多元線性回歸模型線性與非線性估計檢驗實驗報告

1、湖南商學(xué)院模擬實驗報告實驗地點: 實驗樓 時間:課程名稱計量經(jīng)濟學(xué)模擬實驗實驗項目名稱多元線性回歸模型線性與非線性估計檢驗班級 姓名學(xué)號學(xué)時小組成員實驗?zāi)康模?掌握生產(chǎn)函數(shù)的估計、檢驗以及多參數(shù)的線性約束檢驗等內(nèi)容實驗說明：數(shù)據(jù)來源于教材p65頁表4.1.1，工作文件夾是sy3.WF1，實驗?zāi)康氖亲寣W(xué)生掌握生產(chǎn)函數(shù)的估計、檢驗以及多參數(shù)的線性約束檢驗等內(nèi)容。注意：實際GDP是以1978年為100計算、資本存量是以1952年的不變價格計算。實驗內(nèi)容：1.估計雙對數(shù)模型，以及說明各回歸系數(shù)的經(jīng)濟含義； 由于實驗數(shù)據(jù)中已給出變量的對數(shù)形式，所以new objects“eq01”“gdp1 c k1

2、l1Dependent Variable: GDP1Method: Least SquaresDate: 02/27/13 Time: 08:41Sample: 1978 2006Included observations: 29CoefficientStd. Errort-StatisticProb.C-9.0474860.787252-11.492500.0000K10.7475960.02199733.986640.0000L10.6788800.0901477.5308220.0000R-squared0.998348Mean dependent var5.887599Adjusted

3、 R-squared0.998220S.D. dependent var0.800400S.E. of regression0.033765Akaike info criterion-3.841113Sum squared resid0.029641Schwarz criterion-3.699669Log likelihood58.69614Hannan-Quinn criter.-3.796814F-statistic7854.199Durbin-Watson stat0.799482Prob(F-statistic)0.000000Second-Stage SSR0.029641在回歸方

4、程中點viewrepresentations所以該模型函數(shù)形式為Ln GDP= -9.0474855847 + 0.747595717651LnK + 0.678880192961LnL回歸系數(shù)的經(jīng)濟含義:資本每增加1%，GDP平均增加0.74759571765%,勞動每增加1%，GDP平均增加0.67888019296%2.對模型做t檢驗和F檢驗；T(0)=-11.49250,T(1)=33.98664,T(2)=7.530822,P值均為0，所以T檢驗說明回歸模型中系數(shù)不為0，在一定顯著性水平下這個模型是有意義的，模型中解釋變量對于被解釋變量有一定解釋力度。F=7854.199,P=0.0

5、00000，F(xiàn)檢驗說明拒絕原假設(shè)，模型總體存在。3.在5%的顯著性水平下對隨機干擾項的方差做如下檢驗：和輸入scalar deltasqrhat1=0.027/(29-3)4.利用F統(tǒng)計量來檢驗： 打開eq1ViewCoefficient TestsWald CoefficientRestrictions輸入c(2)+c(3)=1okWald Test:Equation: EQ1Test StatisticValuedfProbabilityF-statistic37.38918(1, 26)0.0000Chi-square37.3891810.0000Null Hypothesis Summ

6、ary:Normalized Restriction (= 0)ValueStd. Err.-1 + C(2) + C(3)0.4264760.069746Restrictions are linear in coefficients.從輸出結(jié)果來看P=0.0000，是拒絕原假設(shè)的，所以1+215*.對模型進行非線性O(shè)LS估計：設(shè)定初始值(雙擊序列C，在c(1)、c(2)和c(3)所對應(yīng)的單元格中分別輸入0，option中的收斂精度設(shè)為0.001，迭代次數(shù)100次)，保存模型；objecteq2GDP=C(1)*(KC(2)*(LC(3)optionokDependent Variable:

7、GDPMethod: Least SquaresDate: 03/22/15 Time: 17:28Sample: 1978 2006Included observations: 29Convergence achieved after 1 iterationGDP=C(1)*(KC(2)*(LC(3)VariableCoefficientStd. Errort-StatisticProb.C(1)4.0149733.34E+171.20E-171.0000C(2)1.9420011.44E+151.35E-151.0000C(3)-4.5477188.71E+15-5.22E-161.000

8、0R-squared-1.858693Mean dependent var481.4144Adjusted R-squared-2.078593S.D. dependent var359.3645S.E. of regression630.5381Akaike info criterion15.82872Sum squared resid10337035Schwarz criterion15.97017Log likelihood-226.5165Hannan-Quinn criter.15.87302Durbin-Watson stat0.008228b. 設(shè)定初始值(雙擊序列C，在c(1)

9、、c(2)和c(3)所對應(yīng)的單元格中分別輸入0，option中的收斂精度設(shè)為0.00001，迭代次數(shù)1000次)，保存模型；objecteq3GDP=C(1)*(KC(2)*(LC(3)optionokDependent Variable: GDPMethod: Least SquaresDate: 03/22/15 Time: 17:28Sample: 1978 2006Included observations: 29Convergence achieved after 1 iterationGDP=C(1)*(KC(2)*(LC(3)VariableCoefficientStd. Err

10、ort-StatisticProb.C(1)4.0149733.34E+171.20E-171.0000C(2)1.9420011.44E+151.35E-151.0000C(3)-4.5477188.71E+15-5.22E-161.0000R-squared-1.858693Mean dependent var481.4144Adjusted R-squared-2.078593S.D. dependent var359.3645S.E. of regression630.5381Akaike info criterion15.82872Sum squared resid10337035Schwarz criterion15.97017Log likelihood-226.5165Hannan-Quinn crite