> #------------------------------------------------------------------- > # 2.1 FACTORS AND INTERACTION > #------------------------------------------------------------------- > m<-matrix(scan("/glim/datasets/educexp"),ncol=5,byrow=T) Read 240 items > m [,1] [,2] [,3] [,4] [,5] [1,] 508 235 3944 325 1 [2,] 564 231 4578 323 1 [3,] 322 270 4011 328 1 [4,] 846 261 5233 305 1 [5,] 871 300 4780 303 1 [6,] 774 317 5889 307 1 [7,] 856 387 5663 301 1 [8,] 889 285 5759 310 1 [9,] 715 300 4894 300 1 [10,] 753 221 5012 324 2 [11,] 649 264 4908 329 2 [12,] 830 308 5753 320 2 [13,] 738 379 5439 337 2 [14,] 659 342 4634 328 2 [15,] 664 378 4921 330 2 [16,] 572 232 4869 318 2 [17,] 701 231 4672 309 2 [18,] 443 246 4782 333 2 [19,] 446 230 4296 330 2 [20,] 615 268 4827 318 2 [21,] 661 337 5057 304 2 [22,] 722 344 5540 328 3 [23,] 766 330 5331 323 3 [24,] 631 261 4715 317 3 [25,] 390 214 3828 310 3 [26,] 450 245 4120 321 3 [27,] 476 233 3817 342 3 [28,] 603 250 4243 339 3 [29,] 805 243 4647 287 3 [30,] 523 216 3967 325 3 [31,] 588 212 3946 315 3 [32,] 584 208 3724 332 3 [33,] 445 215 3448 358 3 [34,] 500 221 3680 320 3 [35,] 661 244 3825 355 3 [36,] 680 234 4189 306 3 [37,] 797 269 4336 335 3 [38,] 534 302 4418 335 4 [39,] 541 268 4323 344 4 [40,] 605 323 4813 331 4 [41,] 785 304 5046 324 4 [42,] 698 317 3764 366 4 [43,] 796 332 4504 340 4 [44,] 804 315 4005 378 4 [45,] 809 291 5560 330 4 [46,] 726 312 4989 313 4 [47,] 671 316 4697 305 4 [48,] 909 332 5438 307 4 > urb<-m[,1] > exp<-m[,2] > inc<-m[,3] > n18<-m[,4] > reg<-m[,5] > plot(reg,exp,main="Figure 2.1 Education") > r1<-(reg==1)*1 > r2<-(reg==2)*1 > r3<-(reg==3)*1 > r4<-(reg==4)*1 > cbind(reg,r1,r2,r3,r4) reg r1 r2 r3 r4 [1,] 1 1 0 0 0 [2,] 1 1 0 0 0 [3,] 1 1 0 0 0 [4,] 1 1 0 0 0 [5,] 1 1 0 0 0 [6,] 1 1 0 0 0 [7,] 1 1 0 0 0 [8,] 1 1 0 0 0 [9,] 1 1 0 0 0 [10,] 2 0 1 0 0 [11,] 2 0 1 0 0 [12,] 2 0 1 0 0 [13,] 2 0 1 0 0 [14,] 2 0 1 0 0 [15,] 2 0 1 0 0 [16,] 2 0 1 0 0 [17,] 2 0 1 0 0 [18,] 2 0 1 0 0 [19,] 2 0 1 0 0 [20,] 2 0 1 0 0 [21,] 2 0 1 0 0 [22,] 3 0 0 1 0 [23,] 3 0 0 1 0 [24,] 3 0 0 1 0 [25,] 3 0 0 1 0 [26,] 3 0 0 1 0 [27,] 3 0 0 1 0 [28,] 3 0 0 1 0 [29,] 3 0 0 1 0 [30,] 3 0 0 1 0 [31,] 3 0 0 1 0 [32,] 3 0 0 1 0 [33,] 3 0 0 1 0 [34,] 3 0 0 1 0 [35,] 3 0 0 1 0 [36,] 3 0 0 1 0 [37,] 3 0 0 1 0 [38,] 4 0 0 0 1 [39,] 4 0 0 0 1 [40,] 4 0 0 0 1 [41,] 4 0 0 0 1 [42,] 4 0 0 0 1 [43,] 4 0 0 0 1 [44,] 4 0 0 0 1 [45,] 4 0 0 0 1 [46,] 4 0 0 0 1 [47,] 4 0 0 0 1 [48,] 4 0 0 0 1 > summary(glm(exp~1)) Call: glm(formula = exp ~ 1) Deviance Residuals: Min 1Q Median 3Q Max -70.60 -44.85 -10.10 37.65 108.40 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 278.604 7.097 39.26 <2e-16 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 2417.351) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 113615 on 47 degrees of freedom AIC: 513.15 Number of Fisher Scoring iterations: 2 > summary(glm(exp~r1+r2+r3+r4)) Call: glm(formula = exp ~ r1 + r2 + r3 + r4) Deviance Residuals: Min 1Q Median 3Q Max -65.333 -30.438 -2.760 16.526 99.667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 310.18 13.21 23.485 < 2e-16 *** r1 -22.85 19.69 -1.160 0.252113 r2 -23.85 18.29 -1.304 0.198931 r3 -63.99 17.16 -3.730 0.000545 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1918.880) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 84431 on 44 degrees of freedom AIC: 504.9 Number of Fisher Scoring iterations: 2 > f<-(113615.5-84430.74)/3/1918.88 > c(f,1-pf(f,3,44)) [1] 5.069755969 0.004210708 > summary(glm(exp~r1+r2+r3+r4-1)) Call: glm(formula = exp ~ r1 + r2 + r3 + r4 - 1) Deviance Residuals: Min 1Q Median 3Q Max -65.333 -30.438 -2.760 16.526 99.667 Coefficients: Estimate Std. Error t value Pr(>|t|) r1 287.33 14.60 19.68 <2e-16 *** r2 286.33 12.65 22.64 <2e-16 *** r3 246.19 10.95 22.48 <2e-16 *** r4 310.18 13.21 23.48 <2e-16 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1918.880) Null deviance: 3839389 on 48 degrees of freedom Residual deviance: 84431 on 44 degrees of freedom AIC: 504.9 Number of Fisher Scoring iterations: 2 > for(i in 1:4) print(c(i,mean(exp[reg==i]))) [1] 1.0000 287.3333 [1] 2.0000 286.3333 [1] 3.0000 246.1875 [1] 4.0000 310.1818 > Reg<-factor(reg) > # options(contrasts=c("contr.treatment", "contr.poly")) > summary(glm(exp~Reg)) Call: glm(formula = exp ~ Reg) Deviance Residuals: Min 1Q Median 3Q Max -65.333 -30.438 -2.760 16.526 99.667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 287.33 14.60 19.678 <2e-16 *** Reg2 -1.00 19.32 -0.052 0.9589 Reg3 -41.15 18.25 -2.254 0.0292 * Reg4 22.85 19.69 1.160 0.2521 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1918.880) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 84431 on 44 degrees of freedom AIC: 504.9 Number of Fisher Scoring iterations: 2 > summary(glm(exp~r2+r3+r4)) Call: glm(formula = exp ~ r2 + r3 + r4) Deviance Residuals: Min 1Q Median 3Q Max -65.333 -30.438 -2.760 16.526 99.667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 287.33 14.60 19.678 <2e-16 *** r2 -1.00 19.32 -0.052 0.9589 r3 -41.15 18.25 -2.254 0.0292 * r4 22.85 19.69 1.160 0.2521 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1918.880) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 84431 on 44 degrees of freedom AIC: 504.9 Number of Fisher Scoring iterations: 2 > plot(inc,exp,type="n",main="Figure 2.2 No interaction") > for(i in 1:4) text(inc[reg==i],exp[reg==i],i) > summary(glm(exp~inc)) Call: glm(formula = exp ~ inc) Deviance Residuals: Min 1Q Median 3Q Max -75.23 -28.05 -7.67 21.78 86.11 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 57.221972 42.010935 1.362 0.180 inc 0.047687 0.008967 5.318 3.00e-06 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1529.565) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 70360 on 46 degrees of freedom AIC: 492.15 Number of Fisher Scoring iterations: 2 > glm1<-glm(exp~inc+Reg) > summary(glm1) Call: glm(formula = exp ~ inc + Reg) Deviance Residuals: Min 1Q Median 3Q Max -68.889 -22.018 -7.302 18.234 92.097 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 69.491732 50.060697 1.388 0.1722 inc 0.043811 0.009765 4.487 5.33e-05 *** Reg2 0.818146 16.131272 0.051 0.9598 Reg3 -7.736493 16.959973 -0.456 0.6506 Reg4 35.349149 16.671794 2.120 0.0398 * --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1337.419) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 57509 on 43 degrees of freedom AIC: 488.47 Number of Fisher Scoring iterations: 2 > f<-(70359.97-57509.02)/3/1337.419 > c(f,1-pf(f,3,43)) [1] 3.20292294 0.03250252 > for(i in 1:4) lines(inc[reg==i],fitted(glm1)[reg==i]) > ir1<-inc*r1; ir2<-inc*r2; ir3<-inc*r3; ir4<-inc*r4 > cbind(reg,inc,ir1,ir2,ir3,ir4) reg inc ir1 ir2 ir3 ir4 [1,] 1 3944 3944 0 0 0 [2,] 1 4578 4578 0 0 0 [3,] 1 4011 4011 0 0 0 [4,] 1 5233 5233 0 0 0 [5,] 1 4780 4780 0 0 0 [6,] 1 5889 5889 0 0 0 [7,] 1 5663 5663 0 0 0 [8,] 1 5759 5759 0 0 0 [9,] 1 4894 4894 0 0 0 [10,] 2 5012 0 5012 0 0 [11,] 2 4908 0 4908 0 0 [12,] 2 5753 0 5753 0 0 [13,] 2 5439 0 5439 0 0 [14,] 2 4634 0 4634 0 0 [15,] 2 4921 0 4921 0 0 [16,] 2 4869 0 4869 0 0 [17,] 2 4672 0 4672 0 0 [18,] 2 4782 0 4782 0 0 [19,] 2 4296 0 4296 0 0 [20,] 2 4827 0 4827 0 0 [21,] 2 5057 0 5057 0 0 [22,] 3 5540 0 0 5540 0 [23,] 3 5331 0 0 5331 0 [24,] 3 4715 0 0 4715 0 [25,] 3 3828 0 0 3828 0 [26,] 3 4120 0 0 4120 0 [27,] 3 3817 0 0 3817 0 [28,] 3 4243 0 0 4243 0 [29,] 3 4647 0 0 4647 0 [30,] 3 3967 0 0 3967 0 [31,] 3 3946 0 0 3946 0 [32,] 3 3724 0 0 3724 0 [33,] 3 3448 0 0 3448 0 [34,] 3 3680 0 0 3680 0 [35,] 3 3825 0 0 3825 0 [36,] 3 4189 0 0 4189 0 [37,] 3 4336 0 0 4336 0 [38,] 4 4418 0 0 0 4418 [39,] 4 4323 0 0 0 4323 [40,] 4 4813 0 0 0 4813 [41,] 4 5046 0 0 0 5046 [42,] 4 3764 0 0 0 3764 [43,] 4 4504 0 0 0 4504 [44,] 4 4005 0 0 0 4005 [45,] 4 5560 0 0 0 5560 [46,] 4 4989 0 0 0 4989 [47,] 4 4697 0 0 0 4697 [48,] 4 5438 0 0 0 5438 > glm2<-glm(exp~inc+Reg+ir1+ir2+ir3+ir4) > summary(glm2) Call: glm(formula = exp ~ inc + Reg + ir1 + ir2 + ir3 + ir4) Deviance Residuals: Min 1Q Median 3Q Max -71.108 -18.304 -2.566 15.174 92.366 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 7.748e+01 8.573e+01 0.904 0.3715 inc 1.163e-03 1.979e-02 0.059 0.9534 Reg2 -1.419e+02 1.630e+02 -0.871 0.3891 Reg3 -9.489e+01 1.078e+02 -0.881 0.3838 Reg4 2.272e+02 1.267e+02 1.793 0.0805 . ir1 4.104e-02 2.614e-02 1.570 0.1243 ir2 6.998e-02 3.433e-02 2.039 0.0481 * ir3 6.145e-02 2.505e-02 2.453 0.0186 * --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1220.987) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 48839 on 40 degrees of freedom AIC: 486.62 Number of Fisher Scoring iterations: 2 > f<-(57509.02-48839.48)/3/1220.987 > c(f,1-pf(f,3,40)) [1] 2.36681199 0.08520352 > plot(inc,exp,type="n",main="Figure 2.3 With interaction") > for(i in 1:4) { + text(inc[reg==i],exp[reg==i],i) + lines(inc[reg==i],fitted(glm2)[reg==i]) + } > summary(glm(exp~inc+Reg+inc:Reg)) Call: glm(formula = exp ~ inc + Reg + inc:Reg) Deviance Residuals: Min 1Q Median 3Q Max -71.108 -18.304 -2.566 15.174 92.366 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 77.48124 85.73286 0.904 0.3715 inc 0.04220 0.01708 2.471 0.0178 * Reg2 -141.94612 163.02488 -0.871 0.3891 Reg3 -94.88502 107.75008 -0.881 0.3838 Reg4 227.24923 126.74682 1.793 0.0805 . inc.Reg2 0.02894 0.03284 0.881 0.3834 inc.Reg3 0.02041 0.02298 0.888 0.3797 inc.Reg4 -0.04104 0.02614 -1.570 0.1243 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1220.987) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 48839 on 40 degrees of freedom AIC: 486.62 Number of Fisher Scoring iterations: 2 > summary(glm(exp~Reg+inc:Reg-1)) Call: glm(formula = exp ~ Reg + inc:Reg - 1) Deviance Residuals: Min 1Q Median 3Q Max -71.108 -18.304 -2.566 15.174 92.366 Coefficients: Estimate Std. Error t value Pr(>|t|) Reg1 77.481242 85.732859 0.904 0.371538 Reg2 -64.464873 138.661418 -0.465 0.644518 Reg3 -17.403773 65.268342 -0.267 0.791109 Reg4 304.730472 93.352199 3.264 0.002252 ** Reg1.inc 0.042204 0.017082 2.471 0.017846 * Reg2.inc 0.071144 0.028047 2.537 0.015199 * Reg3.inc 0.062614 0.015365 4.075 0.000212 *** Reg4.inc 0.001163 0.019790 0.059 0.953427 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1220.987) Null deviance: 3839389 on 48 degrees of freedom Residual deviance: 48839 on 40 degrees of freedom AIC: 486.62 Number of Fisher Scoring iterations: 2 > summary(glm(exp~inc,weight=r1)) Call: glm(formula = exp ~ inc, weights = r1) Deviance Residuals: Min 1Q Median 3Q Max -39.69 0.00 0.00 0.00 70.52 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 77.48124 95.44458 0.812 0.444 inc 0.04220 0.01902 2.219 0.062 . --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1513.279) Null deviance: 18046 on 8 degrees of freedom Residual deviance: 10593 on 7 degrees of freedom AIC: 95.177 Number of Fisher Scoring iterations: 2 Warning message: observations with zero weight not used for calculating dispersion in: summary.glm(glm(exp ~ inc, weight = r1)) > summary(glm(exp~inc+urb+n18)) Call: glm(formula = exp ~ inc + urb + n18) Deviance Residuals: Min 1Q Median 3Q Max -81.961 -22.367 -6.034 23.398 80.151 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -290.33668 135.58424 -2.141 0.037821 * inc 0.04896 0.01231 3.978 0.000256 *** urb 0.06896 0.04990 1.382 0.173943 n18 0.91353 0.33745 2.707 0.009625 ** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1302.831) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 57325 on 44 degrees of freedom AIC: 486.31 Number of Fisher Scoring iterations: 2 > summary(glm(exp~inc+urb+n18+Reg)) Call: glm(formula = exp ~ inc + urb + n18 + Reg) Deviance Residuals: Min 1Q Median 3Q Max -74.719 -20.264 -3.283 19.764 86.615 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -183.45164 149.47227 -1.227 0.22670 inc 0.04518 0.01429 3.161 0.00295 ** urb 0.04841 0.05296 0.914 0.36597 n18 0.68102 0.36873 1.847 0.07198 . Reg2 -4.35641 16.53298 -0.263 0.79349 Reg3 -11.53595 16.60137 -0.695 0.49105 Reg4 19.82307 17.80602 1.113 0.27207 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1264.852) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 51859 on 41 degrees of freedom AIC: 487.5 Number of Fisher Scoring iterations: 2 > f<-(57324.58-51858.94)/3/1264.852 > c(f,1-pf(f,3,41)) [1] 1.4403899 0.2449547 > summary(glm(exp~inc+urb+n18+Reg+(inc+urb+n18):Reg)) Call: glm(formula = exp ~ inc + urb + n18 + Reg + (inc + urb + n18):Reg) Deviance Residuals: Min 1Q Median 3Q Max -84.678 -13.218 -1.810 7.624 78.368 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.503e+03 7.927e+02 1.896 0.0670 . inc 4.046e-02 2.956e-02 1.369 0.1806 urb -1.930e-01 1.527e-01 -1.264 0.2155 n18 -4.115e+00 2.273e+00 -1.810 0.0796 . Reg2 -2.038e+03 8.759e+02 -2.327 0.0265 * Reg3 -1.799e+03 8.183e+02 -2.199 0.0353 * Reg4 -9.441e+02 8.865e+02 -1.065 0.2948 inc.Reg2 1.013e-04 5.210e-02 0.002 0.9985 inc.Reg3 3.101e-02 3.656e-02 0.848 0.4026 inc.Reg4 -7.032e-02 4.763e-02 -1.476 0.1496 urb.Reg2 3.305e-01 2.101e-01 1.573 0.1255 urb.Reg3 1.849e-01 1.794e-01 1.031 0.3103 urb.Reg4 3.202e-01 1.887e-01 1.697 0.0994 . n18.Reg2 5.762e+00 2.531e+00 2.276 0.0296 * n18.Reg3 4.870e+00 2.332e+00 2.088 0.0448 * n18.Reg4 3.515e+00 2.417e+00 1.454 0.1556 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1185.193) Null deviance: 113615 on 47 degrees of freedom Residual deviance: 37926 on 32 degrees of freedom AIC: 490.48 Number of Fisher Scoring iterations: 2 > f<-(51858.94-37926.18)/9/1185.193 > c(f,1-pf(f,9,32)) [1] 1.3061876 0.2722586 > > > #------------------------------------------------------------------- > # 2.2 ORTHOGONALITY AND BALANCED DESIGNS > #------------------------------------------------------------------- > m<-matrix(scan("/glim/datasets/medcare"),ncol=3,byrow=T) Read 150 items > m [,1] [,2] [,3] [1,] 2 1 1 [2,] 5 1 1 [3,] 8 1 1 [4,] 6 1 1 [5,] 2 1 1 [6,] 4 1 1 [7,] 3 1 1 [8,] 10 1 1 [9,] 7 1 2 [10,] 5 1 2 [11,] 8 1 2 [12,] 6 1 2 [13,] 3 1 2 [14,] 5 1 2 [15,] 6 1 2 [16,] 4 1 2 [17,] 5 1 2 [18,] 6 1 2 [19,] 8 1 2 [20,] 9 1 2 [21,] 4 2 1 [22,] 6 2 1 [23,] 3 2 1 [24,] 3 2 1 [25,] 7 2 2 [26,] 7 2 2 [27,] 8 2 2 [28,] 6 2 2 [29,] 4 2 2 [30,] 9 2 2 [31,] 8 2 2 [32,] 7 2 2 [33,] 8 3 1 [34,] 7 3 1 [35,] 5 3 1 [36,] 9 3 1 [37,] 9 3 1 [38,] 10 3 1 [39,] 8 3 1 [40,] 6 3 1 [41,] 8 3 1 [42,] 10 3 1 [43,] 5 3 2 [44,] 8 3 2 [45,] 6 3 2 [46,] 6 3 2 [47,] 9 3 2 [48,] 7 3 2 [49,] 7 3 2 [50,] 8 3 2 > sat<-m[,1] > com<-factor(m[,2]) > worry<-factor(m[,3]) > glm0<-glm(sat~1); summary(glm0) Call: glm(formula = sat ~ 1) Deviance Residuals: Min 1Q Median 3Q Max -4.4 -1.4 0.1 1.6 3.6 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 6.400 0.301 21.26 <2e-16 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 4.530612) Null deviance: 222 on 49 degrees of freedom Residual deviance: 222 on 49 degrees of freedom AIC: 220.43 Number of Fisher Scoring iterations: 2 > glmc<-glm(sat~com); summary(glmc) Call: glm(formula = sat ~ com) Deviance Residuals: Min 1Q Median 3Q Max -3.600 -1.556 0.400 1.433 4.400 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.6000 0.4415 12.683 < 2e-16 *** com2 0.4000 0.7210 0.555 0.58167 com3 1.9556 0.6415 3.048 0.00377 ** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 3.898818) Null deviance: 222.00 on 49 degrees of freedom Residual deviance: 183.24 on 47 degrees of freedom AIC: 214.83 Number of Fisher Scoring iterations: 2 > deviance(glm0)-deviance(glmc) [1] 38.75556 > glmw<-glm(sat~worry); summary(glmw) Call: glm(formula = sat ~ worry) Deviance Residuals: Min 1Q Median 3Q Max -4.1818 -1.5714 0.1234 1.4286 3.8182 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 6.1818 0.4566 13.540 <2e-16 *** worry2 0.3896 0.6101 0.639 0.526 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 4.586039) Null deviance: 222.00 on 49 degrees of freedom Residual deviance: 220.13 on 48 degrees of freedom AIC: 222.00 Number of Fisher Scoring iterations: 2 > glmcw<-glm(sat~com+worry); summary(glmcw) Call: glm(formula = sat ~ com + worry) Deviance Residuals: Min 1Q Median 3Q Max -3.17910 -1.46020 0.08706 1.10323 4.82090 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.1791 0.5562 9.312 3.74e-12 *** com2 0.3532 0.7180 0.492 0.62510 com3 2.0647 0.6441 3.205 0.00245 ** worry2 0.7015 0.5690 1.233 0.22388 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 3.856154) Null deviance: 222.00 on 49 degrees of freedom Residual deviance: 177.38 on 46 degrees of freedom AIC: 215.21 Number of Fisher Scoring iterations: 2 > deviance(glmw)-deviance(glmcw) [1] 42.74679 > summary(glm(sat~com+worry+com:worry)) Call: glm(formula = sat ~ com + worry + com:worry) Deviance Residuals: Min 1Q Median 3Q Max -3.000e+00 -1.000e+00 8.882e-16 1.000e+00 5.000e+00 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.0000 0.6528 7.659 1.25e-09 *** com2 -1.0000 1.1307 -0.884 0.38127 com3 3.0000 0.8758 3.425 0.00134 ** worry2 1.0000 0.8427 1.187 0.24176 com2.worry2 2.0000 1.4102 1.418 0.16316 com3.worry2 -2.0000 1.2154 -1.646 0.10699 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 3.409091) Null deviance: 222 on 49 degrees of freedom Residual deviance: 150 on 44 degrees of freedom AIC: 210.82 Number of Fisher Scoring iterations: 2 > summary(glm(sat~com:worry-1)) Call: glm(formula = sat ~ com:worry - 1) Deviance Residuals: Min 1Q Median 3Q Max -3.000e+00 -1.000e+00 -8.882e-16 1.000e+00 5.000e+00 Coefficients: Estimate Std. Error t value Pr(>|t|) com1.worry1 5.0000 0.6528 7.659 1.25e-09 *** com2.worry1 4.0000 0.9232 4.333 8.41e-05 *** com3.worry1 8.0000 0.5839 13.702 < 2e-16 *** com1.worry2 6.0000 0.5330 11.257 1.53e-14 *** com2.worry2 7.0000 0.6528 10.723 7.42e-14 *** com3.worry2 7.0000 0.6528 10.723 7.42e-14 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 3.409091) Null deviance: 2270 on 50 degrees of freedom Residual deviance: 150 on 44 degrees of freedom AIC: 210.82 Number of Fisher Scoring iterations: 2 > > m<-matrix(scan("/glim/datasets/medcareb"),ncol=3,byrow=T) Read 72 items > m [,1] [,2] [,3] [1,] 2 1 1 [2,] 5 1 1 [3,] 8 1 1 [4,] 6 1 1 [5,] 7 1 2 [6,] 5 1 2 [7,] 8 1 2 [8,] 6 1 2 [9,] 4 2 1 [10,] 6 2 1 [11,] 3 2 1 [12,] 3 2 1 [13,] 7 2 2 [14,] 7 2 2 [15,] 8 2 2 [16,] 6 2 2 [17,] 8 3 1 [18,] 7 3 1 [19,] 5 3 1 [20,] 9 3 1 [21,] 5 3 2 [22,] 8 3 2 [23,] 6 3 2 [24,] 6 3 2 > sat<-m[,1] > com<-factor(m[,2]) > worry<-factor(m[,3]) > glm0<-glm(sat~1); summary(glm0) Call: glm(formula = sat ~ 1) Deviance Residuals: Min 1Q Median 3Q Max -4.04167 -1.04167 -0.04167 1.20833 2.95833 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 6.0417 0.3685 16.40 3.5e-14 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 3.259058) Null deviance: 74.958 on 23 degrees of freedom Residual deviance: 74.958 on 23 degrees of freedom AIC: 99.442 Number of Fisher Scoring iterations: 2 > glmc<-glm(sat~com); summary(glmc) Call: glm(formula = sat ~ com) Deviance Residuals: Min 1Q Median 3Q Max -3.8750 -1.0313 0.1875 1.3125 2.5000 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.8750 0.6380 9.209 8.04e-09 *** com2 -0.3750 0.9022 -0.416 0.682 com3 0.8750 0.9022 0.970 0.343 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 3.255952) Null deviance: 74.958 on 23 degrees of freedom Residual deviance: 68.375 on 21 degrees of freedom AIC: 101.24 Number of Fisher Scoring iterations: 2 > deviance(glm0)-deviance(glmc) [1] 6.583333 > glmw<-glm(sat~worry); summary(glmw) Call: glm(formula = sat ~ worry) Deviance Residuals: Min 1Q Median 3Q Max -3.50000 -0.81250 -0.04167 1.41667 3.50000 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.5000 0.5072 10.84 2.71e-10 *** worry2 1.0833 0.7173 1.51 0.145 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 3.087121) Null deviance: 74.958 on 23 degrees of freedom Residual deviance: 67.917 on 22 degrees of freedom AIC: 99.075 Number of Fisher Scoring iterations: 2 > glmcw<-glm(sat~com+worry); summary(glmcw) Call: glm(formula = sat ~ com + worry) Deviance Residuals: Min 1Q Median 3Q Max -3.3333 -1.2917 0.2708 0.9792 2.7917 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.3333 0.7149 7.460 3.37e-07 *** com2 -0.3750 0.8756 -0.428 0.673 com3 0.8750 0.8756 0.999 0.330 worry2 1.0833 0.7149 1.515 0.145 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 3.066667) Null deviance: 74.958 on 23 degrees of freedom Residual deviance: 61.333 on 20 degrees of freedom AIC: 100.63 Number of Fisher Scoring iterations: 2 > deviance(glmw)-deviance(glmcw) [1] 6.583333 > > m<-matrix(scan("/glim/datasets/glue"),ncol=3,byrow=T) Read 36 items > m [,1] [,2] [,3] [1,] 190 80 40 [2,] 189 80 40 [3,] 192 90 40 [4,] 190 90 40 [5,] 196 80 60 [6,] 193 80 60 [7,] 195 90 60 [8,] 196 90 60 [9,] 201 80 80 [10,] 200 80 80 [11,] 203 90 80 [12,] 205 90 80 > stren<-m[,1] > temp<-m[,2] > humid<-m[,3] > glm0<-glm(stren~1); summary(glm0) Call: glm(formula = stren ~ 1) Deviance Residuals: Min 1Q Median 3Q Max -6.8333 -4.3333 -0.3333 4.4167 9.1667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 195.833 1.551 126.2 <2e-16 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 28.87879) Null deviance: 317.67 on 11 degrees of freedom Residual deviance: 317.67 on 11 degrees of freedom AIC: 77.368 Number of Fisher Scoring iterations: 2 > glmt<-glm(stren~temp); summary(glmt) Call: glm(formula = stren ~ temp) Deviance Residuals: Min 1Q Median 3Q Max -6.833 -4.833 -1.333 5.417 8.167 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 178.8333 27.1789 6.580 6.23e-05 *** temp 0.2000 0.3192 0.627 0.545 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 30.56667) Null deviance: 317.67 on 11 degrees of freedom Residual deviance: 305.67 on 10 degrees of freedom AIC: 78.906 Number of Fisher Scoring iterations: 2 > deviance(glm0)-deviance(glmt) [1] 12 > glmh<-glm(stren~humid); summary(glmh) Call: glm(formula = stren ~ humid) Deviance Residuals: Min 1Q Median 3Q Max -2.8333 -0.8333 0.1667 0.4167 3.1667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 177.83333 1.89334 93.926 4.58e-16 *** humid 0.30000 0.03045 9.853 1.82e-06 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 2.966667) Null deviance: 317.667 on 11 degrees of freedom Residual deviance: 29.667 on 10 degrees of freedom AIC: 50.916 Number of Fisher Scoring iterations: 2 > glmht<-glm(stren~humid+temp); summary(glmht) Call: glm(formula = stren ~ humid + temp) Deviance Residuals: Min 1Q Median 3Q Max -1.8333 -0.8333 0.1667 1.1667 2.1667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 160.83333 7.04603 22.826 2.82e-09 *** humid 0.30000 0.02477 12.113 7.11e-07 *** temp 0.20000 0.08089 2.472 0.0354 * --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1.962963) Null deviance: 317.667 on 11 degrees of freedom Residual deviance: 17.667 on 9 degrees of freedom AIC: 46.696 Number of Fisher Scoring iterations: 2 > deviance(glmh)-deviance(glmht) [1] 12 > > xstren<-c(190,189,190,188,196,192,195,197,203,203,203,204) > xtemp<-c(rep(80,6),rep(90,6)) > cbind(xstren,xtemp,humid) xstren xtemp humid [1,] 190 80 40 [2,] 189 80 40 [3,] 190 80 40 [4,] 188 80 40 [5,] 196 80 60 [6,] 192 80 60 [7,] 195 90 60 [8,] 197 90 60 [9,] 203 90 80 [10,] 203 90 80 [11,] 203 90 80 [12,] 204 90 80 > glm0<-glm(xstren~1); summary(glm0) Call: glm(formula = xstren ~ 1) Deviance Residuals: Min 1Q Median 3Q Max -7.8333 -5.8333 -0.3333 7.1667 8.1667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 195.83 1.77 110.6 <2e-16 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 37.60606) Null deviance: 413.67 on 11 degrees of freedom Residual deviance: 413.67 on 11 degrees of freedom AIC: 80.536 Number of Fisher Scoring iterations: 2 > glmt<-glm(xstren~xtemp); summary(glmt) Call: glm(formula = xstren ~ xtemp) Deviance Residuals: Min 1Q Median 3Q Max -5.8333 -2.0833 0.1667 2.1667 5.1667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 110.8333 16.5739 6.687 5.45e-05 *** xtemp 1.0000 0.1947 5.137 0.000439 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 11.36667) Null deviance: 413.67 on 11 degrees of freedom Residual deviance: 113.67 on 10 degrees of freedom AIC: 67.035 Number of Fisher Scoring iterations: 2 > deviance(glm0)-deviance(glmt) [1] 300 > glmh<-glm(xstren~humid); summary(glmh) Call: glm(formula = xstren ~ humid) Deviance Residuals: Min 1Q Median 3Q Max -3.83333 -0.08333 0.16667 1.16667 1.16667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 174.83333 1.61804 108.05 < 2e-16 *** humid 0.35000 0.02602 13.45 9.92e-08 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 2.166667) Null deviance: 413.667 on 11 degrees of freedom Residual deviance: 21.667 on 10 degrees of freedom AIC: 47.145 Number of Fisher Scoring iterations: 2 > glmht<-glm(xstren~humid+xtemp); summary(glmht) Call: glm(formula = xstren ~ humid + xtemp) Deviance Residuals: Min 1Q Median 3Q Max -2.83333 -0.08333 0.16667 1.16667 1.16667 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 160.8333 9.9276 16.201 5.77e-08 *** humid 0.3000 0.0429 6.993 6.37e-05 *** xtemp 0.2000 0.1401 1.427 0.187 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 (Dispersion parameter for gaussian family taken to be 1.962963) Null deviance: 413.667 on 11 degrees of freedom Residual deviance: 17.667 on 9 degrees of freedom AIC: 46.696 Number of Fisher Scoring iterations: 2 > deviance(glmh)-deviance(glmht) [1] 4 > >