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[R.app GUI 1.31 (5538) powerpc-apple-darwin8.11.1] [Workspace restored from /Users/andrejstreibergs/.RData] > tt <- read.table("M3081DataPotato.txt",header=TRUE) > tt y x1 x2 x3 x4 x5 x6 1 9.7 3.7 13 14 0.25 6 33.00 2 9.4 3.8 17 18 0.88 6 30.43 3 10.5 3.8 14 15 0.50 6 34.00 4 10.9 3.9 14 14 0.50 6 34.00 5 11.6 4.3 17 18 0.38 6 36.24 6 10.9 4.2 16 17 0.50 6 31.76 7 11.0 4.3 16 19 0.38 6 34.00 8 10.7 3.9 15 16 0.38 6 32.13 9 11.8 3.6 8 8 0.38 6 37.00 10 9.7 4.0 18 18 0.50 6 36.00 11 11.6 4.0 12 13 0.31 5 45.00 12 10.9 3.9 15 15 0.50 5 50.00 13 10.0 3.8 17 18 0.63 5 46.91 14 10.3 3.8 13 14 0.50 4 57.50 15 10.1 3.6 17 17 0.63 4 60.40 16 9.9 3.8 17 18 0.50 4 53.14 17 9.5 3.5 17 18 0.63 6 34.40 18 10.5 3.8 15 17 0.50 6 33.96 19 10.8 3.9 15 17 0.75 6 35.00 20 10.4 3.9 14 15 0.50 6 35.00 21 10.9 4.0 15 16 0.50 6 34.00 22 11.2 4.4 17 19 0.38 6 34.00 23 9.5 3.8 17 17 0.50 6 33.49 24 10.7 3.9 15 17 0.50 6 33.38 25 10.1 3.8 15 17 0.50 6 41.00 26 10.5 3.8 17 17 0.50 6 36.00 27 10.9 4.0 15 17 0.25 6 34.00 28 15.5 4.3 13 15 0.63 6 41.00 29 13.1 4.0 17 17 0.50 6 35.00 30 11.0 4.0 14 15 0.38 6 36.00 31 12.5 4.2 15 17 0.31 6 37.72 32 11.7 4.2 14 14 0.25 6 36.00 33 11.9 4.4 15 16 0.38 6 36.52 34 11.7 3.4 8 10 0.31 6 38.08 35 17.8 4.3 12 12 0.31 6 38.00 36 11.8 4.5 14 15 0.25 6 33.00 37 10.0 3.7 12 13 0.25 5 48.00 38 10.3 3.7 15 15 0.50 5 48.00 39 9.8 3.8 14 15 0.50 5 47.24 40 10.0 3.7 13 14 0.50 6 37.00 41 10.6 4.1 14 15 0.50 6 33.70 42 11.2 3.9 13 14 0.38 6 38.26 43 10.9 3.7 13 14 0.31 6 38.00 44 11.0 4.1 13 14 0.38 6 37.00 45 11.0 4.1 14 15 0.38 6 38.00 46 11.7 4.5 14 14 0.25 6 36.26 47 11.8 4.4 13 14 0.25 6 37.45 48 12.0 4.2 13 13 0.38 6 38.00 49 11.8 4.6 14 14 0.38 6 36.90 50 11.1 4.0 14 15 0.50 6 37.00 51 11.6 3.9 14 14 0.50 6 37.50 52 11.0 4.0 14 15 0.50 6 36.00 53 11.2 3.9 15 15 0.31 6 35.00 54 11.0 4.2 14 14 0.38 6 37.00 > attach(tt) >#============A FUNCTION TO REPLACE A VECTOR BY THE STANDARDIZED VECTOR========= > stan <- function(z){zm<-mean(z);zs<-sd(z);(z-zm)/zs} > s1<-stan(x1);s2<-stan(x2);s3<-stan(x3);s4<-stan(x4);s5<-stan(x5);s6<-stan(x6) > s11<-s1*s1;s12<-s1*s2;s13<-s1*s3;s14<-s1*s4;s15<-s1*s5;s16<-s1*s6 > s22<-s2*s2;s23<-s2*s3;s24<-s2*s4;s25<-s2*s5;s26<-s2*s6;s33<-s3*s3 > s34<-s3*s4;s35<-s3*s5;s36<-s3*s6;s44<-s4*s4;s45<-s4*s5;s46<-s4*s6 > s55<-s5*s5;s56<-s5*s6;s66<-s6*s6 >#==============FULL QUADRATIC MODEL============================================ > f2<-lm(y~s1+s2+s3+s4+s5+s6+s11+s12+s13+s14+s15+s16+s22+s23+s24+s25+s26+s33+s34+s35+s36+s44+s45+s46+s55+s56+s66);summary(f2);anova(f2);extractAIC(f2) Call: lm(formula = y ~ s1 + s2 + s3 + s4 + s5 + s6 + s11 + s12 + s13 + s14 + s15 + s16 + s22 + s23 + s24 + s25 + s26 + s33 + s34 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66) Residuals: Min 1Q Median 3Q Max -1.46745 -0.39300 -0.05315 0.28248 3.27769 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 10.982860 0.359862 30.520 <2e-16 *** s1 1.095219 0.419719 2.609 0.0148 * s2 0.425343 0.959618 0.443 0.6613 s3 -0.948449 0.972751 -0.975 0.3385 s4 0.085723 0.335044 0.256 0.8001 s5 0.655274 0.932230 0.703 0.4884 s6 0.370504 0.785542 0.472 0.6411 s11 -0.333763 0.256493 -1.301 0.2046 s12 0.246071 0.871247 0.282 0.7798 s13 -0.675534 0.820961 -0.823 0.4181 s14 0.209138 0.440002 0.475 0.6385 s15 0.150697 1.242057 0.121 0.9044 s16 0.332264 0.840303 0.395 0.6958 s22 -0.004858 1.505353 -0.003 0.9974 s23 -0.401632 2.580688 -0.156 0.8775 s24 0.446381 1.070322 0.417 0.6801 s25 -6.472074 4.545332 -1.424 0.1664 s26 -4.475166 3.515467 -1.273 0.2143 s33 0.605767 1.255304 0.483 0.6334 s34 -0.023807 0.829529 -0.029 0.9773 s35 4.820695 4.103536 1.175 0.2507 s36 2.111453 2.835550 0.745 0.4632 s44 0.008341 0.221753 0.038 0.9703 s45 0.796401 1.149265 0.693 0.4945 s46 1.167880 1.070802 1.091 0.2854 s55 -1.217086 2.060213 -0.591 0.5598 s56 -3.260196 4.175548 -0.781 0.4420 s66 -2.009600 2.110802 -0.952 0.3498 --- Signif. codes: 0 Ô***Õ 0.001 Ô**Õ 0.01 Ô*Õ 0.05 Ô.Õ 0.1 Ô Õ 1 Residual standard error: 1.106 on 26 degrees of freedom Multiple R-squared: 0.6821, Adjusted R-squared: 0.3521 F-statistic: 2.067 on 27 and 26 DF, p-value: 0.03404 Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) s1 1 25.359 25.3591 20.7476 0.0001088 *** s2 1 16.211 16.2106 13.2628 0.0011811 ** s3 1 0.493 0.4931 0.4034 0.5308736 s4 1 1.566 1.5664 1.2815 0.2679487 s5 1 0.185 0.1851 0.1515 0.7002977 s6 1 4.925 4.9247 4.0292 0.0552207 . s11 1 0.253 0.2532 0.2071 0.6528091 s12 1 0.434 0.4344 0.3554 0.5562318 s13 1 0.362 0.3625 0.2965 0.5906964 s14 1 1.606 1.6056 1.3137 0.2621725 s15 1 0.000 0.0001 4.448e-05 0.9947296 s16 1 1.532 1.5317 1.2532 0.2731803 s22 1 8.184 8.1843 6.6960 0.0156055 * s23 1 0.018 0.0176 0.0144 0.9054977 s24 1 0.224 0.2236 0.1830 0.6723624 s25 1 0.057 0.0574 0.0470 0.8300887 s26 1 1.423 1.4226 1.1639 0.2905600 s33 1 1.182 1.1815 0.9667 0.3345725 s34 1 0.127 0.1268 0.1038 0.7499415 s35 1 1.397 1.3969 1.1429 0.2948735 s36 1 0.014 0.0143 0.0117 0.9147077 s44 1 0.010 0.0103 0.0084 0.9275830 s45 1 0.651 0.6506 0.5323 0.4721672 s46 1 0.717 0.7169 0.5865 0.4506545 s55 1 0.010 0.0098 0.0081 0.9291777 s56 1 0.151 0.1512 0.1237 0.7278678 s66 1 1.108 1.1079 0.9064 0.3498365 Residuals 26 31.779 1.2223 --- Signif. codes: 0 Ô***Õ 0.001 Ô**Õ 0.01 Ô*Õ 0.05 Ô.Õ 0.1 Ô Õ 1 [1] 28.00000 27.37010 > >#===============REMOVE THE VARIABLE WITH GREATEST P-VALUE FROM MODEL===== > fx <- update(f2,.~.-s22);summary(fx);anova(fx);extractAIC(fx) Call: lm(formula = y ~ s1 + s2 + s3 + s4 + s5 + s6 + s11 + s12 + s13 + s14 + s15 + s16 + s23 + s24 + s25 + s26 + s33 + s34 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66) Residuals: Min 1Q Median 3Q Max -1.46781 -0.39254 -0.05314 0.28183 3.27783 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 10.982469 0.332533 33.027 <2e-16 *** s1 1.094919 0.401645 2.726 0.0111 * s2 0.423989 0.846875 0.501 0.6207 s3 -0.947405 0.900230 -1.052 0.3019 s4 0.085524 0.323152 0.265 0.7933 s5 0.654685 0.897105 0.730 0.4718 s6 0.370393 0.770108 0.481 0.6344 s11 -0.333621 0.247961 -1.345 0.1897 s12 0.244927 0.780927 0.314 0.7562 s13 -0.674708 0.765450 -0.881 0.3859 s14 0.209039 0.430725 0.485 0.6314 s15 0.150849 1.217968 0.124 0.9023 s16 0.332124 0.823498 0.403 0.6899 s23 -0.409291 0.994164 -0.412 0.6838 s24 0.444882 0.946222 0.470 0.6420 s25 -6.465082 3.920921 -1.649 0.1108 s26 -4.470583 3.155657 -1.417 0.1680 s33 0.608783 0.822202 0.740 0.4654 s34 -0.023184 0.791673 -0.029 0.9769 s35 4.814948 3.627719 1.327 0.1955 s36 2.108871 2.669430 0.790 0.4364 s44 0.008335 0.217602 0.038 0.9697 s45 0.795013 1.045868 0.760 0.4538 s46 1.166251 0.926675 1.259 0.2190 s55 -1.215556 1.967489 -0.618 0.5419 s56 -3.255700 3.862719 -0.843 0.4067 s66 -2.006771 1.884289 -1.065 0.2963 --- Signif. codes: 0 Ô***Õ 0.001 Ô**Õ 0.01 Ô*Õ 0.05 Ô.Õ 0.1 Ô Õ 1 Residual standard error: 1.085 on 27 degrees of freedom Multiple R-squared: 0.6821, Adjusted R-squared: 0.376 F-statistic: 2.229 on 26 and 27 DF, p-value: 0.02148 Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) s1 1 25.359 25.3591 21.5456 7.977e-05 *** s2 1 16.211 16.2106 13.7729 0.0009453 *** s3 1 0.493 0.4931 0.4189 0.5229286 s4 1 1.566 1.5664 1.3308 0.2587706 s5 1 0.185 0.1851 0.1573 0.6947697 s6 1 4.925 4.9247 4.1841 0.0506608 . s11 1 0.253 0.2532 0.2151 0.6465245 s12 1 0.434 0.4344 0.3691 0.5485926 s13 1 0.362 0.3625 0.3080 0.5835085 s14 1 1.606 1.6056 1.3642 0.2530240 s15 1 0.000 0.0001 4.619e-05 0.9946273 s16 1 1.532 1.5317 1.3014 0.2639784 s23 1 7.138 7.1385 6.0650 0.0204557 * s24 1 0.006 0.0065 0.0055 0.9413683 s25 1 0.082 0.0819 0.0696 0.7939325 s26 1 1.586 1.5861 1.3476 0.2558661 s33 1 0.204 0.2045 0.1737 0.6801250 s34 1 0.033 0.0327 0.0278 0.8689093 s35 1 2.505 2.5047 2.1280 0.1561634 s36 1 0.018 0.0183 0.0156 0.9016511 s44 1 0.016 0.0164 0.0139 0.9070277 s45 1 0.848 0.8482 0.7207 0.4033925 s46 1 1.213 1.2132 1.0308 0.3189861 s55 1 0.047 0.0466 0.0396 0.8438147 s56 1 0.239 0.2394 0.2034 0.6556248 s66 1 1.335 1.3350 1.1342 0.2963069 Residuals 27 31.779 1.1770 --- Signif. codes: 0 Ô***Õ 0.001 Ô**Õ 0.01 Ô*Õ 0.05 Ô.Õ 0.1 Ô Õ 1 [1] 27.00000 25.37013 > >#======REMOVE THE VARIABLE WITH GREATEST P-VALUE NOW=============== > fx <- update(fx,.~.-s34);summary(fx);anova(fx);extractAIC(fx) Call: lm(formula = y ~ s1 + s2 + s3 + s4 + s5 + s6 + s11 + s12 + s13 + s14 + s15 + s16 + s23 + s24 + s25 + s26 + s33 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66) Residuals: Min 1Q Median 3Q Max -1.46707 -0.39398 -0.05702 0.28205 3.27700 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 10.982396 0.326536 33.633 < 2e-16 *** s1 1.093634 0.392053 2.790 0.00939 ** s2 0.421286 0.826673 0.510 0.61431 s3 -0.942969 0.871416 -1.082 0.28843 s4 0.082266 0.297931 0.276 0.78448 s5 0.655358 0.880665 0.744 0.46298 s6 0.371245 0.755703 0.491 0.62707 s11 -0.332989 0.242573 -1.373 0.18073 s12 0.235529 0.699122 0.337 0.73871 s13 -0.663335 0.647725 -1.024 0.31456 s14 0.208278 0.422200 0.493 0.62564 s15 0.151232 1.195970 0.126 0.90028 s16 0.333091 0.808021 0.412 0.68331 s23 -0.402405 0.948562 -0.424 0.67464 s24 0.425580 0.666674 0.638 0.52842 s25 -6.447826 3.806598 -1.694 0.10139 s26 -4.453202 3.043539 -1.463 0.15456 s33 0.601064 0.764775 0.786 0.43851 s35 4.801020 3.531660 1.359 0.18486 s36 2.094767 2.578353 0.812 0.42339 s44 0.005688 0.194377 0.029 0.97686 s45 0.787731 0.997587 0.790 0.43638 s46 1.160167 0.886826 1.308 0.20144 s55 -1.207879 1.914838 -0.631 0.53329 s56 -3.237160 3.741876 -0.865 0.39433 s66 -1.995798 1.813408 -1.101 0.28045 --- Signif. codes: 0 Ô***Õ 0.001 Ô**Õ 0.01 Ô*Õ 0.05 Ô.Õ 0.1 Ô Õ 1 Residual standard error: 1.065 on 28 degrees of freedom Multiple R-squared: 0.6821, Adjusted R-squared: 0.3983 F-statistic: 2.403 on 25 and 28 DF, p-value: 0.0131 Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) s1 1 25.359 25.3591 22.3429 5.852e-05 *** s2 1 16.211 16.2106 14.2826 0.0007571 *** s3 1 0.493 0.4931 0.4344 0.5151983 s4 1 1.566 1.5664 1.3801 0.2499852 s5 1 0.185 0.1851 0.1631 0.6893652 s6 1 4.925 4.9247 4.3389 0.0465001 * s11 1 0.253 0.2532 0.2230 0.6403870 s12 1 0.434 0.4344 0.3827 0.5411532 s13 1 0.362 0.3625 0.3193 0.5765007 s14 1 1.606 1.6056 1.4147 0.2442720 s15 1 0.000 0.0001 4.79e-05 0.9945270 s16 1 1.532 1.5317 1.3495 0.2551657 s23 1 7.138 7.1385 6.2894 0.0182184 * s24 1 0.006 0.0065 0.0057 0.9402756 s25 1 0.082 0.0819 0.0722 0.7901742 s26 1 1.586 1.5861 1.3974 0.2470972 s33 1 0.204 0.2045 0.1801 0.6744925 s35 1 2.334 2.3343 2.0567 0.1626152 s36 1 0.051 0.0514 0.0453 0.8330741 s44 1 0.089 0.0889 0.0783 0.7816277 s45 1 0.735 0.7353 0.6479 0.4276543 s46 1 1.371 1.3710 1.2080 0.2810980 s55 1 0.044 0.0438 0.0386 0.8457291 s56 1 0.254 0.2538 0.2237 0.6399357 s66 1 1.375 1.3748 1.2113 0.2804523 Residuals 28 31.780 1.1350 --- Signif. codes: 0 Ô***Õ 0.001 Ô**Õ 0.01 Ô*Õ 0.05 Ô.Õ 0.1 Ô Õ 1 [1] 26.00000 23.37184 > f0 <- lm(y~1) > summary(f0) >#===============TO AUTOMATE, FIT THE SMALLEST MODEL (Y BAR ONLY)========= Call: lm(formula = y ~ 1) Residuals: Min 1Q Median 3Q Max -1.6926 -0.7676 -0.1926 0.5074 6.7074 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 11.0926 0.1869 59.35 <2e-16 *** --- Signif. codes: 0 Ô***Õ 0.001 Ô**Õ 0.01 Ô*Õ 0.05 Ô.Õ 0.1 Ô Õ 1 Residual standard error: 1.373 on 53 degrees of freedom >#==BACKWARD STEPWISE REGRESSION STARTING FROM LARGEST MODEL=========== > step(f2,scope=list(upper=f2,lower=f0),direction="backward") Start: AIC=27.37 y ~ s1 + s2 + s3 + s4 + s5 + s6 + s11 + s12 + s13 + s14 + s15 + s16 + s22 + s23 + s24 + s25 + s26 + s33 + s34 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s22 1 0.0000 31.779 25.370 - s34 1 0.0010 31.780 25.372 - s44 1 0.0017 31.781 25.373 - s15 1 0.0180 31.797 25.401 - s23 1 0.0296 31.808 25.420 - s4 1 0.0800 31.859 25.506 - s12 1 0.0975 31.876 25.536 - s16 1 0.1911 31.970 25.694 - s24 1 0.2126 31.991 25.730 - s2 1 0.2401 32.019 25.777 - s6 1 0.2719 32.051 25.830 - s14 1 0.2761 32.055 25.837 - s33 1 0.2846 32.063 25.852 - s55 1 0.4266 32.205 26.090 - s45 1 0.5869 32.366 26.358 - s5 1 0.6039 32.383 26.387 - s36 1 0.6777 32.457 26.510 - s56 1 0.7451 32.524 26.622 - s13 1 0.8276 32.606 26.758 - s66 1 1.1079 32.887 27.221 - s3 1 1.1620 32.941 27.309 31.779 27.370 - s46 1 1.4539 33.233 27.786 - s35 1 1.6868 33.466 28.163 - s26 1 1.9807 33.760 28.635 - s11 1 2.0696 33.848 28.777 - s25 1 2.4781 34.257 29.425 - s1 1 8.3224 40.101 37.931 Step: AIC=25.37 y ~ s1 + s2 + s3 + s4 + s5 + s6 + s11 + s12 + s13 + s14 + s15 + s16 + s23 + s24 + s25 + s26 + s33 + s34 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s34 1 0.0010 31.780 23.372 - s44 1 0.0017 31.781 23.373 - s15 1 0.0181 31.797 23.401 - s4 1 0.0824 31.861 23.510 - s12 1 0.1158 31.895 23.567 - s16 1 0.1914 31.970 23.694 - s23 1 0.1995 31.978 23.708 - s24 1 0.2602 32.039 23.810 - s6 1 0.2723 32.051 23.831 - s14 1 0.2772 32.056 23.839 - s2 1 0.2950 32.074 23.869 - s55 1 0.4493 32.228 24.128 - s5 1 0.6268 32.406 24.425 - s33 1 0.6453 32.424 24.456 - s45 1 0.6801 32.459 24.514 - s36 1 0.7346 32.513 24.604 - s56 1 0.8361 32.615 24.773 - s13 1 0.9145 32.693 24.902 31.779 25.370 - s3 1 1.3036 33.082 25.541 - s66 1 1.3350 33.114 25.592 - s46 1 1.8642 33.643 26.448 - s35 1 2.0734 33.852 26.783 - s11 1 2.1307 33.910 26.874 - s26 1 2.3622 34.141 27.242 - s25 1 3.2000 34.979 28.551 - s1 1 8.7469 40.526 36.500 Step: AIC=23.37 y ~ s1 + s2 + s3 + s4 + s5 + s6 + s11 + s12 + s13 + s14 + s15 + s16 + s23 + s24 + s25 + s26 + s33 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s44 1 0.0010 31.781 21.373 - s15 1 0.0181 31.798 21.403 - s4 1 0.0865 31.866 21.519 - s12 1 0.1288 31.909 21.590 - s16 1 0.1929 31.973 21.699 - s23 1 0.2043 31.984 21.718 - s6 1 0.2739 32.054 21.835 - s14 1 0.2762 32.056 21.839 - s2 1 0.2948 32.075 21.870 - s55 1 0.4516 32.231 22.134 - s24 1 0.4625 32.242 22.152 - s5 1 0.6285 32.408 22.429 - s33 1 0.7011 32.481 22.550 - s45 1 0.7077 32.488 22.561 - s36 1 0.7492 32.529 22.630 - s56 1 0.8495 32.629 22.796 - s13 1 1.1904 32.970 23.358 31.780 23.372 - s3 1 1.3290 33.109 23.584 - s66 1 1.3748 33.155 23.659 - s46 1 1.9425 33.722 24.576 - s35 1 2.0975 33.877 24.823 - s11 1 2.1388 33.919 24.889 - s26 1 2.4299 34.210 25.350 - s25 1 3.2565 35.036 26.640 - s1 1 8.8318 40.612 34.614 Step: AIC=21.37 y ~ s1 + s2 + s3 + s4 + s5 + s6 + s11 + s12 + s13 + s14 + s15 + s16 + s23 + s24 + s25 + s26 + s33 + s35 + s36 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s15 1 0.0253 31.806 19.417 - s4 1 0.0994 31.880 19.542 - s12 1 0.1386 31.919 19.608 - s23 1 0.2529 32.034 19.802 - s16 1 0.2702 32.051 19.831 - s6 1 0.2730 32.054 19.835 - s2 1 0.2950 32.076 19.872 - s14 1 0.3329 32.114 19.936 - s55 1 0.4516 32.232 20.135 - s5 1 0.6366 32.417 20.444 - s36 1 0.7653 32.546 20.658 - s33 1 0.7743 32.555 20.673 - s45 1 0.7852 32.566 20.691 - s56 1 0.8519 32.633 20.802 - s24 1 0.8581 32.639 20.812 31.781 21.373 - s13 1 1.2089 32.990 21.389 - s3 1 1.3357 33.117 21.597 - s66 1 1.3844 33.165 21.676 - s35 1 2.1214 33.902 22.863 - s46 1 2.1701 33.951 22.940 - s11 1 2.3760 34.157 23.267 - s26 1 2.5030 34.284 23.467 - s25 1 3.3122 35.093 24.727 - s1 1 8.8446 40.625 32.632 Step: AIC=19.42 y ~ s1 + s2 + s3 + s4 + s5 + s6 + s11 + s12 + s13 + s14 + s16 + s23 + s24 + s25 + s26 + s33 + s35 + s36 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s4 1 0.0838 31.890 17.559 - s12 1 0.1167 31.923 17.614 - s23 1 0.2797 32.086 17.889 - s2 1 0.2932 32.099 17.912 - s6 1 0.3031 32.109 17.929 - s16 1 0.3339 32.140 17.980 - s14 1 0.5121 32.318 18.279 - s5 1 0.6143 32.420 18.449 - s55 1 0.7393 32.545 18.657 - s45 1 0.7659 32.572 18.701 - s24 1 0.8406 32.647 18.825 - s33 1 0.8573 32.663 18.853 - s36 1 0.9658 32.772 19.032 31.806 19.417 - s13 1 1.2042 33.010 19.423 - s56 1 1.2916 33.098 19.566 - s3 1 1.3148 33.121 19.604 - s66 1 1.7519 33.558 20.312 - s46 1 2.2137 34.020 21.050 - s35 1 2.3145 34.121 21.210 - s11 1 2.4741 34.280 21.462 - s26 1 2.9633 34.769 22.227 - s25 1 3.7498 35.556 23.435 - s1 1 17.7358 49.542 41.347 Step: AIC=17.56 y ~ s1 + s2 + s3 + s5 + s6 + s11 + s12 + s13 + s14 + s16 + s23 + s24 + s25 + s26 + s33 + s35 + s36 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s12 1 0.1204 32.010 15.762 - s23 1 0.2441 32.134 15.970 - s2 1 0.2528 32.143 15.985 - s6 1 0.4384 32.328 16.296 - s14 1 0.4528 32.343 16.320 - s16 1 0.4983 32.388 16.396 - s5 1 0.6851 32.575 16.706 - s24 1 0.7573 32.647 16.826 - s33 1 0.8146 32.705 16.921 - s45 1 0.8494 32.739 16.978 - s55 1 0.9391 32.829 17.126 - s36 1 1.0393 32.929 17.290 31.890 17.559 - s3 1 1.2406 33.131 17.619 - s13 1 1.2542 33.144 17.642 - s56 1 1.4004 33.290 17.879 - s66 1 1.6979 33.588 18.360 - s46 1 2.1300 34.020 19.050 - s35 1 2.2690 34.159 19.270 - s11 1 2.5818 34.472 19.762 - s26 1 3.1080 34.998 20.580 - s25 1 3.7819 35.672 21.610 - s1 1 17.6528 49.543 39.348 Step: AIC=15.76 y ~ s1 + s2 + s3 + s5 + s6 + s11 + s13 + s14 + s16 + s23 + s24 + s25 + s26 + s33 + s35 + s36 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s23 1 0.1358 32.146 13.990 - s2 1 0.1564 32.167 14.025 - s16 1 0.4236 32.434 14.472 - s6 1 0.4899 32.500 14.582 - s14 1 0.6344 32.645 14.822 - s24 1 0.6523 32.663 14.851 - s33 1 0.7227 32.733 14.968 - s45 1 0.7326 32.743 14.984 - s5 1 0.7431 32.753 15.001 - s55 1 0.8227 32.833 15.132 - s36 1 0.9205 32.931 15.293 - s3 1 1.1203 33.131 15.620 32.010 15.762 - s56 1 1.2808 33.291 15.880 - s66 1 1.5788 33.589 16.362 - s46 1 2.1384 34.149 17.254 - s35 1 2.2178 34.228 17.379 - s13 1 2.2522 34.262 17.434 - s11 1 2.7149 34.725 18.158 - s26 1 3.2444 35.255 18.975 - s25 1 4.0480 36.058 20.192 - s1 1 17.9750 49.985 37.828 Step: AIC=13.99 y ~ s1 + s2 + s3 + s5 + s6 + s11 + s13 + s14 + s16 + s24 + s25 + s26 + s33 + s35 + s36 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s2 1 0.0599 32.206 12.091 - s16 1 0.3378 32.484 12.555 - s6 1 0.5098 32.656 12.840 - s24 1 0.5719 32.718 12.943 - s14 1 0.6009 32.747 12.991 - s45 1 0.6150 32.761 13.014 - s55 1 0.6952 32.841 13.146 - s5 1 0.7095 32.856 13.169 - s36 1 0.7927 32.939 13.306 - s3 1 1.0044 33.150 13.652 - s56 1 1.1537 33.300 13.894 32.146 13.990 - s66 1 1.4855 33.632 14.430 - s46 1 2.0466 34.193 15.323 - s35 1 2.1344 34.280 15.462 - s33 1 2.5740 34.720 16.150 - s11 1 2.8119 34.958 16.519 - s13 1 3.3981 35.544 17.417 - s26 1 3.5810 35.727 17.694 - s25 1 4.3043 36.450 18.776 - s1 1 17.8956 50.042 35.889 Step: AIC=12.09 y ~ s1 + s3 + s5 + s6 + s11 + s13 + s14 + s16 + s24 + s25 + s26 + s33 + s35 + s36 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s16 1 0.3329 32.539 10.646 - s24 1 0.5380 32.744 10.986 - s14 1 0.5849 32.791 11.063 - s6 1 0.6161 32.822 11.114 - s45 1 0.6287 32.835 11.135 - s5 1 0.7590 32.965 11.349 - s36 1 0.7591 32.965 11.349 - s55 1 0.8660 33.072 11.524 32.206 12.091 - s56 1 1.2514 33.457 12.149 - s66 1 1.4694 33.675 12.500 - s46 1 2.0100 34.216 13.360 - s35 1 2.1937 34.400 13.649 - s33 1 2.5869 34.793 14.263 - s11 1 2.8011 35.007 14.595 - s26 1 3.5212 35.727 15.694 - s13 1 3.5396 35.745 15.722 - s25 1 4.4944 36.700 17.145 - s3 1 5.3225 37.528 18.350 - s1 1 17.8541 50.060 33.909 Step: AIC=10.65 y ~ s1 + s3 + s5 + s6 + s11 + s13 + s14 + s24 + s25 + s26 + s33 + s35 + s36 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s6 1 0.4379 32.977 9.368 - s24 1 0.4504 32.989 9.389 - s45 1 0.4734 33.012 9.426 - s55 1 0.6496 33.188 9.714 - s5 1 0.7496 33.288 9.876 - s36 1 0.7824 33.321 9.929 - s14 1 0.8332 33.372 10.012 - s56 1 1.0357 33.575 10.338 32.539 10.646 - s66 1 1.3722 33.911 10.877 - s46 1 1.8206 34.359 11.586 - s35 1 2.3424 34.881 12.400 - s11 1 2.9429 35.482 13.322 - s33 1 3.3370 35.876 13.918 - s26 1 3.6001 36.139 14.313 - s25 1 4.5788 37.118 15.756 - s13 1 5.4789 38.018 17.050 - s3 1 6.1950 38.734 18.057 - s1 1 20.8692 53.408 35.405 Step: AIC=9.37 y ~ s1 + s3 + s5 + s11 + s13 + s14 + s24 + s25 + s26 + s33 + s35 + s36 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s45 1 0.2740 33.251 7.815 - s24 1 0.3149 33.292 7.881 - s5 1 0.3293 33.306 7.905 - s55 1 0.9181 33.895 8.851 32.977 9.368 - s14 1 1.2661 34.243 9.403 - s56 1 1.4205 34.397 9.646 - s46 1 1.5631 34.540 9.869 - s66 1 1.9947 34.972 10.540 - s36 1 2.2336 35.210 10.907 - s11 1 2.8792 35.856 11.888 - s33 1 4.8792 37.856 14.820 - s26 1 6.2640 39.241 16.760 - s35 1 6.6105 39.587 17.234 - s13 1 8.4887 41.465 19.737 - s25 1 9.5554 42.532 21.109 - s3 1 10.4600 43.437 22.245 - s1 1 22.8549 55.832 35.801 Step: AIC=7.82 y ~ s1 + s3 + s5 + s11 + s13 + s14 + s24 + s25 + s26 + s33 + s35 + s36 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s24 1 0.1391 33.390 6.041 - s5 1 0.2196 33.470 6.171 - s55 1 0.7519 34.003 7.023 - s56 1 1.2201 34.471 7.761 33.251 7.815 - s66 1 1.8202 35.071 8.693 - s36 1 2.3857 35.637 9.557 - s46 1 2.4735 35.724 9.690 - s14 1 2.5362 35.787 9.784 - s11 1 2.6118 35.863 9.898 - s26 1 6.0655 39.316 14.863 - s33 1 6.3456 39.596 15.247 - s35 1 7.3177 40.569 16.556 - s25 1 9.4637 42.715 19.340 - s3 1 10.5407 43.792 20.685 - s13 1 10.8171 44.068 21.024 - s1 1 22.5910 55.842 33.811 Step: AIC=6.04 y ~ s1 + s3 + s5 + s11 + s13 + s14 + s25 + s26 + s33 + s35 + s36 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s5 1 0.1506 33.541 4.284 - s55 1 0.8924 34.282 5.465 33.390 6.041 - s56 1 1.2645 34.654 6.048 - s66 1 1.7511 35.141 6.801 - s14 1 2.4489 35.839 7.863 - s11 1 2.5073 35.897 7.951 - s46 1 2.5366 35.927 7.995 - s36 1 2.5464 35.936 8.009 - s26 1 6.4276 39.818 13.548 - s35 1 7.2445 40.634 14.644 - s33 1 7.5371 40.927 15.032 - s25 1 9.6066 42.997 17.695 - s3 1 10.4519 43.842 18.747 - s13 1 11.6811 45.071 20.240 - s1 1 24.4968 57.887 33.753 Step: AIC=4.28 y ~ s1 + s3 + s11 + s13 + s14 + s25 + s26 + s33 + s35 + s36 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC - s55 1 0.9845 34.525 3.846 - s56 1 1.2419 34.782 4.247 33.541 4.284 - s66 1 1.7180 35.259 4.981 - s14 1 2.3547 35.895 5.948 - s11 1 2.5412 36.082 6.227 - s36 1 2.6464 36.187 6.385 - s46 1 2.7169 36.257 6.490 - s26 1 6.7853 40.326 12.232 - s35 1 7.2062 40.747 12.793 - s33 1 7.4790 41.020 13.154 - s25 1 9.7455 43.286 16.058 - s3 1 10.3014 43.842 16.747 - s13 1 11.5501 45.091 18.263 - s1 1 25.2357 58.776 32.577 Step: AIC=3.85 y ~ s1 + s3 + s11 + s13 + s14 + s25 + s26 + s33 + s35 + s36 + s46 + s56 + s66 Df Sum of Sq RSS AIC - s56 1 0.5328 35.058 2.6729 - s66 1 0.9818 35.507 3.3600 34.525 3.8458 - s36 1 1.6665 36.191 4.3914 - s14 1 1.7863 36.311 4.5699 - s11 1 2.1028 36.628 5.0385 - s46 1 3.9084 38.433 7.6370 - s35 1 6.4222 40.947 11.0583 - s26 1 6.6582 41.183 11.3685 - s33 1 6.7630 41.288 11.5059 - s25 1 10.1190 44.644 15.7258 - s13 1 10.5657 45.091 16.2634 - s3 1 12.1037 46.629 18.0746 - s1 1 25.2716 59.797 31.5061 Step: AIC=2.67 y ~ s1 + s3 + s11 + s13 + s14 + s25 + s26 + s33 + s35 + s36 + s46 + s66 Df Sum of Sq RSS AIC 35.058 2.6729 - s36 1 1.5903 36.648 3.0685 - s14 1 1.9654 37.023 3.6184 - s11 1 2.0338 37.092 3.7181 - s66 1 2.1982 37.256 3.9568 - s46 1 3.8629 38.921 6.3173 - s35 1 6.0748 41.133 9.3021 - s26 1 6.4132 41.471 9.7447 - s33 1 6.5269 41.585 9.8925 - s25 1 9.8788 44.937 14.0786 - s13 1 10.0885 45.146 14.3300 - s3 1 11.5922 46.650 16.0993 - s1 1 25.9818 61.040 30.6171 Call: lm(formula = y ~ s1 + s3 + s11 + s13 + s14 + s25 + s26 + s33 + s35 + s36 + s46 + s66) Coefficients: (Intercept) s1 s3 s11 s13 10.9620 0.9508 -0.6004 -0.2201 -0.6718 s14 s25 s26 s33 s35 0.3286 -4.7043 -3.3069 0.3610 3.5816 s36 s46 s66 1.5646 0.4989 -0.1421 >#===========FINAL MODEL. AIC DOES NOT DECREASE REMOVING ANOTHER VAR============ > >#===============FORWARD REGRESSION STARTING FROM THE SMALLEST MODEL============ > step(f0,scope=list(upper=f2,lower=f0),direction="forward") Start: AIC=35.26 y ~ 1 Df Sum of Sq RSS AIC + s1 1 25.3591 74.618 21.463 + s3 1 11.5074 88.470 30.658 + s2 1 11.4439 88.533 30.697 + s4 1 8.0129 91.964 32.750 + s66 1 6.4875 93.490 33.639 + s5 1 6.4063 93.571 33.686 + s56 1 5.8912 94.086 33.982 + s55 1 4.7057 95.271 34.658 + s11 1 3.8296 96.147 35.153 99.977 35.262 + s24 1 2.9400 97.037 35.650 + s33 1 1.5987 98.378 36.391 + s16 1 1.2992 98.678 36.555 + s6 1 0.9870 98.990 36.726 + s44 1 0.9243 99.053 36.760 + s23 1 0.7941 99.183 36.831 + s34 1 0.5407 99.436 36.969 + s22 1 0.3818 99.595 37.055 + s45 1 0.2263 99.751 37.139 + s46 1 0.2079 99.769 37.149 + s14 1 0.2026 99.774 37.152 + s26 1 0.1979 99.779 37.155 + s35 1 0.1592 99.818 37.176 + s15 1 0.0981 99.879 37.209 + s13 1 0.0190 99.958 37.251 + s12 1 0.0058 99.971 37.259 + s25 1 0.0033 99.974 37.260 + s36 1 0.0007 99.976 37.261 Step: AIC=21.46 y ~ s1 Df Sum of Sq RSS AIC + s2 1 16.2106 58.407 10.237 + s3 1 16.1051 58.513 10.334 + s22 1 8.0389 66.579 17.308 + s23 1 7.5676 67.050 17.689 + s33 1 6.7356 67.882 18.355 + s14 1 5.4740 69.144 19.349 74.618 21.463 + s12 1 1.5507 73.067 22.329 + s16 1 1.5447 73.073 22.334 + s35 1 1.4015 73.216 22.440 + s34 1 1.3044 73.314 22.511 + s4 1 1.2383 73.380 22.560 + s25 1 1.1076 73.510 22.656 + s66 1 1.0715 73.546 22.682 + s13 1 1.0062 73.612 22.730 + s56 1 0.9378 73.680 22.780 + s5 1 0.8908 73.727 22.815 + s15 1 0.7021 73.916 22.953 + s55 1 0.6344 73.984 23.002 + s11 1 0.4656 74.152 23.125 + s36 1 0.4132 74.205 23.164 + s24 1 0.3545 74.263 23.206 + s44 1 0.2957 74.322 23.249 + s6 1 0.2430 74.375 23.287 + s46 1 0.1942 74.424 23.323 + s26 1 0.0949 74.523 23.395 + s45 1 0.0222 74.596 23.447 Step: AIC=10.24 y ~ s1 + s2 Df Sum of Sq RSS AIC 58.407 10.237 + s12 1 1.63426 56.773 10.704 + s25 1 1.60452 56.803 10.732 + s22 1 1.42808 56.979 10.900 + s4 1 1.42385 56.983 10.904 + s35 1 1.40623 57.001 10.921 + s23 1 1.08164 57.326 11.227 + s13 1 1.01060 57.397 11.294 + s33 1 0.90834 57.499 11.390 + s36 1 0.70862 57.699 11.578 + s14 1 0.64343 57.764 11.639 + s26 1 0.60515 57.802 11.674 + s46 1 0.57076 57.837 11.706 + s3 1 0.49310 57.914 11.779 + s34 1 0.48994 57.917 11.782 + s16 1 0.37577 58.032 11.888 + s45 1 0.26209 58.145 11.994 + s11 1 0.26041 58.147 11.995 + s6 1 0.25151 58.156 12.004 + s24 1 0.11945 58.288 12.126 + s5 1 0.10998 58.297 12.135 + s56 1 0.01921 58.388 12.219 + s66 1 0.01034 58.397 12.227 + s55 1 0.00381 58.404 12.233 + s15 1 0.00311 58.404 12.234 + s44 1 0.00073 58.407 12.236 Call: lm(formula = y ~ s1 + s2) Coefficients: (Intercept) s1 s2 11.0926 0.7596 -0.5572 >#=====WE'RE AT A LOCAL MINIMUM. AIC INCREASES ADDING ANOTHER SINGLE VARIABLE====== >#======FIT AN INTERMEDIATE MODEL INVOLVING A FEW BUT NOT SPECIAL QUADRATIC TERMS====== > f3<-lm(y~s33+s34+s35+s36+s44+s45+s46+s55+s56+s66);summary(f3);anova(f3);extractAIC(f3) Call: lm(formula = y ~ s33 + s34 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66) Residuals: Min 1Q Median 3Q Max -2.06553 -0.62393 -0.08465 0.38995 6.00595 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 10.953752 0.282311 38.800 <2e-16 *** s33 -0.002771 0.135375 -0.020 0.9838 s34 0.213890 0.379884 0.563 0.5763 s35 -0.910012 0.886184 -1.027 0.3102 s36 -1.393876 0.948281 -1.470 0.1489 s44 0.036757 0.188043 0.195 0.8459 s45 0.586615 0.758160 0.774 0.4433 s46 1.256219 0.626998 2.004 0.0514 . s55 1.094099 1.220775 0.896 0.3751 s56 1.956880 2.481886 0.788 0.4348 s66 0.539785 1.300368 0.415 0.6801 --- Signif. codes: 0 Ô***Õ 0.001 Ô**Õ 0.01 Ô*Õ 0.05 Ô.Õ 0.1 Ô Õ 1 Residual standard error: 1.351 on 43 degrees of freedom Multiple R-squared: 0.2148, Adjusted R-squared: 0.03223 F-statistic: 1.176 on 10 and 43 DF, p-value: 0.3326 Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) s33 1 1.599 1.5987 0.8757 0.35461 s34 1 1.615 1.6145 0.8844 0.35225 s35 1 0.065 0.0647 0.0355 0.85154 s36 1 0.723 0.7231 0.3961 0.53245 s44 1 0.025 0.0247 0.0135 0.90799 s45 1 0.645 0.6452 0.3534 0.55530 s46 1 7.291 7.2910 3.9938 0.05202 . s55 1 5.368 5.3684 2.9407 0.09357 . s56 1 3.833 3.8328 2.0995 0.15460 s66 1 0.315 0.3146 0.1723 0.68013 Residuals 43 78.499 1.8256 --- Signif. codes: 0 Ô***Õ 0.001 Ô**Õ 0.01 Ô*Õ 0.05 Ô.Õ 0.1 Ô Õ 1 [1] 11.00000 42.20182 >#===========DO STEPWISE SEARCH IN BOTH FORWARD AND BACKWARD DIRECTIONS===== > step(f3,scope=list(upper=f2,lower=f0),direction="both") Start: AIC=42.2 y ~ s33 + s34 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66 Df Sum of Sq RSS AIC + s1 1 20.7173 57.782 27.656 + s15 1 11.1778 67.322 35.907 + s3 1 10.5941 67.905 36.373 + s2 1 6.8837 71.616 39.246 - s33 1 0.0008 78.500 40.202 - s44 1 0.0698 78.569 40.250 + s24 1 5.4892 73.010 40.287 - s66 1 0.3146 78.814 40.418 - s34 1 0.5787 79.078 40.598 + s13 1 5.0601 73.439 40.604 - s45 1 1.0929 79.592 40.948 - s56 1 1.1349 79.634 40.977 - s55 1 1.4664 79.966 41.201 - s35 1 1.9251 80.425 41.510 + s12 1 3.3185 75.181 41.869 + s6 1 3.1726 75.327 41.974 78.499 42.202 - s36 1 3.9443 82.444 42.849 + s4 1 1.5613 76.938 43.117 + s23 1 1.5068 76.993 43.155 + s22 1 1.4767 77.023 43.176 + s16 1 1.3220 77.178 43.285 + s5 1 0.7688 77.731 43.670 + s14 1 0.6798 77.820 43.732 + s26 1 0.4880 78.012 43.865 + s11 1 0.4153 78.084 43.915 + s25 1 0.2720 78.228 44.014 - s46 1 7.3282 85.828 45.021 Step: AIC=27.66 y ~ s33 + s34 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66 + s1 Df Sum of Sq RSS AIC + s3 1 8.4569 49.325 21.110 + s2 1 7.0900 50.692 22.587 - s33 1 0.4565 58.239 26.081 - s66 1 0.5072 58.289 26.128 - s55 1 0.5673 58.349 26.183 - s44 1 0.6219 58.404 26.234 - s56 1 0.6293 58.412 26.241 + s6 1 3.3788 54.403 26.402 - s35 1 1.5649 59.347 27.099 - s36 1 1.8931 59.675 27.396 + s16 1 2.2167 55.566 27.543 57.782 27.656 + s11 1 2.0233 55.759 27.731 + s14 1 2.0034 55.779 27.750 - s45 1 2.9208 60.703 28.318 + s24 1 1.1732 56.609 28.548 - s34 1 3.3488 61.131 28.698 + s13 1 0.8888 56.893 28.819 + s12 1 0.5287 57.254 29.159 + s26 1 0.3799 57.402 29.299 + s5 1 0.2879 57.494 29.386 + s22 1 0.0460 57.736 29.613 + s25 1 0.0410 57.741 29.617 + s23 1 0.0260 57.756 29.631 + s4 1 0.0097 57.773 29.647 + s15 1 0.0002 57.782 29.655 - s46 1 5.9433 63.725 30.942 - s1 1 20.7173 78.499 42.202 Step: AIC=21.11 y ~ s33 + s34 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66 + s1 + s3 Df Sum of Sq RSS AIC - s33 1 0.0011 49.326 19.112 - s44 1 0.0064 49.332 19.117 + s12 1 3.0837 46.242 19.624 + s11 1 2.8282 46.497 19.922 - s34 1 0.8187 50.144 19.999 + s13 1 2.5293 46.796 20.268 - s45 1 1.1763 50.502 20.383 + s4 1 2.2660 47.059 20.571 - s66 1 1.3689 50.694 20.589 - s35 1 1.4965 50.822 20.724 - s55 1 1.5683 50.894 20.801 - s56 1 1.6512 50.977 20.889 49.325 21.110 - s36 1 2.1448 51.470 21.409 + s16 1 1.3681 47.957 21.592 + s6 1 1.2154 48.110 21.763 + s25 1 0.8895 48.436 22.128 + s24 1 0.5612 48.764 22.493 + s5 1 0.3412 48.984 22.736 + s14 1 0.3206 49.005 22.758 + s15 1 0.1038 49.222 22.997 + s23 1 0.0639 49.261 23.041 + s26 1 0.0556 49.270 23.050 + s2 1 0.0340 49.291 23.073 + s22 1 0.0001 49.325 23.110 - s46 1 3.9238 53.249 23.244 - s3 1 8.4569 57.782 27.656 - s1 1 18.5800 67.905 36.373 Step: AIC=19.11 y ~ s34 + s35 + s36 + s44 + s45 + s46 + s55 + s56 + s66 + s1 + s3 Df Sum of Sq RSS AIC - s44 1 0.0057 49.332 17.118 + s11 1 2.7793 46.547 17.980 - s34 1 0.8699 50.196 18.056 - s45 1 1.1778 50.504 18.386 + s4 1 2.2622 47.064 18.577 - s66 1 1.3829 50.709 18.605 + s12 1 2.1404 47.186 18.716 - s55 1 1.5763 50.903 18.810 - s56 1 1.6606 50.987 18.900 49.326 19.112 - s35 1 1.8852 51.212 19.137 + s13 1 1.3858 47.941 19.573 + s16 1 1.3529 47.974 19.610 + s6 1 1.2162 48.110 19.764 + s25 1 0.8671 48.459 20.154 - s36 1 2.8644 52.191 20.160 + s24 1 0.5522 48.774 20.504 + s5 1 0.3345 48.992 20.744 + s14 1 0.3213 49.005 20.759 + s15 1 0.1047 49.222 20.997 + s26 1 0.0538 49.273 21.053 + s2 1 0.0352 49.291 21.073 + s23 1 0.0109 49.316 21.100 + s22 1 0.0011 49.325 21.110 + s33 1 0.0011 49.325 21.110 - s46 1 4.1036 53.430 21.427 - s3 1 8.9122 58.239 26.081 - s1 1 19.1707 68.497 34.842 Step: AIC=17.12 y ~ s34 + s35 + s36 + s45 + s46 + s55 + s56 + s66 + s1 + s3 Df Sum of Sq RSS AIC + s11 1 2.7432 46.589 16.029 - s45 1 1.2354 50.568 16.454 - s34 1 1.2486 50.581 16.468 + s4 1 2.2418 47.090 16.607 - s66 1 1.4896 50.822 16.724 + s12 1 2.1156 47.217 16.751 - s55 1 1.6017 50.934 16.843 - s56 1 1.7292 51.061 16.978 49.332 17.118 - s35 1 1.9311 51.263 17.191 + s13 1 1.3868 47.945 17.578 + s16 1 1.2855 48.047 17.692 + s6 1 1.2178 48.114 17.768 + s25 1 0.8393 48.493 18.191 - s36 1 2.9069 52.239 18.210 + s24 1 0.5197 48.812 18.546 + s14 1 0.3270 49.005 18.759 + s5 1 0.3262 49.006 18.760 + s15 1 0.1054 49.227 19.003 + s26 1 0.0497 49.282 19.064 + s2 1 0.0402 49.292 19.074 + s23 1 0.0075 49.325 19.110 + s44 1 0.0057 49.326 19.112 + s33 1 0.0005 49.332 19.117 + s22 1 0.0002 49.332 19.118 - s46 1 4.4689 53.801 19.801 - s3 1 9.8112 59.143 24.913 - s1 1 20.5011 69.833 33.885 Step: AIC=16.03 y ~ s34 + s35 + s36 + s45 + s46 + s55 + s56 + s66 + s1 + s3 + s11 Df Sum of Sq RSS AIC - s66 1 1.1548 47.744 15.351 - s55 1 1.3323 47.921 15.551 - s56 1 1.4329 48.022 15.664 - s45 1 1.5818 48.171 15.831 + s25 1 1.7155 44.873 16.003 46.589 16.029 + s4 1 1.6786 44.910 16.047 + s6 1 1.0830 45.506 16.758 + s12 1 1.0397 45.549 16.810 - s11 1 2.7432 49.332 17.118 + s13 1 0.7255 45.864 17.181 + s5 1 0.6134 45.976 17.313 - s34 1 2.9219 49.511 17.313 + s16 1 0.5797 46.009 17.352 - s35 1 3.0565 49.646 17.460 + s15 1 0.3722 46.217 17.595 + s22 1 0.2173 46.372 17.776 + s26 1 0.0961 46.493 17.917 + s24 1 0.0947 46.494 17.919 + s23 1 0.0881 46.501 17.926 + s33 1 0.0618 46.527 17.957 + s44 1 0.0419 46.547 17.980 + s14 1 0.0074 46.582 18.020 + s2 1 0.0021 46.587 18.026 - s36 1 4.5635 51.153 19.075 - s46 1 6.3637 52.953 20.942 - s3 1 11.2059 57.795 25.668 - s1 1 23.1701 69.759 35.827 Step: AIC=15.35 y ~ s34 + s35 + s36 + s45 + s46 + s55 + s56 + s1 + s3 + s11 Df Sum of Sq RSS AIC - s55 1 0.1928 47.937 13.568 - s56 1 0.3469 48.091 13.742 + s25 1 2.6043 45.139 14.322 + s4 1 2.1449 45.599 14.869 47.744 15.351 + s66 1 1.1548 46.589 16.029 + s6 1 1.1447 46.599 16.040 + s12 1 1.1042 46.640 16.087 - s45 1 2.5065 50.250 16.114 + s5 1 0.8614 46.882 16.368 + s16 1 0.7634 46.980 16.480 + s13 1 0.7427 47.001 16.504 - s11 1 3.0780 50.822 16.724 + s15 1 0.2137 47.530 17.108 + s22 1 0.1110 47.633 17.225 + s2 1 0.1022 47.642 17.235 + s26 1 0.0945 47.649 17.244 + s24 1 0.0887 47.655 17.250 + s14 1 0.0798 47.664 17.260 + s44 1 0.0252 47.719 17.322 + s23 1 0.0248 47.719 17.323 + s33 1 0.0149 47.729 17.334 - s34 1 3.9106 51.654 17.602 - s35 1 4.1532 51.897 17.855 - s36 1 5.2520 52.996 18.986 - s46 1 7.4212 55.165 21.153 - s3 1 10.0634 57.807 23.679 - s1 1 24.7402 72.484 35.897 Step: AIC=13.57 y ~ s34 + s35 + s36 + s45 + s46 + s56 + s1 + s3 + s11 Df Sum of Sq RSS AIC - s56 1 0.7802 48.717 12.440 47.937 13.568 + s4 1 1.4760 46.461 13.880 + s6 1 1.2956 46.641 14.089 + s25 1 1.1103 46.826 14.303 + s12 1 1.0143 46.922 14.413 + s16 1 0.9557 46.981 14.481 + s13 1 0.7531 47.183 14.713 + s5 1 0.6242 47.312 14.861 - s11 1 3.0482 50.985 14.897 + s55 1 0.1928 47.744 15.351 - s45 1 3.4826 51.419 15.356 + s2 1 0.1704 47.766 15.376 + s22 1 0.1484 47.788 15.401 + s24 1 0.1288 47.808 15.423 + s14 1 0.0963 47.840 15.460 + s15 1 0.0419 47.895 15.521 + s23 1 0.0413 47.895 15.522 + s33 1 0.0236 47.913 15.542 + s66 1 0.0153 47.921 15.551 + s44 1 0.0040 47.933 15.564 + s26 1 0.0027 47.934 15.565 - s34 1 3.7371 51.674 15.622 - s36 1 5.4153 53.352 17.348 - s35 1 5.7732 53.710 17.709 - s46 1 7.3660 55.303 19.287 - s3 1 10.0890 58.026 21.883 - s1 1 26.6351 74.572 35.430 Step: AIC=12.44 y ~ s34 + s35 + s36 + s45 + s46 + s1 + s3 + s11 Df Sum of Sq RSS AIC 48.717 12.440 + s16 1 1.7330 46.984 12.484 + s5 1 1.3165 47.400 12.961 + s25 1 1.0544 47.662 13.258 - s11 1 2.6818 51.399 13.334 + s4 1 0.9871 47.730 13.335 + s56 1 0.7802 47.937 13.568 + s66 1 0.6906 48.026 13.669 + s55 1 0.6260 48.091 13.742 + s12 1 0.6162 48.101 13.753 + s13 1 0.4706 48.246 13.916 + s15 1 0.4130 48.304 13.980 - s34 1 3.3782 52.095 14.061 + s22 1 0.2897 48.427 14.118 + s2 1 0.2172 48.500 14.199 + s23 1 0.1256 48.591 14.301 + s14 1 0.1213 48.595 14.305 + s33 1 0.0928 48.624 14.337 + s24 1 0.0807 48.636 14.351 + s26 1 0.0057 48.711 14.434 + s44 1 0.0006 48.716 14.439 + s6 1 0.0000 48.717 14.440 - s36 1 4.9494 53.666 15.665 - s45 1 5.3365 54.053 16.053 - s35 1 5.6200 54.337 16.336 - s46 1 7.2050 55.922 17.888 - s3 1 10.5292 59.246 21.007 - s1 1 30.8354 79.552 36.921 Call: lm(formula = y ~ s34 + s35 + s36 + s45 + s46 + s1 + s3 + s11) Coefficients: (Intercept) s34 s35 s36 s45 11.0038 0.4337 -1.2556 -1.3839 1.1211 s46 s1 s3 s11 1.2335 0.9291 -0.4878 -0.2270 > #============NOTE THAT ALL MODELS ARE DIFFERENT AND HAVE DIFFERENT AIC'S==========