 14 Total 25 Logistic Regression Table 95% Odds CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -3.05970 1.25935 -2.43 0.015 Months of experience (X) 0.161486 0.0649801 2.49 0.013 1.18 1.03 1.33 Log-Likelihood = -12.712 Test that all slopes are zero: G = 8.872, DF = 1, P-Value = 0.003 Goodness-of-Fit Tests Method Chi-Square DF P Pearson 19.6226 17 0.294 Deviance 19.8794 17 0.280 Hosmer-Lemeshow 5.9457 8 0.653 3

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5 Binary Logistic Regression: Task success versus Months of ex, Age, Gender Link Function: Logit Response Information Variable Value Count Task success 1 11 (Event) 0 14 Total 25 Logistic Regression Table Odds 95% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -2.53002 2.09690 -1.21 0.228 Months of experience 0.163344 0.0661327 2.47 0.014 1.18 1.03 1.34 Age -0.0091584 0.0408756 -0.22 0.823 0.99 0.91 1.07 Gender -0.358858 1.10029 -0.33 0.744 0.70 0.08 6.04 Log-Likelihood = -12.650 Test that all slopes are zero: G = 8.996, DF = 3, P-Value = 0.029 Goodness-of-Fit Tests Method Chi-Square DF P Pearson 24.8743 21 0.253 Deviance 25.3007 21 0.234 Hosmer-Lemeshow 7.4477 8 0.489

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Suppose you are a field biologist and you believe that adult population of salamanders in the Northeast has gotten smaller over the past few years. You would like to determine whether any association exists between the length of time a hatched salamander survives and level of water toxicity, as well as whether there is a regional effect. Survival time is coded as 1 if < 10 days, 2 = 10 to 30 days, and 3 = 31 to 60 days. 6

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Ordinal Logistic Regression: Survival versus ToxicLevel Link Function: Logit Response Information Variable Value Count Survival 1 15 2 46 3 12 Total 73 Logistic Regression Table Odds 95% CI Predictor Coef SE Coef Z P Ratio Lower Upper Const(1) -6.86978 1.61172 -4.26 0.000 Const(2) -3.35691 1.40131 -2.40 0.017 ToxicLevel 0.119939 0.0337103 3.56 0.000 1.13 1.06 1.20 Log-Likelihood = -59.374 Test that all slopes are zero: G = 14.546, DF = 1, P-Value = 0.000 Goodness-of-Fit Tests Method Chi-Square DF P Pearson 113.052 107 0.326 Deviance 90.113 107 0.880 7

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