回歸分析大作業(yè)

1、精選優(yōu)質文檔-傾情為你奉上回歸大作業(yè)國內旅游消費影響的回歸分析一、問題引入我國第三產業(yè)發(fā)展迅速，在2010年其已占國內生產總值的43.14%，而旅游業(yè)在第三產業(yè)中占有重要地位，且與餐飲、住宿、休閑、運輸?shù)犬a業(yè)聯(lián)系密切，所以此次分析以探究國內旅游消費的影響為目的，并建立回歸模型。二、模型設計運用多元線性模型擬合，若擬合效果不顯著，則進行l(wèi)og或平方根變換或使用多項式擬合等其他模型。1、相關性分析，首先確定與因變量有相關性的變量。2、建立全模型多元線性回歸，若回歸方程F檢驗未通過，則查找原因、更換模型；若有部分回歸系數(shù)檢驗未通過，則進行選元（步驟2），剔除部分變量再繼續(xù)；若所有檢驗都良好，則模型初

2、步確立，跳過步驟2。3、運用逐步回歸方法篩選變量，并進行t檢驗，若效果顯著，則可初步確立多元線性回歸模型；若仍有部分變量未通過檢驗，則再單獨進行變量篩選，綜合運用AIC準則等確定剔除變量，直至所有變量都通過t檢驗。4、回歸診斷。進行殘差分析，檢驗殘差是否滿足正態(tài)分布，是否有相關性，也即自變量間是否有自相關性，檢驗是否存在異常值和強影響值，是否存在異方差性，是否存在多重共線性。若以上問題存在，則需修改模型，或重新篩選變量，或增減樣本。5、模型最終確立。三、數(shù)據(jù)yearincomenumberexpenselevelroadrail199448108.5524195.3320.0111.785.9

3、0199559810.5629218.7345.1115.706.24199670142.5640256.2377.6118.586.49199778060.9644328.1394.6122.646.60199883024.3695345.0417.8127.856.64199988479.2719394.0452.3135.176.74200098000.5744426.6491.0140.276.872001.2784449.5521.2169.807.012002.7878441.8557.6176.527.192003.0870395.7596.9180.987.302004.811

4、02427.5645.3187.077.442005.51212436.1695.2334.527.542006.91394446.9761.9345.707.712007.01610482.6843.4358.377.802008.71712511.0916.8373.027.972009.51902535.41001.6386.088.552010.02103598.21062.6400.829.12yearairrailtranroadtranshiptranairtrantravel1994104.562616540391023.51995112.902392451171375.719

5、96116.65947972289555551638.41997142.50933082257356302112.71998150.58950852054557552391.21999152.221915160942831.92000150.291938667223175.52001155.361864575243522.42002163.771869385943878.42003174.95972601714287593442.32004204.9419040121234710.72005199.8520227138275285.92006211.3522047159686229.72007

6、234.3022835185767770.62008246.1820334192518749.32009234.51223142305210183.72010276.51223922676912579.8數(shù)據(jù)來源：中國統(tǒng)計年鑒2011數(shù)據(jù)說明：Year：年份。Income：國民總收入，單位億元。Number：旅游人數(shù)。Expense：人均旅游花費，單位元。Level：居民消費水平指數(shù)，以1978年為基年。Road：公路里程，單位萬公里。Rail：鐵路里程，單位萬公里。Air：民航里程，單位萬公里。Roadtran：公路客運量，單位萬人。Railtran：鐵路客運量，單位萬人。Shiptran：

7、水路客運量，單位萬人。Airtran：民航客運量，單位萬人。Travel：國內旅游消費總額，單位億元。四、回歸分析1、相關性首先分析相關性，畫出散布陣。 可較為直觀地看出，travel與各變量間有較強的相關性，除了road，和shiptran兩項，做相關性檢驗，可見,travel與road是線性相關的，相關系數(shù)為0.93，p-value = 4.563e-08，而travel與shiptran不相關，p-value = 0.9983，所以可先排除shiptran，再做回歸。2、全回歸模型直接建立多元回歸模型，得結果：Coefficients: Estimate Std. Error t val

8、ue Pr(>|t|) (Intercept) -5.972e+03 3.193e+03 -1.870 0. income 2.151e-02 4.779e-03 4.501 0. * number 1.039e+00 1.446e+00 0.719 0. expense 6.805e+00 1.124e+00 6.052 0. *level -5.815e+00 1.261e+00 -4.610 0. * road -1.468e+00 1.019e+00 -1.441 0. rail 6.274e+02 4.462e+02 1.406 0. air -4.155e+00 2.790e

9、+00 -1.490 0. railtran 2.524e-02 8.492e-03 2.972 0. * roadtran -4.093e-04 4.554e-04 -0.899 0. airtran 1.058e-01 1.272e-01 0.832 0. -Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 84.55 on 6 degrees of freedomMultiple R-squared: 0.9998, Adjusted R-squared: 0.9994 F-statistic:

10、 2462 on 10 and 6 DF, p-value: 5.061e-10其中，R2=0.9998, F檢驗的p-value: 2.632e-08，可見回歸模型的檢驗是成立的，但回歸系數(shù)并不是全能通過檢驗，所以應該進行選元。3、選元先進行逐步回歸，逐步回歸排除了roadtran，number兩個變量，以AIC準則為主要判斷依據(jù)，調整后的AIC值為153.73，達到最小值。再檢驗一下回歸模型：Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -4.393e+03 2.102e+03 -2.090 0. . i

11、ncome 1.898e-02 2.320e-03 8.179 3.72e-05 *expense 7.038e+00 9.369e-01 7.512 6.85e-05 *level -5.427e+00 1.057e+00 -5.133 0. *road -1.460e+00 9.339e-01 -1.564 0. rail 3.697e+02 2.865e+02 1.290 0. air -3.589e+00 2.496e+00 -1.438 0. railtran 2.166e-02 6.843e-03 3.165 0. * airtran 2.032e-01 5.464e-02 3.7

12、19 0. * -Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 78.95 on 8 degrees of freedomMultiple R-squared: 0.9997, Adjusted R-squared: 0.9994 F-statistic: 3529 on 8 and 8 DF, p-value: 2.252e-13 可見回歸模型改善，自由度調整負相關系數(shù)達到了0.9994，有所提高，這與AIC準則的判斷相符，而回歸系數(shù)的檢驗也有所好轉，但仍然有road，rail，air通不過檢驗

13、。若去掉一個變量回歸，可見： Df Sum of Sq RSS AIC<none> 49866 153.73income 1 189.75expense 1 187.19level 1 176.50road 1 15241 65107 156.26rail 1 10380 60246 154.94air 1 12886 62752 155.63railtran 1 62438 165.53airtran 1 86215 168.79去掉rail，AIC增加最小，同時RSS增加最小，而回歸方程系數(shù)檢驗：Coefficients: Estimate Std. Error t value

14、 Pr(>|t|) (Intercept) -1.773e+03 5.648e+02 -3.140 0. * income 1.935e-02 2.386e-03 8.112 1.98e-05 *expense 7.977e+00 6.116e-01 13.043 3.77e-07 *level -5.126e+00 1.069e+00 -4.797 0. *road -2.214e+00 7.550e-01 -2.933 0. * air -5.129e+00 2.272e+00 -2.257 0. . railtran 1.495e-02 4.613e-03 3.241 0. * a

15、irtran 2.603e-01 3.323e-02 7.832 2.62e-05 * 只有air一項在a=0.05的情況下是不能通過檢驗的，若排除air，則：Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -2.450e+03 5.683e+02 -4.310 0.00154 * income 1.834e-02 2.782e-03 6.593 6.13e-05 *expense 7.465e+00 6.742e-01 11.072 6.21e-07 *level -5.389e+00 1.261e+00 -

16、4.273 0.00163 * road -2.381e+00 8.921e-01 -2.669 0.02355 * railtran 1.933e-02 4.970e-03 3.889 0.00301 * airtran 2.451e-01 3.864e-02 6.343 8.42e-05 *所有回歸系數(shù)通過檢驗，回歸模型初步確立。4、回歸診斷計算得出殘差，進行W正態(tài)性檢驗，得到p-value = 0.9066，不能拒絕正態(tài)性假設。而回歸值與標準化殘差的殘差圖為：從圖中也可看出，殘差分布均勻且無規(guī)律，所以線性回歸的基本假設滿足，且沒有自相關性。而再看：綜合看上面四幅圖，11和15號觀測值可能

17、為強影響值，但產生原因還需要探究，可能是統(tǒng)計過程上的，亦可能是分析方法上的，去掉后回歸效果減弱，所以暫不剔除。再檢驗多重共線性，kappa=1346.411>1000，所以存在多重共線性，接近零的特征值及其相應特征向量為：0.，,61, 0.2, 0.3, -0.4, 0.5, -0.6, -0. 0.,51, -0.2, 0.3, -0.4, 0.5, -0.6, 0.可見，1,3，6之間即income與level，airtran之間可能存在嚴重的多重共線性關系，更可能的是在income與level之間，這在經濟意義上也可以理解，國民收入越高，消費水平越高，而坐飛機的人才越多，前兩者關

18、系更直接。所以引起原因可能是有多余的自變量，分別去掉income，level，airtran做回歸，并計算kappa值。從結果知，不管去掉哪一個，kappa值均減少一半左右，而只有去掉level時，回歸方程幾乎無影響，Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -3.824e+03 7.511e+02 -5.091 0. *income 1.217e-02 3.811e-03 3.194 0. * expense 5.483e+00 7.843e-01 6.991 2.3e-05 *road -4.247e

19、+00 1.247e+00 -3.407 0. * railtran 2.708e-02 7.416e-03 3.651 0. * airtran 1.929e-01 5.876e-02 3.284 0. * -Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 155.7 on 11 degrees of freedomMultiple R-squared: 0.9985, Adjusted R-squared: 0.9978 F-statistic: 1450 on 5 and 11 DF, p-v

20、alue: 4.078e-15 所以可以剔除level。再做一下異方差性的檢驗，用等級相關系數(shù)法，計算殘差的絕對值與自變量間的等級相關系數(shù)，分別為0.，0.，0.，0，0.發(fā)現(xiàn)并無相關的，所以模型擬合良好。5、模型確立Travel=-3.824e+03+1.217e-02*income+5.483*expense-4.247*road+2.708e-02*railtran+1.929e-01*airtran五、模型評注從模型來看，國內旅游消費量可由國民收入、人均旅游花費、鐵路客運量、民航客運量、公路里程來建模模擬預測，這與實際意義相符。前兩者可歸納為人民生活水平，后三者是國家交通建設方面，而恰

21、恰包括了公路、鐵路、航空三個方面。所以回歸方程的建立與其實際意義大致相符，影響因素也基本確定。但是受開始自變量選擇的影響，有可能存在重要變量為選入。六、程序代碼及輸出（編程語言：R）> x=read.csv("數(shù)據(jù).csv",head=T)> a=x,2:13> plot(a) > cor.test(road,travel) /*相關性檢驗*/ Pearson's product-moment correlationdata: road and travel t = 10.0692, df = 15, p-value = 4.563e-08a

22、lternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0. 0. sample estimates: cor 0.> cor.test(shiptran,travel) Pearson's product-moment correlationdata: shiptran and travel t = 0.0021, df = 15, p-value = 0.9983alternative hypothesis: true correlation is no

23、t equal to 0 95 percent confidence interval: -0. 0. sample estimates: cor 0.>model=lm(travelincome+number+expense+level+road+rail+air+railtran+roadtran+airtran)> summary(model) /*建立回歸模型*/Call:lm(formula = travel income + number + expense + level + road + rail + air + railtran + roadtran + airt

24、ran)Residuals: Min 1Q Median 3Q Max -72.549 -44.860 3.562 44.806 90.603 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -5.972e+03 3.193e+03 -1.870 0. income 2.151e-02 4.779e-03 4.501 0. * number 1.039e+00 1.446e+00 0.719 0. expense 6.805e+00 1.124e+00 6.052 0. *level -5.815e+00 1.

25、261e+00 -4.610 0. * road -1.468e+00 1.019e+00 -1.441 0. rail 6.274e+02 4.462e+02 1.406 0. air -4.155e+00 2.790e+00 -1.490 0. railtran 2.524e-02 8.492e-03 2.972 0. * roadtran -4.093e-04 4.554e-04 -0.899 0. airtran 1.058e-01 1.272e-01 0.832 0. -Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual s

26、tandard error: 84.55 on 6 degrees of freedomMultiple R-squared: 0.9998, Adjusted R-squared: 0.9994 F-statistic: 2462 on 10 and 6 DF, p-value: 5.061e-10> model1=step(model) /*逐步回歸*/Start: AIC=155.17travel income + number + expense + level + road + rail + air + railtran + roadtran + airtran Df Sum

27、of Sq RSS AIC- number 1 3693 46589 154.57- airtran 1 4948 47844 155.02<none> 42897 155.17- roadtran 1 5775 48671 155.31- rail 1 14137 57033 158.01- road 1 14850 57746 158.22- air 1 15862 58758 158.52- railtran 1 63136 168.55- income 1 178.26- level 1 178.90- expense 1 186.50Step: AIC=154.57tra

28、vel income + expense + level + road + rail + air + railtran + roadtran + airtran Df Sum of Sq RSS AIC- roadtran 1 3276 49866 153.73<none> 46589 154.57- rail 1 11735 58325 156.39- air 1 15657 62246 157.50- road 1 17009 63598 157.86- airtran 1 58169 166.34- railtran 1 64855 167.40- income 1 176.

29、91- level 1 178.18- expense 1 189.12Step: AIC=153.73travel income + expense + level + road + rail + air + railtran + airtran Df Sum of Sq RSS AIC<none> 49866 153.73- rail 1 10380 60246 154.94- air 1 12886 62752 155.63- road 1 15241 65107 156.26- railtran 1 62438 165.53- airtran 1 86215 168.79-

30、 level 1 176.50- expense 1 187.19- income 1 189.75> summary(model1)Call:lm(formula = travel income + expense + level + road + rail + air + railtran + airtran)Residuals: Min 1Q Median 3Q Max -66.673 -57.766 2.796 46.749 91.039 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -4.39

31、3e+03 2.102e+03 -2.090 0. . income 1.898e-02 2.320e-03 8.179 3.72e-05 *expense 7.038e+00 9.369e-01 7.512 6.85e-05 *level -5.427e+00 1.057e+00 -5.133 0. *road -1.460e+00 9.339e-01 -1.564 0. rail 3.697e+02 2.865e+02 1.290 0. air -3.589e+00 2.496e+00 -1.438 0. railtran 2.166e-02 6.843e-03 3.165 0. * ai

32、rtran 2.032e-01 5.464e-02 3.719 0. * -Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 78.95 on 8 degrees of freedomMultiple R-squared: 0.9997, Adjusted R-squared: 0.9994 F-statistic: 3529 on 8 and 8 DF, p-value: 2.252e-13 > model2=drop1(model1) /*減少一個變量做回歸*/> model2Sing

33、le term deletionsModel:travel income + expense + level + road + rail + air + railtran + airtran Df Sum of Sq RSS AIC<none> 49866 153.73income 1 189.75expense 1 187.19level 1 176.50road 1 15241 65107 156.26rail 1 10380 60246 154.94air 1 12886 62752 155.63railtran 1 62438 165.53airtran 1 86215 1

34、68.79> model3=update(model1,.-rail) /*剔除rail*/> summary(model3)Call:lm(formula = travel income + expense + level + road + air + railtran + airtran)Residuals: Min 1Q Median 3Q Max -77.120 -62.739 -7.682 57.073 96.157 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -1.773e+03 5

35、.648e+02 -3.140 0. * income 1.935e-02 2.386e-03 8.112 1.98e-05 *expense 7.977e+00 6.116e-01 13.043 3.77e-07 *level -5.126e+00 1.069e+00 -4.797 0. *road -2.214e+00 7.550e-01 -2.933 0. * air -5.129e+00 2.272e+00 -2.257 0. . railtran 1.495e-02 4.613e-03 3.241 0. * airtran 2.603e-01 3.323e-02 7.832 2.62

36、e-05 *-Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 81.82 on 9 degrees of freedomMultiple R-squared: 0.9997, Adjusted R-squared: 0.9994 F-statistic: 3756 on 7 and 9 DF, p-value: 7.348e-15 > model4=update(model3,.-air)> summary(model4)Call:lm(formula = travel income +

37、 expense + level + road + railtran + airtran)Residuals: Min 1Q Median 3Q Max -165.78 -44.43 12.86 49.24 123.92 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -2.450e+03 5.683e+02 -4.310 0.00154 * income 1.834e-02 2.782e-03 6.593 6.13e-05 *expense 7.465e+00 6.742e-01 11.072 6.21e-0

38、7 *level -5.389e+00 1.261e+00 -4.273 0.00163 * road -2.381e+00 8.921e-01 -2.669 0.02355 * railtran 1.933e-02 4.970e-03 3.889 0.00301 * airtran 2.451e-01 3.864e-02 6.343 8.42e-05 *-Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 97.14 on 10 degrees of freedomMultiple R-squared

39、: 0.9995, Adjusted R-squared: 0.9991 F-statistic: 3108 on 6 and 10 DF, p-value: 9.282e-16 > resid=resid(model4)> resid 1 2 3 4 5 6 32. -8. 12. -83. 50. 47. 7 8 9 10 11 12 -54. -28. 123. 80. -165. 33. 13 14 15 16 17 -28. -44. -112. 96. 49. > shapiro.test(resid) /*W正態(tài)性檢驗*/ Shapiro-Wilk normal

40、ity testdata: resid W = 0.9756, p-value = 0.9066> y=predict(model4)> rstandard=rstandard(model4)> plot(y,rstandard)> plot(model4,1)> plot(model4,2)> plot(model4,3)> plot(model4,4)> attach(x)> aa=data.frame(travel,income,expense,level,road,railtran,airtran)> b=aa,2:7>

41、 bb=cor(b)> kappa(bb,exact=T) /*計算kappa值*/1 1366.411> eigen(bb) /*求解矩陣特征值及特征向量*/$values1 5. 0. 0. 0. 0.6 0.$vectors ,1 ,2 ,3 ,4 ,51, -0. -0. 0. 0. -0.2, -0. 0. 0. -0. 0.3, -0. 0. -0. 0. -0.4, -0. -0. -0. -0. 0.5, -0. -0. 0. -0. -0.6, -0. -0. 0. 0. 0. ,61, 0.2, 0.3, -0.4, 0.5, -0.6, -0.> bbb

42、=kappa(cor(b,colnames(b)!="level") /*去掉變量level后求kappa值*/> bbb1 529.9542> kappa(cor(b,colnames(b)!="income")1 537.9962> kappa(cor(b,colnames(b)!="airtran")1 624.6458> summary(update(model4,.-level)Call:lm(formula = travel income + expense + road + railtran +

43、airtran)Residuals: Min 1Q Median 3Q Max -322.63 -58.04 -11.62 95.45 214.69 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -3.824e+03 7.511e+02 -5.091 0. *income 1.217e-02 3.811e-03 3.194 0. * expense 5.483e+00 7.843e-01 6.991 2.3e-05 *road -4.247e+00 1.247e+00 -3.407 0. * railtran

44、 2.708e-02 7.416e-03 3.651 0. * airtran 1.929e-01 5.876e-02 3.284 0. * -Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 155.7 on 11 degrees of freedomMultiple R-squared: 0.9985, Adjusted R-squared: 0.9978 F-statistic: 1450 on 5 and 11 DF, p-value: 4.078e-15 > summary(updat

45、e(model4,.-income)Call:lm(formula = travel expense + level + road + railtran + airtran)Residuals: Min 1Q Median 3Q Max -466.59 -84.23 -15.25 150.26 246.75 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -4.844e+03 9.639e+02 -5.025 0. *expense 7.056e+00 1.480e+00 4.767 0. *level -1.

46、075e+00 2.377e+00 -0.452 0. road -4.336e+00 1.855e+00 -2.337 0. * railtran 3.611e-02 9.409e-03 3.838 0. * airtran 3.690e-01 7.443e-02 4.958 0. *-Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 Residual standard error: 214.1 on 11 degrees of freedomMultiple R-squared: 0.9971, Adjusted R-squared: 0.995

47、8 F-statistic: 765.5 on 5 and 11 DF, p-value: 1.357e-13 > summary(update(model4,.-airtran)Call:lm(formula = travel income + expense + level + road + railtran)Residuals: Min 1Q Median 3Q Max -556.44 -72.17 47.38 95.54 239.22 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -3.239e+03 1.185e+03 -2.733 0. * income 2.692e-02 5.194e-03 5.183 0. *expense 6.359e+00 1.392e+00 4.569 0. *level -2.861e+00 2.557e+00 -1.11