回歸分析的一般步驟

1、回歸分析的一般步驟案例1為了研究貨運量與工業(yè)總產(chǎn)值、農(nóng)業(yè)總產(chǎn)值、居民非商品支出的關系。收集了這三者的數(shù)據(jù)。試完成下列問題（顯著性水平:二0.05）（1）構造多元線性計量經(jīng)濟模型，并進行參數(shù)估計；（2）對模型參數(shù)以及變量之間線性關系進行顯著性檢驗；（3）是否需要對模型進行調整，給出調整后的模型，并重新估計模型參數(shù)。解：（1）根據(jù)經(jīng)濟理論可以認為，貨運量與工業(yè)總產(chǎn)值、農(nóng)業(yè)總產(chǎn)值、居民非商品支出具有較強的關系，分別以r, X 1, X 2, X 3表示，建立如下的線性模型：Y = p +p X +p X +p X + ui 01 1i 2 2i3 3ii利用Eviews軟件得到的結果如表1所示。表1

2、Dependent Variable: YMethod: Least SquaresDate: 11/22/08 Time: 16:41Sample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb.C-340.4483157.9296-2.1556960.0745X14.0204401.6985522.3669810.0558X26.4167412.7597412.3251250.0059X311.435377.2222231.5833590.1644R-squared0.831115Mean

3、 dependent var231.5000Adjusted R-squared0.746673S.D.dependent var43.40059S.E. of regression21.84423Akaike info criterion9.294925Sum squared resid2863.022Schwarz criterion9.415959Log likelihood-42.47463F-statistic9.842380Durbin-Watson stat2.228638Prob(F-statistic)0.009845根據(jù)多元線性回歸關于Eviews輸出結果可以得到參數(shù)的估計

4、值為：p 0 =340.448, p 1 = 4.020, p 2 = 6.416, p 3 = 11.435從而初步得到的回歸方程為Y = 340.448 + 4.020X + 6.416X +11.435Xi1i2i3i（2）從Eviews輸出的結果可以看出：調整的樣本可決系數(shù)為0.746673，說 明回歸方程擬合優(yōu)度比較好?；貧w方程顯著性檢驗的F值為9.842380，其對應的 檢驗概率為0.009845，小于顯著性水平:=0.05，說明變量之間線性關系顯著。解 釋變量的檢驗概率都大于0.05,說明這兩個變量X 1, X3沒有通過t檢驗，而X2通 過了t檢驗，所以需要對這個模型做出調整。（

5、3）根據(jù)（2）的分析，需要刪除不顯著的解釋變量，鑒于X3最不顯著，所以首先剔除X，重新擬合得到的回歸結果如表2。3表2Dependent Variable: YMethod: Least SquaresDate: 11/22/08 Time: 16:53Sample: 1 10Included observations: 10VariableCoefficientStd. Error t-StatisticProb.C-459.6237153.0576-3.0029460.0199X14.6756301.8160712.5745860.0368X28.9709612.4684613.63423

6、20.0084R-squared0.760549Mean dependent var231.5000Adjusted R-squared0.692134S.D. dependent var43.40059S.E. of regression24.08112Akaike info criterion9.444058Sum squared resid4059.301Schwarz criterion9.534834Log likelihood-44.22029F-statistic11.11674Durbin-Watson stat1.894940Prob(F-statistic)0.006718

7、顯然此時的估計結果都比較滿意，無論是回歸方程檢驗，還是參數(shù)顯著性檢 驗的檢驗概率，都顯著小于0.05。D-W值為1.894940，顯著性水平:=0.05下查Durbin-Watson表，其中n=10，解釋變量的個數(shù)為1,得到下限臨界值* = 1.077， 上限臨界值du = 1.361，因為統(tǒng)計量du = 1.361D-W=1.8949404-匕=1.361，這 時表明隨機誤差項不存在自相關?？梢哉J為此時得到的模型是適合的，因此最終 的模型為Y =459.624 + 4.676X + 8.971Xi1i2i兩個回歸系數(shù)的經(jīng)濟意義為：當農(nóng)業(yè)總產(chǎn)值不變時，工業(yè)總產(chǎn)值每增加1 億元，貨運量就增加約4

8、.676萬噸，當工業(yè)總產(chǎn)值不變時，農(nóng)業(yè)總產(chǎn)值每增加1 億元，貨運量就增加約8.971萬噸。案例2利用表中的數(shù)據(jù)，對隨機誤差項具有異方差的回歸模型給出一般解 決方法和步驟。解：第一步，用OLS估計參數(shù)。根據(jù)經(jīng)濟理論可以設模型為丫 =0 +P X + u i 01 i i利用Eviews軟件得到的結果如表1所示。表1Dependent Variable: YMethod: Least SquaresDate: 11/22/08 Time: 17:28Sample: 1 38Included observations: 38VariableCoefficientStd. Error t-Statis

9、ticProb.C3.77260633.532080.1125070.9110X0.0636940.0124425.1193660.0000R-squared0.421295Mean dependent var100.9732Adjusted R-squared0.405220S.D. dependent var220.9185S.E. of regression170.3767Akaike info criterion13.16510Sum squared resid1045016.Schwarz criterion13.25129Log likelihood-248.1368F-stati

10、stic26.20790Durbin-Watson stat2.024988Prob(F-statistic)0.000010根據(jù)表整理可以得到如下結果Y = 3.773 + 0.064X。ii從回歸結果看，在顯著性水平:二0.05下，X的系數(shù)是顯著的，且F值很大，但是決定系數(shù)為0.421295較小，且截距項并不顯著，所以此模型并不理想。第二步，異方差檢驗（White檢驗）表2White Heteroskedasticity Test:F-statistic2.163749Probability0.0130019Obs*R-squared4.181423Probability0.0123599

11、Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 11/22/08 Time: 17:38Sample: 1 38Included observations: 38VariableCoefficientStd. Errort-StatisticProb.C-19186.2332216.87-0.5955340.5553X60.6915829.609192.0497550.0479R-squared0.110037Mean dependent var27500.42Adjusted R-squared0.059

12、182S.D. dependent var143442.9S.E. of regression139133.5Akaike info criterion26.59991Sum squared resid6.78E+11Schwarz criterion26.72920Log likelihood-502.3983F-statistic2.163749Durbin-Watson stat2.020277Prob(F-statistic)0.130019由表2中得到White檢驗的檢驗概率為0.0123599,小于=0.05, 拒絕原假設，故隨機誤差項存在異方差。第三步，異方差處理表3Depend

13、ent Variable: LY Method: Least SquaresDate: 11/22/08 Time: 17:50Sample: 1 38Included observations: 37VariableCoefficientStd. Error t-StatisticProb.C-4.2489130.591023-7.1890770.0000LX1.1239740.09145012.290540.0000R-squared0.811886Mean dependent var2.687126Adjusted R-squared0.806511S.D. dependent var2

14、.428033S.E. of regression1.068028Akaike info criterion3.022043Sum squared resid39.92392Schwarz criterion3.109120Log likelihood-53.90780F-statistic151.0573Durbin-Watson stat1.952035Prob(F-statistic)0.000000表4White Heteroskedasticity Test:F-statistic4.055962Probability0.045662Obs*R-squared7.121401Prob

15、ability0.041105XA2-0.0063240.003506-1.8034920.0799Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 11/22/08 Time: 17:51Sample: 1 38Included observations: 37VariableCoefficientStd. Error t-StatisticProb.C0.5487182.4810490.2211640.0263LX0.0893040.8965550.0996080.0212LXA2-0.0004980.082257-0.0060510.0952R-squared0.953281Mean dependent var1.079025Adjusted R-squared0.911349S.D.dependent var2.858163S.E. of regression2.936197Akaike info criterion5.069712Sum squared resid293.1226Schw