[教育]應(yīng)用統(tǒng)計(jì)方法第四章-回歸分析

1、2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,1,第四章 回歸分析,多元回歸方法：在眾多的相關(guān)的變量中，根據(jù)問(wèn)題的要求，考察其中一個(gè)或幾個(gè)變量與其余變量的依賴關(guān)系。多元回歸問(wèn)題：如果只考察某一個(gè)變量（常稱為響應(yīng)變量，因變量，指標(biāo)）與其余多個(gè)變量（自變量或因素）的相互依賴關(guān)系。多因變量的多元回歸問(wèn)題（多對(duì)多回歸）,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,2,例如：若某公司管理人員要預(yù)測(cè)來(lái)年該公司的銷(xiāo)售額y時(shí)，研究認(rèn)為影響銷(xiāo)售額的因素不只是廣

2、告宣傳費(fèi)x1,還有個(gè)人可支配收入x2,價(jià)格x3,研究與發(fā)展費(fèi)用x4,各種投資x5,銷(xiāo)售費(fèi)用x6.,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,3,多元線性回歸回歸變量的選擇與逐步回歸。可化為多元線性回歸的問(wèn)題,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,4,第一節(jié) 多元線性回歸,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,5,,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,6,一、多元線性回歸模型的基本假定解釋變量x1,x2,…,xm是確定性變

3、量，不是隨機(jī)變量，而且解釋變量之間互不相關(guān)隨機(jī)誤差項(xiàng)具有零均值和同方差 隨機(jī)誤差項(xiàng)在不同樣本點(diǎn)之間是相互獨(dú)立的，不存在序列相關(guān),2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,7,隨機(jī)誤差項(xiàng)與解釋變量之間不相關(guān) 隨機(jī)誤差項(xiàng)服從零均值，同方差的正態(tài)分布,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,8,二、建立回歸方程設(shè)令 即,,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,9,20

4、24/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,10,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,11,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,12,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,13,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,14,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,15,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,16,例2中，方差分析表為：,,,,,,,y,,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,17,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第

5、四章,18,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,19,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,20,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,21,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,22,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,23,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,24,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,25,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,26,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,27,2024/3/

6、26,應(yīng)用統(tǒng)計(jì)方法第四章,28,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,29,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,30,data d411; input x1-x4 y ; cards;7 26 6 60 78.51 29 15 52 74.311 56 8 20 104.311 31 8 47 87.67 52 6 33 95.911 55 9 22 109.23 71 17 6

7、102.71 31 22 44 72.52 54 18 22 93.121 47 4 26 115.91 40 23 34 83.811 66 9 12 113.310 68 8 12 109.4；proc reg data=d411; model y=x1-x4 ;run;quit;,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,31,data d411; input x1-x4 y ; ca

8、rds;7 26 6 60 78.51 29 15 52 74.311 56 8 20 104.311 31 8 47 87.67 52 6 33 95.911 55 9 22 109.23 71 17 6 102.71 31 22 44 72.52 54 18 22 93.121 47 4 26 115.91 40 23 34 83.811 66 9 12 113.3

9、10 68 8 12 109.4;proc reg data=d411; model y=x1-x4 / selection=stepwise sle=0.10 sls=0.10; run;quit;,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,32,The SAS System 13:43 Wednesday, March 10, 2008 7

10、 The REG Procedure Model: MODEL1 Dependent Variable: y Analy

11、sis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model

12、4 2667.89944 666.97486 111.48 |t| Intercept 1 62.40537 70.07096 0.89 0.3991 x1 1 1.55110 0.74477 2.08 0.0708

13、 x2 1 0.51017 0.72379 0.70 0.5009 x3 1 0.10191 0.75471 0.14 0.8959 x4 1 -0.14406

14、 0.70905 -0.20 0.8441,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,33,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,34,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,35,data d411; input x1-x4 y ; cards;7 26 6 60 78.51 29 15 52 74.311 56 8 20 104.311 31 8 47 87.67

15、52 6 33 95.911 55 9 22 109.23 71 17 6 102.71 31 22 44 72.52 54 18 22 93.121 47 4 26 115.91 40 23 34 83.811 66 9 12 113.310 68 8 12 109.4;proc reg data=d411; model y=x1 x2 ;run;quit;,2024/3/26,

16、應(yīng)用統(tǒng)計(jì)方法第四章,36,The SAS System 13:43 Wednesday, March 10, 2008 11 The REG Procedure Model: MODEL1

17、 Dependent Variable: y Analysis of Variance Sum of Mean Source DF Square

18、s Square F Value Pr > F Model 2 2657.85859 1328.92930 229.50 |t| Intercept 1 52.57735 2.28617 23.00 <.0001

19、 x1 1 1.46831 0.12130 12.10 <.0001 x2 1 0.66225 0.04585 14.44 <.0001擬合的很好，x1,x2對(duì)y的影響顯著,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,3

20、7,Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model

21、 1 1831.89616 1831.89616 22.80 0.0006 Error 11 883.86692 80.35154 Corrected Total 12 2715.76308 Pa

22、rameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 117.56793 5.26221 40108 499.16 F Model

23、 2 2641.00096 1320.50048 176.63 <.0001 Error 10 74.76211 7.47621 Corrected Total 12 2715.76308,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,38,Stepwise

24、 Selection: Step 3 Variable x2 Entered: R-Square = 0.9823 and C(p) = 3.0182 Analysis of Variance Sum of Mea

25、nSource DF Squares Square F Value Pr > FModel 3 2667.79035 889.26345 166.83 <.000Error 9 47.97273 5.

26、33030Corrected Total 12 2715.76308,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,39,Stepwise Selection: Step 4 Variable x4 Removed: R-Square = 0.9787 and C(p) = 2.6782 An

27、alysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model

28、 2 2657.85859 1328.92930 229.50 F Intercept 52.57735 2.28617 3062.60416 528.91 <.0001 x1 1.46831 0.12130 848.43186 146.52 &

29、lt;.0001 x2 0.66225 0.04585 1207.78227 208.58 <.0001 Bounds on condition number: 1.0551, 4.2205,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,40,All variables left in the

30、 model are significant at the 0.1000 level. No other variable met the 0.1000 significance level for entry into the model. Summary of Stepwise Selection Varia

31、ble Variable Number Partial Model Step Entered Removed Vars In R-Square R-Square C(p) F Value Pr > F 1 x4 1 0.6745 0.67

32、45 138.731 22.80 0.0006 2 x1 2 0.2979 0.9725 5.4959 108.22 <.0001 3 x2 3 0.0099 0.9823

33、 3.0182 5.03 0.0517 4 x4 2 0.0037 0.9787 2.6782 1.86 0.2054,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,41,三.回歸變量的選擇與逐步回歸 （1）enter:強(qiáng)迫進(jìn)入法 （2）stepwise:逐步

34、選擇法 （3）remove:強(qiáng)迫消除法 （4）backward:向后剔除法 （5）forward:向前引入法,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,42,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,43,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,44,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,45,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,46,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,47,2024/3/26

35、,應(yīng)用統(tǒng)計(jì)方法第四章,48,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,49,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,50,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,51,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,52,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,53,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,54,data d411; input x1-x4 y ; cards;7 26 6 60 78.51 29 15 52

36、 74.311 56 8 20 104.311 31 8 47 87.67 52 6 33 95.911 55 9 22 109.23 71 17 6 102.71 31 22 44 72.52 54 18 22 93.121 47 4 26 115.91 40 23 34 83.811 66 9 12 113.310 68 8 12 109.4;proc reg data

37、=d411; model y=x1-x4 / selection=rsquare b adjrsq cp aic mse sbc; run;quit;,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,55,The REG Procedure Model: MODEL1

38、 Dependent Variable: y R-Square Selection Method Number in Adjusted Model R-Square R-Square C(p) AIC

39、MSE SBC 1 0.6745 0.6450 138.7308 58.8516 80.35154 59.98154 1 0.6663 0.6359 142.4864 59.1780 82.39421 60.30789 1

40、 0.5339 0.4916 202.5488 63.5195 115.06243 64.64937 1 0.2859 0.2210 315.1543 69.0674 176.30913 70.19730 ---------------------------------------------

41、-------------------------------------------- 2 0.9787 0.9744 2.6782 25.4200 5.79045 27.11484 2 0.9725 0.9670 5.4959 28.7417 7.47621

42、 30.43655 2 0.9353 0.9223 22.3731 39.8526 17.57380 41.54743 2 0.8470 0.8164 62.4377 51.0371 41.54427 52.73199 2 0.680

43、1 0.6161 138.2259 60.6293 86.88801 62.32417 2 0.5482 0.4578 198.0947 65.1167 122.70721 66.81153 ------------------------------------------------------

44、----------------------------------- 3 0.9823 0.9764 3.0182 24.9739 5.33030 27.23368 3 0.9823 0.9764 3.0413 25.0112 5.34562 27.2709

45、9 3 0.9813 0.9750 3.4968 25.7276 5.64846 27.98735 3 0.9728 0.9638 7.3375 30.5759 8.20162 32.83568 -----------------------------

46、------------------------------------------------------------ 4 0.9824 0.9736 5.0000 26.9443 5.98295 29.76903,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,56,Number in ------------------

47、--------Parameter Estimates-------------------------- Model R-Square Intercept x1 x2 x3 x4 1 0.6745 117.56793 . .

48、 . -0.73816 1 0.6663 57.42368 . 0.78912 . . 1 0.5339 81.47934 1.86875 . .

49、 . 1 0.2859 110.20266 . . -1.25578 . ------------------------------------------------------------------------------------------------

50、2 0.9787 52.57735 1.46831 0.66225 . . 2 0.9725 103.09738 1.43996 . . -0.61395 2 0.9353

51、131.28241 . . -1.19985 -0.72460 2 0.8470 72.07467 . 0.73133 -1.00839 . 2 0.6801 94.16007

52、 . 0.31090 . -0.45694 2 0.5482 72.34899 2.31247 . 0.49447 . -------------------------------------------------------------------

53、----------------------------- 3 0.9823 71.64831 1.45194 0.41611 . -0.23654 3 0.9823 48.19363 1.69589 0.65691 0.25002

54、 . 3 0.9813 111.68441 1.05185 . -0.41004 -0.64280 3 0.9728 203.64196 . -0.92342 -1.44797 -1.55704 -------

55、----------------------------------------------------------------------------------------- 4 0.9824 62.40537 1.55110 0.51017 0.10191 -0.14406,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,57,2024/3/

56、26,應(yīng)用統(tǒng)計(jì)方法第四章,58,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,59,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,60,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,61,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,62,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,63,data d431; input year x1-x5 y1 y2; cards;1949 0.9 0.8 0.14 6.63 0

57、.24 1.47 7.311950 1.0 2.1 0.15 7.07 0.46 1.25 7.421951 2.9 6.3 0.33 7.60 1.02 2.05 11.131952 5.0 4.4 0.78 12.88 1.61 2.49 1

58、6.081953 8.2 13.3 1.18 15.86 1.63 3.16 22.861954 13.1 16.8 1.56 18.79 1.93 3.87 29.521955 23.8 17.8 2.11 14.63 2.31 4.50 34.541956 34.8

59、 27.8 3.09 19.79 3.32 6.09 41.221957 35.4 22.1 3.58 16.50 4.44 6.78 47.541958 47.0 32.2 7.31 26.22 7.18 10.73 60.001959 62.6 33.2 9.61 2

60、8.00 8.77 17.65 78.001960 68.0 55.6 12.85 27.56 9.89 26.84 96.201961 35.3 24.4 6.76 10.95 5.58 24.20 52.371962 31.3 17.9 5.08 10.15 6.03 2

61、0.08 37.771963 35.2 24.8 5.54 14.23 7.18 19.28 40.071964 45.3 37.8 7.14 20.38 8.80 22.89 50.361965 49.5 78.8 11.20 26.56 10.45 28.94 65.331966

62、 59.7 101.6 15.89 33.18 12.51 39.05 83.641967 47.8 74.9 10.86 23.90 11.42 39.09 68.161968 17.7 40.2 5.10 17.56 9.03 26.81 41.641969 36.0 73.3

63、13.14 27.20 8.05 37.19 67.301970 62.0 138.6 25.54 36.28 10.30 54.09 103.571971 97.0 247.0 31.31 41.53 14.18 77.39 135.801972 95.2 270.0 28.79 40.24 1

64、5.19 84.02 118.101973 118.4 233.5 28.03 38.20 15.77 88.39 119.621974 99.9 205.0 26.50 31.54 12.29 86.32 112.391975 151.0 288.0 38.61 46.87 17.36 107.94 1

65、44.411976 108.0 262.2 31.46 38.62 15.10 102.76 130.661977 162.5 358.6 46.21 52.48 20.48 118.84 175.101978 238.2 454.8 55.86 55.96 26.40 139.30 214.44 ; proc prin

66、t; run; proc reg data=d431; model y1 y2=x1-x5; mtest x3,x4,x5;run;quit;,2024/3/26,應(yīng)用統(tǒng)計(jì)方法第四章,64,The SAS System 07:49 Sunday, March 21, 2008 4 The REG Pro

67、cedure Model: MODEL1 Multivariate Test 1 Multivariate Statistics and F Approximations

68、 S=2 M=0 N=10.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.17390860 10.72 6

69、 46 <.0001 Pillai's Trace 1.08953122 9.57 6 48 <.0001 Hotelling-Lawley Trace 3.23532937 12.16 6 28.955 <.0001

70、 Roy's Greatest Root 2.66743672 21.34 3 24 <.0001 NOTE: F Statistic for Roy's Greatest Root is an upper bound. NOTE: F Statistic