spss多元回歸分析案例

1、企業(yè)治理對居民消費率影響因素的探究-以湖北省為例改革開放以來,我國經(jīng)濟始終保持著高速增長的趨勢 ,三十多年間綜合國力得 到顯著增強,但我國居民消費率一宜偏低,甚至一宜有下降的趨勢.居民消費率的偏低必然會導(dǎo)致我國內(nèi)需的不足,進(jìn)而會影響我國經(jīng)濟的長期健康開展.本模型以湖北省1995年-2021年數(shù)據(jù)為例,探究各因素對居民消費率的影響及多元關(guān)系.注：計算我國居民的消費率,用居民的人均消費除以人均 GDP,得到居民的消費率.通常來說,影響居民消費率的因素是多方面的,如 ：居民 總收入,人均GDP,人口結(jié)構(gòu)狀況1 兒童撫養(yǎng)系數(shù), 老年撫養(yǎng)系數(shù),居民消 費價格指數(shù)增長率等因素.總消費C億元總GDP 億元消

2、費率19951095.972109.3851.9619971438.122856.4750.3520001594.083545.3944.9620011767.383880.5345.5420021951.544212.8246.3220032188.054757.4545.991.人口年齡結(jié)構(gòu)一種比擬精準(zhǔn)的描述是：兒童撫養(yǎng)系數(shù)0-14歲人口與15-64歲人口的比值、老年撫養(yǎng)系數(shù)65歲及以上人口與15-64歲人口的比值或總撫養(yǎng)系數(shù)兒童和老年撫養(yǎng)系數(shù)之和.0-14歲人口比例與65歲及以上人口比例可由?湖北省統(tǒng)計年鑒?查得.20042452.625633.2443.5420052785.42659

3、0.1942.2720063124.377617.4741.0220073709.699333.439.7520214225.3811328.9237.3020214456.3112961.134.3820215136.7815806.0932.50注：數(shù)據(jù)來自 湖北省統(tǒng)計年鑒?、計量經(jīng)濟模型分析一、數(shù)據(jù)搜集根據(jù)以上分析,本模型在影響居民消費率因素中引入6個解釋變X1居民總收入億元,X2:人口增長率.,X3:居民消費價格指數(shù)增長率,X4:少兒撫養(yǎng)系數(shù),X5:老年撫養(yǎng)系數(shù),X6:居民消費占收入比重.X2:人口Y:消費率X1:總收入增長率%億元c/ C199551.961590.759.27199

4、750.352033.688.12200044.962247.253.7率(%)17.145.39.4268.92.841.19.4470.720.4399.5770.93X3:居民消費價格X6:居民X4:少兒X5:老年指數(shù)增長消費比重?fù)狃B(yǎng)系數(shù) 撫養(yǎng)系數(shù)200145.542139.712.440.737.839.7282.6200246.322406.552.21-0.436.189.8181.09200345.992594.612.322.234.439.8784.33200443.542660.112.44.932.699.892.2200542.273172.413.052.931.09

5、9.7387.8200641.023538.43.131.630.179.988.3200739.754168.523.234.829.4610.0488.99202137.34852.582.716.328.6210.187.07202134.385335.543.48-0.428.0510.2583.52202132.56248.754.342.927.8310.4182.2二、計憤經(jīng)濟學(xué)模型建立假定各個影響因素與Y的關(guān)系是線性的,那么多元線性回歸模型為yt=0X12X23X34X45X56X6利用SPSS統(tǒng)計分析軟件輸出分析結(jié)果如下:Descriptive StatisticsMeanS

6、td. DeviationNY42.76005.7457413X13.3068E31436.4549013Variables Entered/RemovedbModelVariablesEnteredVariablesRemovedMethod1X4, X3, X2, X6,X1, X5 aEntera. All requested variables entered.b. Dependent Variable: YX23.8769表 2A53813X33.52314.5718613X682.20387.5374413X56.8638.4378513X423.52542.9375213這局部被

7、結(jié)果說明在對模型進(jìn)行回歸分析時所采用的方法是全部引入法Enter.CorrelationsYX1X2X3X6X5X4Pearson CorrelationY1.000-.965.480.354-.566-.960.927X1-.9651.000-.288-.215.451.932-.877X2.480-.2881.000.656-.767-.577.623X3.354-.215.6561.000-.293-.365.392X6-.566.451-.767-.2931.000.722-.795X5-.960.932-.577-.365.7221.000-.982X4.927-.877.623.3

8、92-.795-.9821.000Sig. (1-tailed)Y.000.049.118.022.000.000X1.000.170.240.061.000.000X2.049.170.007.001.020.011X3.118.240.007.166.110.093X6.022.061.001.166.003.001X5.000.000.020.110.003.000X4.000.000.011.093.001.000N13131313131313X113131313131313X213131313131313X313131313131313X613131313131313X5131313

9、13131313X413131313131313這局部列出了各變M之間的相關(guān)性,從表格可以看出Y與xi的相關(guān)性最大.且 自變M之間也存在相關(guān)性,如X1與X5, X1與X4,相關(guān)系數(shù)分別為0.932和0.877 ,說明他們之間也存在相關(guān)性Model Summary bModelRR SquareAdjusted RSquareStd. Error of theEstimateDurbin-Watson1.991 a.982.9641.091502.710a. Predictors: (Constant), X4, X3, X2, X6, X1, X5b. Dependent Variable:Y

10、這局部結(jié)果得到的是常用統(tǒng)計M,相關(guān)系數(shù)R=0.991 ,判定系數(shù),=0.982 ,調(diào) 整的判定系數(shù) 滬=0.964,回歸估計的標(biāo)準(zhǔn)誤差 S=1.09150.說明樣本的回歸效果比擬好ANOVA bModelSum of SquaresdfMean SquareFSig.1Regression389.015664.83654.421.000aResidual7.14861.191Total1396.16312a. Predictors: (Constant), X4, X3, X2, X6, X1, X5b. Dependent Variable: Y該表格是方差分析表,從這局部結(jié)果看出：統(tǒng)計M

11、F=54.421,顯著性水平的值P值為0,說明因變M與自變M的線性關(guān)系明顯.Sum of Squares 一欄中分別代表回歸平方和為389.015,、殘差平方和7.148、總平方和為396.163.Coefficients aModelUnstandardized CoefficientsStandardizedCoefficientstSig.BStd. ErrorBeta1(Constant)-33.36466.059-.505.632X1-.006.002-1.475-2.663.037X2.861.391.3352.201.070X3.036.121.029.301.774X6-.09

12、1.198-.120-.460.662X512.7159.581.9691.327.233X4.527.818.269.644.543aDepend lent Variable: Y該表格為回歸系數(shù)分析,其中Unstandardized Coefficients為非標(biāo)準(zhǔn)化系數(shù),Standardized Coefficients 為標(biāo)準(zhǔn)化系數(shù),t為回歸系數(shù)檢驗統(tǒng)計Sig.為相伴概率值.從表格中可以看出該多元線性回歸方程：Y=-33.364-0.006X 1+O.86IX 2+0.036X 3+0.527X 4+12.715X 5-0.091X6+&、計量經(jīng)濟學(xué)檢驗一、多重共線性的檢驗及修

13、正、檢驗多重共線性從表3相關(guān)系數(shù)矩陣中可以看出,個個解釋變M之間的相關(guān)程度較高所以應(yīng)該存在多重共線性、多重共線性的修正一一逐步迭代法運用spss軟件中的剔除變M法,選擇 stepwise逐步回歸 輸出表7：進(jìn)入與剔除變M表Variables Entered/RemovedaModelVariablesEnteredVariablesRemovedMethod1X1Stepwise (Criteria: Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).2X2Stepwise (Criteri

14、a: Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).a. Dependent Variable: Y可以看到進(jìn)入變M為X1與X2.表8:Model Summary cModelRR SquareAdjusted RSquareStd. Error of theEstimateDurbin-Watson1.965a.932.9251.570162.988b.976.971.976731.983a. Predictors: (Constant), X1ModelRR SquareAdjust

15、ed RSquareStd. Error of theEstimateDurbin-Watson1.965 a.932.9251.570162.988b.976.971.976731.983a. Predictors: (Constant), X1b. Predictors: (Constant), X1, X2c. Dependent Variable: YModel Summaryc表8是模型的概況,我們看到下列圖中標(biāo)出來的五個參數(shù),分別是負(fù)相關(guān)系數(shù)、決 定系數(shù)、校正決定系數(shù)、隨機誤差的估計值和 D-W值,這些值除了隨機誤差 的估計值,D-W越接近2越好都是越大說明模型的效果越好,根據(jù)比擬

16、,第 二個模型應(yīng)該是最好的.表9：方差分析表ANOVA cModelSum of SquaresdfMean SquareFSig.1Regression369.0431369.043149.689.000 aResidual27.119112.465Total396.163122Regression386.6232193.311202.632.000 bResidual9.54010.954Total396.16312a. Predictors: (Constant), X1b. Predictors: (Constant), X1, X2c. Dependent Variable: Y方差

17、分析表,四個模型都給出了方差分析的結(jié)果,這個表格可以檢驗是否所有偏回歸系數(shù)全為0, sig值小于0.05可以證實模型的偏回歸系數(shù)至少有一個不為零.表10:參數(shù)檢驗Coefficients aStandardizedModelUnstandardized CoefficientsCoefficientstSig.BStd. ErrorBeta1(Constant)55.5261.13149.109.000X1-.004.000-.965-12.235.0002(Constant)52.497.99652.686.000X1-.004.000-.902-17.599.000X2.565.132.2

18、204.293.001a. Dependent Variable: Y參數(shù)的檢驗,這個表格給出了對偏回歸系數(shù)和標(biāo)準(zhǔn)偏回歸系數(shù)的檢驗,偏回歸系數(shù)用于不同模型的比擬,標(biāo)準(zhǔn)偏回歸系數(shù)用于同一個模型的不同系數(shù)的檢驗,具值越大說明對因變M的影響越大.綜上可得：模型2為最優(yōu)模型.得出回歸方程Y=52.497-0.004X1+0.056X2+&二、異方差的檢驗輸出殘差圖：如圖1ScatterplotDependent variable: Yoo-Regression Standardized Predicted Value從圖1看出,e2并不隨x的增大而變化,說明模型不存在異方差三、自相關(guān)檢驗-用D-W檢驗由輸出結(jié)果表 8得：DW= 1.983 ,查表得DL=0.861 , DU=1.562 ,4-DU=2.438所以DU<DW<4-DU=2.438,因此誤差項之間不存在自相關(guān)性.四、統(tǒng)計檢驗1. 擬合優(yōu)度檢驗：由表 8相關(guān)系數(shù)R=0.988,判定系數(shù),=0.976,調(diào)整的判定系數(shù) 護(hù)=0.971,回歸估計的標(biāo)準(zhǔn)誤差 S=0O 9673.說明樣本的回歸效果比擬好2. F值檢驗：由表9F= 202,632 0查表得,置信度為95%,自由度為1,12的F臨界值為4.474, F值遠(yuǎn)遠(yuǎn)大于臨