Durbin-Wa3.01559 Prob(F-statist0.001tson stat 7 ic) 476
如所预料，研发费用和销售量正相关。常数项不显著，那是无关紧要得的。应用Glejser来检验是否存在异方差。
1）将残差的绝对值对销量回归：
Dependent Variable: ABS_RESID Method: Least Squares
Date: 05/14/03 Time: 23:40 Sample: 1 18
Included observations: 18 Variable CoefficStd. t-StatiProb.ient Error stic X 0.011930.0052.093050.0529 704 6 6
C 578.568678.60.852470.406
6 949 2 5 R-squared 0.21495 Mean dependent 1650.1 var 427
Adjusted 0.16588 S.D. dependent 2069.R-squared 5 var 045 S.E. of 1889.65 Akaike info 18.03regressio7 criterion 062 n Sum 5713285 Schwarz 18.12squared 5 criterion 955 resid Log -160.27 F-statistic 4.380likelihoo56 883 d
Durbin-Wa1.74330 Prob(F-statist0.052tson stat 4 ic) 634 2）将残差的绝对值对销量正平方根回归： Dependent Variable: ABS_RESID Method: Least Squares
Date: 05/14/03 Time: 23:42 Sample: 1 18
Included observations: 18 Variable Coefficient Std. t-Statistic Prob. Error SQR_X 7.971933 3.363148 2.370378 0.0307 C -507.0178 1007.684 -0.503151 0.6217 R-squared 0.259900 Mean dependent var 1650.427 Adjusted 0.213643 S.D. dependent var 2069.045
R-squared S.E. of 1834.762 Akaike info criterion 17.97166 regression Sum squared 53861631 Schwarz criterion 18.07059 resid Log -159.7449 F-statistic 5.618693 likelihood Durbin-Watson 1.785736 Prob(F-statistic) 0.030672 stat 3）将残差的绝对值对销量的倒数回归： Dependent Variable: ABS_RESID Method: Least Squares
Date: 05/14/03 Time: 23:44 Sample: 1 18
Included observations: 18 Variable CoefficStd. t-StatiProb.ient Error stic INVERST_X -19924412318-1.61740.12570 142 90 3
C 2273.69604.63.760040.001
5 991 3 7 R-squared 0.14053 Mean dependent 1650.7 var 427
Adjusted 0.08682 S.D. dependent 2069.R-squared 0 var 045 S.E. of 1977.18 Akaike info 18.12regressio9 criterion 118 n Sum 6254839 Schwarz 18.22squared 5 criterion 011 resid Log -161.09 F-statistic 2.616likelihoo06 274 d
Durbin-Wa1.50557 Prob(F-statist0.125tson stat 1 ic) 315 分析上面残差对销量、销量的平方根、销量的倒数分别回归的结果（解释变量：销量的平方根显著），可以看见原回归中存在异方差性。
修正：从对原模型的回归结果的残差描图，我们能看到误差绝对值正比于销售量的平方根，以及从上面1）～3）的回归中可以看到：2）中的销量的平方根显著性最好，因而，可利用销售量的平方根除以原来的回归式两边，变换得到以下结果：
YX??11X??2X?u'
回归得：
Dependent Variable: Y_SQR_X Method: Least Squares
Date: 05/15/03 Time: 00:06 Sample: 1 18
Included observations: 18 Variable CoefficStd. t-StatiProb.ient Error stic INVERST_S-246.67381.1-0.64720.526QR_X 81 279 32 7 SQR_X 0.036790.0075.172330.000
8 114 3 1 R-squared 0.36489 Mean dependent 8.8551 var 279
Adjusted 0.32519 S.D. dependent 8.834R-squared 7 var 377 S.E. of 7.25712 Akaike info 6.906regressio3 criterion 283 n Sum 842.653 Schwarz 7.005squared 5 criterion 214 resid Log -60.156 Durbin-Watson 2.885likelihoo55 stat 304 d 与原来的回归结果相比较，斜率系数相差甚微，但是后者的方差要小些，表明原来的回归确实高估了标准误差。
对于调整后回归式中第一个项不显著？？？？
7. 解答：（1）直接回归得到下面结果：
Dependent Variable: Y Method: Least Squares
Date: 05/15/03 Time: 17:09 Sample: 1 20
Included observations: 20 Variable CoefficStd. t-StatiProb.ient Error stic X 0.757430.1495.051550.0003 941 9 1
C 4.610281.0844.249470.000R-squared Adjusted R-squared S.E. of regression Sum 206.976 Schwarz 5.474squared 1 criterion 321 resid Log -51.747 F-statistic 25.51likelihoo48 825 d
Durbin-Wa2.60721 Prob(F-statist0.000tson stat 2 ic) 083
可以看见回归中系数是显著的，F检验通过，拟合效果尚可。分析残差，看看是否有异方差存在。做ARCH（p＝3）检验，结果如下：
ARCH Test: F-statist1.00638 Probability 0.421ic 8 158 Obs*R-squ3.20402 Probability 0.361ared 3 226 Test Equation:
Dependent Variable: RESID^2 Method: Least Squares
Date: 05/15/03 Time: 17:12 Sample(adjusted): 4 20
Included observations: 17 after adjusting endpoints Variable CoefficStd. t-StatiProb.ient Error stic C 10.37066.1901.675160.1172 820 1 8
RESID^2(-0.335300.2761.211290.247
1) 8 818 6 3 RESID^2(--0.40630.271-1.49910.157
2) 36 045 49 7 RESID^2(-0.098430.2850.345190.735
3) 1 143 7 5 R-squared 0.18847 Mean dependent 10.542 var 712
Adjusted 0.00119 S.D. dependent 14.61
2 0.586380
0.56340
2
3.39096
9 906 8 Mean dependent var
S.D. dependent var
Akaike info criterion 5 8.530000 5.131954 5.374748
R-squared 6 var S.E. of 14.6084 Akaike info regressio6 criterion n Sum 2774.29 Schwarz squared 1 criterion resid Log -67.428 F-statistic likelihoo92 d
Durbin-Wa1.93744 Prob(F-statisttson stat 6 ic)
可以初步判断无异方差存在。再做white检验验证：
White Heteroskedasticity Test: F-statist0.53902 Probability ic 1 Obs*R-squ1.19265 Probability ared 3 Test Equation:
Dependent Variable: RESID^2 Method: Least Squares
Date: 05/15/03 Time: 17:14 Sample: 1 20
Included observations: 20 Variable CoefficStd. t-Statiient Error stic C 19.132411.821.617311 977 0
X -2.32303.322-0.6992
06 171 43
X^2 0.061840.1130.54678
8 112 4 R-squared 0.05963 Mean dependent 3 var
Adjusted -0.0509 S.D. dependent R-squared 99 var S.E. of 13.7653 Akaike info regressio9 criterion n Sum 3221.26 Schwarz squared 0 criterion
720
8.403402 8.599453 1.006388 0.421158
0.592965 0.550832 Prob. 0.1242 0.493
9 0.591
6 10.34880 13.42726 8.219673 8.369032