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gam1 <- gam(cyl ~ mpg, data=mtcars, family = tw)
predict_intervals(gam1)
#> CI_log_lower CI_log_upper CI_lower CI_upper PI_log_lower
-#> Mazda RX4 1.693646 1.804030 5.439277 6.074074 1.1662610
-#> Mazda RX4 Wag 1.693646 1.804030 5.439277 6.074074 1.8110088
-#> Datsun 710 1.606247 1.730401 4.984068 5.642919 1.0034906
-#> Hornet 4 Drive 1.674934 1.787307 5.338442 5.973347 1.1068712
-#> Hornet Sportabout 1.800873 1.901851 6.054933 6.698284 2.0486438
-#> Valiant 1.827583 1.928273 6.218840 6.877620 2.0640773
-#> Duster 360 1.982915 2.115567 7.263886 8.294290 2.8448797
-#> Merc 240D 1.524925 1.670101 4.594798 5.312702 1.0322301
-#> Merc 230 1.606247 1.730401 4.984068 5.642919 1.0248659
-#> Merc 280 1.778608 1.879648 5.921606 6.551196 1.9697433
-#> Merc 280C 1.841246 1.941814 6.304391 6.971385 2.1004980
-#> Merc 450SE 1.902021 2.009097 6.699422 7.456580 2.0909209
-#> Merc 450SL 1.862497 1.964217 6.439794 7.129331 1.8968296
-#> Merc 450SLC 1.949661 2.069029 7.026309 7.917130 2.9378513
-#> Cadillac Fleetwood 2.132653 2.318922 8.437221 10.164706 3.7279391
-#> Lincoln Continental 2.132653 2.318922 8.437221 10.164706 3.7649699
-#> Chrysler Imperial 1.969090 2.093769 7.164151 8.115446 2.1927865
-#> Fiat 128 1.105230 1.374306 3.019919 3.952333 0.0000000
-#> Honda Civic 1.212810 1.447856 3.362922 4.253983 0.8876852
-#> Toyota Corolla 1.024916 1.321726 2.786860 3.749889 0.0000000
-#> Toyota Corona 1.669887 1.783683 5.311568 5.951734 1.1991007
-#> Dodge Challenger 1.937983 2.054702 6.944733 7.804512 2.3065907
-#> AMC Javelin 1.949661 2.069029 7.026309 7.917130 2.9142130
-#> Camaro Z28 2.022016 2.166548 7.553537 8.728104 2.9231763
-#> Pontiac Firebird 1.778608 1.879648 5.921606 6.551196 1.9387057
-#> Fiat X1-9 1.377445 1.562646 3.964757 4.771430 0.9073613
-#> Porsche 914-2 1.443156 1.611220 4.234037 5.008917 0.9840626
-#> Lotus Europa 1.212810 1.447856 3.362922 4.253983 0.7879997
-#> Ford Pantera L 1.926393 2.039274 6.864703 7.685026 2.6827793
-#> Ferrari Dino 1.757537 1.858452 5.798140 6.413802 1.9124706
-#> Maserati Bora 1.957202 2.079554 7.079493 8.000901 2.8974318
-#> Volvo 142E 1.674934 1.787307 5.338442 5.973347 1.1771170
+#> Mazda RX4 1.694488 1.804020 5.443860 6.074018 1.8230570
+#> Mazda RX4 Wag 1.694488 1.804020 5.443860 6.074018 1.2616901
+#> Datsun 710 1.605943 1.732586 4.982554 5.655261 1.0773294
+#> Hornet 4 Drive 1.675856 1.786635 5.343366 5.969333 1.1170088
+#> Hornet Sportabout 1.803500 1.904438 6.070859 6.715636 1.9206078
+#> Valiant 1.830228 1.929547 6.235308 6.886391 1.9957167
+#> Duster 360 1.985149 2.112860 7.280134 8.271868 2.9367182
+#> Merc 240D 1.525177 1.672104 4.595958 5.323358 0.9716396
+#> Merc 230 1.605943 1.732586 4.982554 5.655261 1.6347308
+#> Merc 280 1.780923 1.882042 5.935331 6.566900 1.8318592
+#> Merc 280C 1.843635 1.943043 6.319471 6.979959 1.9589951
+#> Merc 450SE 1.901415 2.008996 6.695363 7.455824 2.1276195
+#> Merc 450SL 1.865449 1.966944 6.458832 7.148796 1.9923725
+#> Merc 450SLC 1.951506 2.070314 7.039283 7.927314 2.8105906
+#> Cadillac Fleetwood 2.123780 2.312536 8.362688 10.100004 4.0419831
+#> Lincoln Continental 2.123780 2.312536 8.362688 10.100004 3.9113869
+#> Chrysler Imperial 1.969797 2.093198 7.169218 8.110809 2.7310920
+#> Fiat 128 1.106400 1.378713 3.023454 3.969788 0.0000000
+#> Honda Civic 1.211071 1.449323 3.357078 4.260231 0.0000000
+#> Toyota Corolla 1.026011 1.324955 2.789915 3.762018 0.0000000
+#> Toyota Corona 1.670818 1.782955 5.316514 5.947407 1.7521206
+#> Dodge Challenger 1.939120 2.054819 6.952629 7.805421 2.8415848
+#> AMC Javelin 1.951506 2.070314 7.039283 7.927314 2.7572946
+#> Camaro Z28 2.023051 2.164080 7.561357 8.706591 2.9412437
+#> Pontiac Firebird 1.780923 1.882042 5.935331 6.566900 1.8821008
+#> Fiat X1-9 1.373687 1.560676 3.949889 4.762040 0.9238679
+#> Porsche 914-2 1.441476 1.609874 4.226932 5.002181 0.9295837
+#> Lotus Europa 1.211071 1.449323 3.357078 4.260231 0.8173513
+#> Ford Pantera L 1.927088 2.039325 6.869476 7.685418 2.8283211
+#> Ferrari Dino 1.757895 1.858195 5.800217 6.412151 1.8874253
+#> Maserati Bora 1.958955 2.079620 7.091909 8.001430 2.8004221
+#> Volvo 142E 1.675856 1.786635 5.343366 5.969333 1.9116608
#> PI_log_upper PI_lower PI_upper
-#> Mazda RX4 11.398325 3.209968 89172.279
-#> Mazda RX4 Wag 10.645012 6.116615 41982.644
-#> Datsun 710 10.242810 2.727787 28079.923
-#> Hornet 4 Drive 10.659906 3.024879 42612.621
-#> Hornet Sportabout 11.326492 7.757374 82991.375
-#> Valiant 11.785019 7.878026 131270.941
-#> Duster 360 14.022612 17.199490 1230107.114
-#> Merc 240D 9.260437 2.807319 10513.731
-#> Merc 230 10.739089 2.786722 46124.035
-#> Merc 280 11.897582 7.168836 146910.950
-#> Merc 280C 12.223973 8.170238 203612.406
-#> Merc 450SE 12.902860 8.092364 401458.651
-#> Merc 450SL 12.294169 6.664731 218418.577
-#> Merc 450SLC 13.002398 18.875245 443475.676
-#> Cadillac Fleetwood 15.824197 41.593301 7453523.568
-#> Lincoln Continental 15.588485 43.162407 5888341.076
-#> Chrysler Imperial 13.469203 8.960145 707294.765
-#> Fiat 128 7.824441 1.000000 2500.987
-#> Honda Civic 8.165618 2.429499 3517.894
-#> Toyota Corolla 7.265710 1.000000 1430.401
-#> Toyota Corona 10.539373 3.317132 37773.867
-#> Dodge Challenger 13.030296 10.040137 456021.832
-#> AMC Javelin 13.212447 18.434300 547133.125
-#> Camaro Z28 13.912934 18.600274 1102327.252
-#> Pontiac Firebird 11.163129 6.949750 70483.179
-#> Fiat X1-9 9.290945 2.477776 10839.422
-#> Porsche 914-2 9.163858 2.675303 9545.810
-#> Lotus Europa 7.977980 2.198993 2916.034
-#> Ford Pantera L 12.474458 14.625686 261570.196
-#> Ferrari Dino 11.510515 6.769793 99759.223
-#> Maserati Bora 13.465295 18.127530 704536.535
-#> Volvo 142E 10.687757 3.245005 43816.098
+#> Mazda RX4 10.864623 6.190755 52293.295
+#> Mazda RX4 Wag 11.039701 3.531385 62299.041
+#> Datsun 710 10.290502 2.936826 29451.557
+#> Hornet 4 Drive 10.753358 3.055700 46786.894
+#> Hornet Sportabout 11.886842 6.825106 145341.577
+#> Valiant 12.308198 7.357474 221504.497
+#> Duster 360 13.362451 18.853871 635680.585
+#> Merc 240D 9.419378 2.642273 12324.914
+#> Merc 230 10.347353 5.128077 31174.416
+#> Merc 280 11.517856 6.245488 100494.272
+#> Merc 280C 12.103947 7.092197 180583.246
+#> Merc 450SE 12.637262 8.394859 307817.310
+#> Merc 450SL 12.471215 7.332910 260723.177
+#> Merc 450SLC 13.060705 16.619731 470101.934
+#> Cadillac Fleetwood 16.031801 56.939146 9173242.472
+#> Lincoln Continental 15.693317 49.968205 6539147.116
+#> Chrysler Imperial 13.265571 15.349640 576984.592
+#> Fiat 128 7.407253 1.000000 1647.893
+#> Honda Civic 8.048537 1.000000 3129.214
+#> Toyota Corolla 7.381091 1.000000 1605.341
+#> Toyota Corona 10.929270 5.766819 55785.565
+#> Dodge Challenger 12.986320 17.142912 436402.323
+#> AMC Javelin 13.081036 15.757156 479757.314
+#> Camaro Z28 14.050452 18.939387 1264834.142
+#> Pontiac Firebird 11.608099 6.567287 109984.968
+#> Fiat X1-9 8.914775 2.519015 7441.109
+#> Porsche 914-2 8.958651 2.533454 7774.863
+#> Lotus Europa 8.135689 2.264494 3414.167
+#> Ford Pantera L 13.004353 16.917036 444343.277
+#> Ferrari Dino 11.223951 6.602347 74903.098
+#> Maserati Bora 13.356861 16.451589 632136.448
+#> Volvo 142E 10.492352 6.764313 36038.829