The SAS System 1 13:52 Tuesday, March 20, 2018 Obs county distance apprentices pop urban direction logpop 1 Midlothian 21 225 56 18.8 3 4.02535 2 West Lothian 24 22 18 37.9 2 2.89037 3 East Lothian 33 44 30 43.4 3 3.40120 4 Kinross 33 3 7 30.3 1 1.94591 5 Fife 36 41 94 41.3 1 4.54329 6 Peebles 41 9 9 29.3 3 2.19722 7 Clackmannan 41 2 11 47.4 1 2.39790 8 Selkirk 52 5 5 41.9 3 1.60944 9 Lanark 54 23 147 68.1 2 4.99043 10 Berwick 56 11 31 15.2 3 3.43399 11 Roxburgh 67 9 34 31.8 3 3.52636 12 Stirling 71 13 51 31.1 2 3.93183 13 Perth 78 26 126 14.4 1 4.83628 14 Dunbarton 79 0 21 27.3 2 3.04452 15 Angus 85 5 99 55.3 1 4.59512 16 Dumfries 86 3 55 25.9 3 4.00733 17 Renfrew 92 1 78 69.9 2 4.35671 18 Ayr 110 2 84 26.4 2 4.43082 19 Kircudbright 110 0 29 11.3 3 3.36730 20 Kincardine 125 1 26 12.3 1 3.25810 21 Bute 132 0 12 43.6 2 2.48491 22 Aberdeen 156 3 123 23.1 1 4.81218 23 Wigtown 157 0 22 23.2 3 3.09104 24 Banff 159 4 36 12.9 1 3.58352 25 Moray 174 2 27 27.6 1 3.29584 26 Nairn 175 0 8 45.3 1 2.07944 27 Argyll 179 1 72 12.7 2 4.27667 28 Inverness 234 7 74 10.8 1 4.30407 29 Ross 274 4 55 10.7 1 4.00733 30 Caithness 274 1 23 28.3 1 3.13549 31 Sutherland 283 0 23 10.3 1 3.13549 32 Orkney 366 0 29 9.0 1 3.36730 33 Shetland 491 1 22 7.7 1 3.09104 The SAS System 2 13:52 Tuesday, March 20, 2018 The GENMOD Procedure Model Information Data Set WORK.APPRENTICE Distribution Poisson Link Function Log Dependent Variable apprentices Number of Observations Read 33 Number of Observations Used 33 Class Level Information Class Levels Values direction 3 1 2 3 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 32 1350.4386 42.2012 Scaled Deviance 32 1350.4386 42.2012 Pearson Chi-Square 32 3520.0641 110.0020 Scaled Pearson X2 32 3520.0641 110.0020 Log Likelihood 773.1176 Full Log Likelihood -722.3925 AIC (smaller is better) 1446.7849 AICC (smaller is better) 1446.9140 BIC (smaller is better) 1448.2814 Algorithm converged. Analysis Of Maximum Likelihood Parameter Estimates Standard Wald 95% Confidence Wald Parameter DF Estimate Error Limits Chi-Square Intercept 1 2.6520 0.0462 2.5614 2.7426 3291.40 Scale 0 1.0000 0.0000 1.0000 1.0000 The SAS System 3 13:52 Tuesday, March 20, 2018 The GENMOD Procedure Analysis Of Maximum Likelihood Parameter Estimates Parameter Pr > ChiSq Intercept <.0001 Scale NOTE: The scale parameter was held fixed. The SAS System 4 13:52 Tuesday, March 20, 2018 The GENMOD Procedure Model Information Data Set WORK.APPRENTICE Distribution Poisson Link Function Log Dependent Variable apprentices Number of Observations Read 33 Number of Observations Used 33 Class Level Information Class Levels Values direction 3 1 2 3 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance 27 212.4584 7.8688 Scaled Deviance 27 212.4584 7.8688 Pearson Chi-Square 27 101129.5757 3745.5398 Scaled Pearson X2 27 101129.5757 3745.5398 Log Likelihood 1342.1077 Full Log Likelihood -153.4023 AIC (smaller is better) 318.8047 AICC (smaller is better) 322.0355 BIC (smaller is better) 327.7837 Algorithm converged. Analysis Of Maximum Likelihood Parameter Estimates Standard Wald 95% Confidence Wald Parameter DF Estimate Error Limits Chi-Square Intercept 1 2.1472 0.3363 1.4881 2.8062 40.77 distance 1 -0.0324 0.0018 -0.0360 -0.0288 308.84 logpop 1 1.0614 0.0799 0.9049 1.2179 176.68 urban 1 -0.0279 0.0041 -0.0359 -0.0200 47.52 direction 1 1 -0.8128 0.1427 -1.0926 -0.5331 32.43 direction 2 1 -0.7096 0.1842 -1.0705 -0.3486 14.84 direction 3 0 0.0000 0.0000 0.0000 0.0000 . The SAS System 5 13:52 Tuesday, March 20, 2018 The GENMOD Procedure Analysis Of Maximum Likelihood Parameter Estimates Standard Wald 95% Confidence Wald Parameter DF Estimate Error Limits Chi-Square Scale 0 1.0000 0.0000 1.0000 1.0000 Analysis Of Maximum Likelihood Parameter Estimates Parameter Pr > ChiSq Intercept <.0001 distance <.0001 logpop <.0001 urban <.0001 direction 1 <.0001 direction 2 0.0001 direction 3 . Scale NOTE: The scale parameter was held fixed.