1、例4.15 P179（一個(gè)正態(tài)總體的區(qū)間估計(jì)）為估計(jì)一件物體的重量a，將其稱了10kg）為10.1,10,9.8,10.5,9.7,10.1,9.9,10.2,10.3,9.9，假設(shè)所稱出物體重量服從正態(tài)分布求該物體重量a的置信系數(shù)為0.95的置信區(qū)間。,x-c(10.1,10,9.8,10.5,9.7,10.1,9.9,10.2,10.3,9.9) t.test(x) 程序結(jié)果： One Sample t-test data: x t = 131.59, df = 9, p-value = 4.296e-16 alternative hypothesis: true mean is not

2、equal to 0 95 percent confidence interval: 9.877225 10.222775 sample estimates: mean of x 10.05 得到的區(qū)間估計(jì)為：9.88,10.22,例4.18 P185(均值差的區(qū)間估計(jì)）現(xiàn)從生產(chǎn)線上隨機(jī)抽取樣本x1,x2，x12和y1,y2，y17，都服從正態(tài)分布，其均值分別為u1=201.1,u2=499.7，標(biāo)準(zhǔn)差分別為2.4,4.7。給定置信系數(shù)0.95，試求u1-u2的區(qū)間估計(jì)。,x-rnorm(12,501.1,2.4) y-rnorm(17,499.7,4.7) 兩樣本方差不同t.test(x,y

3、) 程序結(jié)果： Welch Two Sample t-test data: x and y t = -0.6471, df = 25.304, p-value = 0.5234 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -3.657121 1.907620 sample estimates: mean of x mean of y 500.7888 501.6635 u1-u2的置信系數(shù)為0.95的區(qū)間估計(jì)為-3.66,1.91 方差相同t

4、.test(x,y, var.equal=TRUE),例4.19 P186(配對(duì)數(shù)據(jù)情形下均值差的區(qū)間估計(jì)）抽查患者10名。記錄下治療前后血紅蛋白的含量數(shù)據(jù)。試求治療前后變化的區(qū)間估計(jì)。 （a=0.05）。,x-c(11.3,15.0,15.0,13.5,12.8,10.0,11.0,12.0,13.0,12.3) y-c(14.0,13.8,14.0,13.5,13.5,12.0,14.7,11.4,13.8,12.0) t.test(x-y) 程序結(jié)果： One Sample t-test data: x - y t = -1.3066, df = 9, p-value = 0.2237

5、alternative hypothesis: true mean is not equal to 0 95 percent confidence interval: -1.8572881 0.4972881 sample estimates: mean of x -0.68 治療前后變化的區(qū)間估計(jì)為-1.86,0.497,例4.22 P193（一個(gè)總體求均值的單側(cè)置信區(qū)間估計(jì)）從一批燈泡中隨機(jī)地取5只作壽命試驗(yàn)測得壽命以小時(shí)計(jì)為 1050 1100 1120 1250 1280 設(shè)燈泡的壽命服從正態(tài)分布.求燈泡壽命平均值的置信度為0.95的單側(cè)置信下限,x-c(1050,1100,1120,

6、1250,1280) t.test(x,alternative=greater) 程序結(jié)果： One Sample t-test data: x t = 26.003, df = 4, p-value = 6.497e-06 alternative hypothesis: true mean is greater than 0 95 percent confidence interval: 1064.9 Inf sample estimates: mean of x 1160 95%的燈泡壽命在1064.9小時(shí)以上,習(xí)題4.6 P201甲、乙兩種稻種分布播種在10塊試驗(yàn)田中，每塊試驗(yàn)田甲、乙稻

7、種各種一半，假設(shè)兩稻種產(chǎn)量X,Y均服從正態(tài)分布，且方差相等，收獲后10塊試驗(yàn)田的產(chǎn)量如下所示（單位：千克）。求出兩稻種產(chǎn)量的期望差u1-u2的置信區(qū)間（a=0.05).,x-c(140,137,136,140,145,148,140,135,144,141) y-c(135,118,115,140,128,131,130,115,131,125) t.test(x,y,var.equal=T) 程序結(jié)果 Two Sample t-test data: x and y t = 4.6287, df = 18, p-value = 0.0002087 alternative hypothesis:

8、 true difference in means is not equal to 0 95 percent confidence interval: 7.536261 20.063739 sample estimates: mean of x mean of y 140.6 126.8 置信區(qū)間為7.536261,20.063739,習(xí)題4.7 甲、乙兩組生產(chǎn)同種導(dǎo)線，現(xiàn)從甲組生產(chǎn)的導(dǎo)線中隨機(jī)抽取4根，從乙組生產(chǎn)的導(dǎo)線中隨機(jī)抽取5根，它們的電阻值分別為：甲：0.143,0.142,0.143,0.137；乙：0.140,0.142,0.136,0.138,0.140；假設(shè)兩組電阻值分別服從正

9、態(tài)分布，方差相同但未知，試求u1-u2的置信系數(shù)為0.95的區(qū)間估計(jì)。,x-c(0.143,0.142,0.143,0.137) y-c(0.140,0.142,0.136,0.138,0.140) a-rnorm(4,mean(x),var(x) b-rnorm(5,mean(y),var(y) t.test(a,b) 程序結(jié)果： Welch Two Sample t-test data: a and b t = 636.28, df = 5.788, p-value = 3.028e-15 alternative hypothesis: true difference in means i

10、s not equal to 0 95 percent confidence interval: 0.002041440 0.002057343 sample estimates: mean of x mean of y 0.1412494 0.1392000 區(qū)間為：0.00204,0.00205,例5.2 P209（單個(gè)正態(tài)總體均值的假設(shè)檢驗(yàn)）某種元件的壽命X（小時(shí)），服從正態(tài)分布,其中f方差和均值均未知，16只元件的壽命如下：問是否有理由認(rèn)為元件的平均壽命大于255小時(shí)。,x-c(159,280,101,212,224,379,179,264,222,362,168,250,149,26

11、0,485,170) t.test(x,alternative=greater,mu=225) 程序結(jié)果： One Sample t-test data: x t = 0.66852, df = 15, p-value = 0.257 alternative hypothesis: true mean is greater than 225 95 percent confidence interval: 198.2321 Inf sample estimates: mean of x 241.5 計(jì)算出P值為0.257大于0.05，所以，接受原假設(shè)，即認(rèn)為元件的平均壽命不大于255小時(shí),例5.

12、6 P221（二項(xiàng)分布總體的假設(shè)檢驗(yàn)）有一批蔬菜種子的平均發(fā)芽率為P=0.85,現(xiàn)在隨機(jī)抽取500粒，用種衣劑進(jìn)行浸種處理，結(jié)果有445粒發(fā)芽，問種衣劑有無效果。,binom.test(445,500,p=0.85) 程序結(jié)果： Exact binomial test data: 445 and 500 number of successes = 445, number of trials = 500, p-value = 0.01207 alternative hypothesis: true probability of success is not equal to 0.85 95 pe

13、rcent confidence interval: 0.8592342 0.9160509 sample estimates: probability of success 0.89 P值=0.012070.05，拒絕原假設(shè)，認(rèn)為種衣劑對(duì)種子發(fā)芽率有顯著效果。,習(xí)題5.1 P249正常男子血小板計(jì)數(shù)均值為225*109/L,今測得20名男性油漆作業(yè)工人的血小板計(jì)數(shù)值如下。問油漆工人的血小板計(jì)數(shù)與正常成年男子有無差異？,x-c(220,188,162,230,145,160,237,188,247,113,126,245,164,231,250,183,190,158,224,175) t.t

14、est(x,alternative=two.side,mu=225) 程序結(jié)果： One Sample t-test data: x t = -3.5588, df = 19, p-value = 0.002096 alternative hypothesis: true mean is not equal to 225 95 percent confidence interval: 172.2743 211.3257 sample estimates: mean of x 191.8 P值=0.0020960.05,拒絕原假設(shè)，認(rèn)為油漆工人的血小板計(jì)數(shù)與正常成年男子有差異。,習(xí)題5.3為研究

15、某鐵劑治療和飲食治療營養(yǎng)性缺鐵性貧血的效果，將16名患者按年齡、體重、病程和病情相近的原則配成8對(duì)，分別使用飲食療法和補(bǔ)充鐵劑治療的方法，三個(gè)月后測得兩種患者血紅蛋白如表5.1所示，問兩種方法治療后的患者血紅蛋白有無差異.,x0.05,接受原假設(shè)，兩種方法治療后的患者血紅蛋白無差異,例6.2 P257（回歸方程的顯著性檢驗(yàn)）求例6.1的回歸方程，并對(duì)相應(yīng)的方程做檢驗(yàn)。,x-c(0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.20,0.21,0.23) y-c(42.0,43.5,45.0,45.5,45.0,47.5,49.0,53.0,50.0,5

16、5.0,55.0,60.0) lm.sol-lm(y1+x) summary(lm.sol) 程序結(jié)果見下一張PPT 回歸方程為： 從回歸結(jié)果可以看出，回歸方程通過了回歸參數(shù)的檢驗(yàn)與回歸方程的檢驗(yàn)。,例6.2的程序結(jié)果,程序結(jié)果：Call: lm(formula = y 1 + x) Residuals: Min 1Q Median 3Q Max -2.0431 -0.7056 0.1694 0.6633 2.2653 Coefficients: Estimate Std. Error t value Pr(|t|) (Intercept) 28.493 1.580 18.04 5.88e-0

17、9 * x 130.835 9.683 13.51 9.50e-08 *- Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 1.319 on 10 degrees of freedom Multiple R-squared: 0.9481, Adjusted R-squared: 0.9429 F-statistic: 182.6 on 1 and 10 DF, p-value: 9.505e-08,例6.4 P260（預(yù)測）求例6.1中X=x0=0.16時(shí)相應(yīng)的Y的概率為0.95的預(yù)測區(qū)間,new

18、-data.frame(x=0.16) lm.pred-predict(lm.sol,new,interval=prediction,level=0.95) lm.pred 程序結(jié)果：fit lwr upr 49.42639 46.36621 52.48657 預(yù)測值為49.43，預(yù)測區(qū)間46.37,52.49,例6.5 P261（全面展示一元回歸模型的計(jì)算過程）Forbes數(shù)據(jù),X-matrix(c(194.5, 20.79, 1.3179, 131.79,194.3, 20.79, 1.3179, 131.79,197.9, 22.40, 1.3502, 135.02,198.4, 22.

19、67, 1.3555, 135.55,199.4, 23.15, 1.3646, 136.46,199.9, 23.35, 1.3683, 136.83,200.9, 23.89, 1.3782, 137.82,201.1, 23.99, 1.3800, 138.00,201.4, 24.02, 1.3806, 138.06,201.3, 24.01, 1.3805, 138.05,203.6, 25.14, 1.4004, 140.04,204.6, 26.57, 1.4244, 142.44,209.5, 28.49, 1.4547, 145.47,208.6, 27.76, 1.4434

20、, 144.34,210.7, 29.04, 1.4630, 146.30,211.9, 29.88, 1.4754, 147.54,212.2, 30.06, 1.4780, 147.80), ncol=4, byrow=T,dimnames = list(1:17, c(F, h, log, log100) forbes-data.frame(X) plot(forbes$F, forbes$log100) 程序結(jié)果是出現(xiàn)散點(diǎn)圖,lm.sol|t|) (Intercept) -42.13087 3.33895 -12.62 2.17e-09 * F 0.89546 0.01645 54.4

21、5 2e-16 * - Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 0.3789 on 15 degrees of freedom Multiple R-squared: 0.995, Adjusted R-squared: 0.9946 F-statistic: 2965 on 1 and 15 DF, p-value: 2.2e-16,abline(lm.sol) 程序結(jié)果：得到散點(diǎn)圖和相應(yīng)的回歸直線 y.res|t|) (Intercept) -41.30180 1.00038 -41.2

22、9 5.01e-16 * F 0.89096 0.00493 180.73 2e-16 * - Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 0.1133 on 14 degrees of freedom Multiple R-squared: 0.9996, Adjusted R-squared: 0.9995 F-statistic: 3.266e+04 on 1 and 14 DF, p-value: 2.2e-16,例6.14 P292某公司為了研究產(chǎn)品的營銷策略，對(duì)產(chǎn)品的銷售情況進(jìn)行了調(diào)

23、查，設(shè)Y為某地區(qū)該產(chǎn)品的家庭人均購買量（單位：元），X為家庭收入（單位：元），表6.8給出了53個(gè)家庭的數(shù)據(jù)。試通過這些數(shù)據(jù)建立Y與X的關(guān)系。,X-scan() 679 292 1012 493 582 1156 997 2189 1097 2078 1818 1700 747 2030 1643 414 354 1276 745 435 540 874 1543 1029 710 1434 837 1748 1381 1428 1255 1777 370 2316 1130 463 770 724 808 790 783 406 1242 658 1746 468 1114 413 1787

24、 3560 1495 2221 1526 Y-scan() 0.79 0.44 0.56 0.79 2.70 3.64 4.73 9.50 5.34 6.85 5.84 5.21 3.25 4.43 3.16 0.50 0.17 1.88 0.77 1.39 0.56 1.56 5.28 0.64 4.00 0.31 4.20 4.88 3.48 7.58 2.63 4.99 0.59 8.19 4.79 0.51 1.74 4.10 3.94 0.96 3.29 0.44 3.24 2.14 5.71 0.64 1.90 0.51 8.33 14.94 5.11 3.85 3.93,lm.s

25、ol|t|) (Intercept) -0.8313037 0.4416121 -1.882 0.0655 . X 0.0036828 0.0003339 11.030 4.11e-15 * - Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 1.577 on 51 degrees of freedom Multiple R-squared: 0.7046, Adjusted R-squared: 0.6988 F-statistic: 121.7 on 1 and 51 DF, p-value:

26、4.106e-15 y.rst-rstandard(lm.sol); y.fit-predict(lm.sol) plot(y.rsty.fit) abline(0.1,0.5);abline(-0.1,-0.5) 程序結(jié)果：畫出了標(biāo)準(zhǔn)化后的殘差圖,lm.new|t|) (Intercept) 5.822e-01 1.299e-01 4.481 4.22e-05 * X 9.529e-04 9.824e-05 9.699 3.61e-13 * - Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 0.

27、464 on 51 degrees of freedom Multiple R-squared: 0.6485, Adjusted R-squared: 0.6416 F-statistic: 94.08 on 1 and 51 DF, p-value: 3.614e-13 yn.rst-rstandard(lm.new); yn.fit-predict(lm.new) plot(yn.rstyn.fit),習(xí)題6.1 P331為估計(jì)山上積雪融化后對(duì)下游灌溉的影響，在山上建立一個(gè)觀測站，測量最大積雪深度X（米）與當(dāng)年灌溉面積Y（公頌），測得連續(xù)10年的數(shù)據(jù)如表6.1所示。,snow|t|) x

28、 385.51 5.09 75.74 6.17e-14 * - Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 104.6 on 9 degrees of freedom Multiple R-squared: 0.9984, Adjusted R-squared: 0.9983 F-statistic: 5736 on 1 and 9 DF, p-value: 6.169e-14,現(xiàn)測得今年的數(shù)據(jù)是X=7m，給出今年灌溉面積的預(yù)測值與相應(yīng)的區(qū)間估計(jì)。（a=0.05）,4）X-data.frame(x=7) lm.pred-predict(lm.sol,X,interval=prediction,level=0.95) lm.pred #擬合新數(shù)據(jù)，并生成置信區(qū)間 程序