统计建模与R软件第六章习题.doc

第六章1 a x y plot(x,y)X与Y线性相关 b x y lm.sol summary(lm.sol)Call:lm(formula = y 1 + x)Residuals: Min 1Q Median 3Q Max -128.591 -70.978 -3.727 49.263 167.228 Coefficients: Estimate Std. Error t value Pr(|t|) (Intercept) 140.95 125.11 1.127 0.293 x 364.18 19.26 18.908 6.33e-08 *-Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 96.42 on 8 degrees of freedomMultiple R-Squared: 0.9781, Adjusted R-squared: 0.9754 F-statistic: 357.5 on 1 and 8 DF, p-value: 6.33e-08 回归方程为Y=140.95+364.18X，极为显著 d new lm.pred lm.pred fit lwr upr1, 2690.227 2454.971 2925.484Y(7)= 2690.227, 2454.971,2925.4842 out-data.frame(+ x1 - c(0.4,0.4,3.1,0.6,4.7,1.7,9.4,10.1,11.6,12.6,10.9,23.1,23.1,21.6,23.1,1.9,26.8,29.9),+ x2 - c(52,34,19,34,24,65,44,31,29,58,37,46,50,44,56,36,58,51),+ x3 - c(158,163,37,157,59,123,46,117,173,112,111,114,134,73,168,143,202,124),+ y lm.sol summary(lm.sol)Call:lm(formula = y x1 + x2 + x3, data = out)Residuals: Min 1Q Median 3Q Max -27.575 -11.160 -2.799 11.574 48.808 Coefficients: Estimate Std. Error t value Pr(|t|) (Intercept) 44.9290 18.3408 2.450 0.02806 * x1 1.8033 0.5290 3.409 0.00424 *x2 -0.1337 0.4440 -0.301 0.76771 x3 0.1668 0.1141 1.462 0.16573 -Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 19.93 on 14 degrees of freedomMultiple R-Squared: 0.551, Adjusted R-squared: 0.4547 F-statistic: 5.726 on 3 and 14 DF, p-value: 0.009004 回归方程为 y=44.9290+1.8033x1-0.1337x2+0.1668x3由计算结果可以得到，回归系数与回归方程的检验都是显著的3 a x y lm.sol summary(lm.sol)Call:lm(formula = y 1 + x)Residuals: Min 1Q Median 3Q Max -9.84130 -2.33691 -0.02137 1.05921 17.83201 Coefficients: Estimate Std. Error t value Pr(|t|) (Intercept) -1.4519 1.8353 -0.791 0.436 x 1.5578 0.2807 5.549 7.93e-06 *-Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 5.168 on 26 degrees of freedomMultiple R-Squared: 0.5422, Adjusted R-squared: 0.5246 F-statistic: 30.8 on 1 and 26 DF, p-value: 7.931e-06 线性回归方程为 y=-1.4519+1.5578x，并且未通过t检验和F检验 plot(x,y) abline(-1.4519,1.5578)c x y y.res-resid(lm.sol);y.fit plot(y.resy.fit) y.rst plot(y.rsty.fit)普通残差标准化残差d（4） lm.new plot(x,y) lines(x,y=0.5875222+0.08489065*x2+0.4466549*x) y.res-resid(lm.new);y.fit plot(y.resy.fit) y.rst plot(y.rsty.fit)4 lm.sol summary(lm.sol)Call:lm(formula = Y X1 + X2, data = toothpaste)Residuals: Min 1Q Median 3Q Max -0.497785 -0.120312 -0.008672 0.110844 0.581059 Coefficients: Estimate Std. Error t value Pr(|t|) (Intercept) 4.4075 0.7223 6.102 1.62e-06 *X1 1.5883 0.2994 5.304 1.35e-05 *X2 0.5635 0.1191 4.733 6.25e-05 *-Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 0.2383 on 27 degrees of freedomMultiple R-squared: 0.886, Adjusted R-squared: 0.8776 F-statistic: 105 on 2 and 27 DF, p-value: 1.845e-13 source(Reg_Diag.R);Reg_Diag(lm.sol) residual s1 standard s2 student s3 hat_matrix s4 DFFITS1 -0.047231639 -0.21248023 -0.20868284 0.13012303 -0.080711402 -0.098070223 -0.42151698 -0.41500522 0.04704358 -0.092207713 0.074288624 0.33492116 0.32934525 0.13385955 0.129473814 -0.006645926 -0.03003380 -0.02947287 0.13797634 -0.011791395 0.581059204 * 2.55701395 * 2.88236603 * 0.09091719 0.911528866 -0.107785364 -0.46031439 -0.45349258 0.03475104 -0.086046747 0.300758350 1.31532456 1.33418993 0.07955382 0.392237398 0.424810360 2.05723960 * 2.19842345 * 0.24932956 * 1.266991129 -0.027532493 -0.12804079 -0.12568545 0.18600211 -0.0600803310 -0.026629932 -0.11546376 -0.11333335 0.06356511 -0.0295276111 -0.497785364 -2.12587089 * -2.28622467 * 0.03475104 -0.4337935912 0.061913782 0.26540305 0.26078220 0.04194215 0.0545641513 0.112816344 0.48968055 0.48267493 0.06556908 0.1278588114 -0.150249714 -0.65395500 -0.64687388 0.07069034 -0.1784101015 0.104927089 0.45112292 0.44436784 0.04761107 0.0993549316 0.154341375 0.66319490 0.65616401 0.04652075 0.1449372917 0.057639541 0.25360011 0.24915642 0.09056633 0.0786266818 -0.146012230 -0.64156026 -0.63442169 0.08813106 -0.1972315219 -0.124487198 -0.53776150 -0.53055795 0.05659354 -0.1299471720 -0.040713930 -0.18584177 -0.18248454 0.15505538 -0.0781727521 -0.199843357 -0.88485598 -0.88118586 0.10202733 -0.2970258322 -0.359558498 -1.59386063 -1.64328265 0.10408399 -0.5601064823 -0.387785364 -1.65609855 -1.71455446 0.03475104 -0.3253235524 -0.010697936 -0.04979066 -0.04886215 0.18729463 -0.0234568025 -0.283315771 -1.25181018 -1.26568782 0.09823492 -0.4177465226 0.017855655 0.08230563 0.08077720 0.17144488 0.0367443327 0.279286070 1.27482211 1.29043074 0.15505538 0.5527948628 0.022483501 0.09864705 0.09682047 0.08548985 0.0296026229 0.174895100 0.76513625 0.75910825 0.08017207 0.2241103830 0.147269942 0.66281470 0.65578162 0.13089383 0.25449685 s5 cooks_distance s6 COVRATIO s71 2.251190e-03 1.2809524 2 2.923723e-03 1.1521157 3 5.778631e-03 1.2769056 4 4.812656e-05 1.2989982 5 * 2.179654e-01 0.5361673 *6 2.542824e-03 1.1330964 7 4.984335e-02 0.9974548 8 * 4.685683e-01 * 0.8945237 9 1.248734e-03 1.3732722 10 3.016556e-04 1.1941261 11 5.423517e-02 0.6696819 12 1.027897e-03 1.1597812 13 5.608624e-03 1.1668135 14 1.084362e-02 1.1487064 15 3.391268e-03 1.1494743 16 7.153137e-03 1.1180504 17 2.134879e-03 1.2226245 18 1.326021e-02 1.1728006 19 5.782640e-03 1.1493238 20 2.112633e-03 1.3203083 21 2.965359e-02 1.1417402 22 9.837757e-02 0.9293112 23 3.291392e-02 0.8413370 24 1.904437e-04 1.3775853 25 5.690208e-02 1.0379534 26 4.672410e-04 1.3505881 27 9.941147e-02 1.1001732 28 3.032306e-04 1.2232439 29 1.700877e-02 1.1399973 30 2.205512e-02 1.2266609 toothpaste lm.sol summary(lm.sol)Call:lm(formula = Y X1 + X2, data = toothpaste)Residuals: Min 1Q Median 3Q Max -0.37130 -0.10114 0.03066 0.10016 0.30162 Coefficients: Estimate Std. Error t value Pr(|t|) (Intercep