The Null Hypothesis - H0: β_{1 }= 0 i.e. there is homoscedasticity errors and no heteroscedasticity exists
The Alternative Hypothesis - H1: β_{1 }≠ 0 i.e. there is no homoscedasticity error and there is heteroscedasticity
MTB > let c33=loge(c20)
MTB > let c34=loge(c7)
MTB > let c35=loge(c8)
MTB > let c36=loge(c9)
MTB > let c37=loge(c10)
C33 = lnsqres
C34 = lntotexp
C35 = lnincome
C36 = lnage
C37 = lnnk
Regression Analysis: lnsqres versus lntotexp
The regression equation is
lnsqres = - 5.41 - 0.155 lntotexp
Predictor Coef SE Coef T P
Constant -5.4069 0.6430 -8.41 0.000
lntotexp -0.1550 0.1420 -1.09 0.275
S = 2.15075 R-Sq = 0.1% R-Sq(adj) = 0.0%
Analysis of Variance
Source DF SS MS F P
Regression 1 5.515 5.515 1.19 0.275
Residual Error 1517 7017.227 4.626
Total 1518 7022.743
Since β_{1 }≠ 0 and is 0.155, H1 would be accepted suggesting that there are no homoscedasticity errors but there is indication that there is heteroscedasticity.
Regression Analysis: lnsqres versus lnincome
The regression equation is
lnsqres = - 5.77 - 0.070 lnincome
Predictor Coef SE Coef T P
Constant -5.7687 0.7111 -8.11 0.000
lnincome -0.0698 0.1465 -0.48 0.634
S = 2.15143 R-Sq = 0.0% R-Sq(adj) = 0.0%
Analysis of Variance
Source DF SS MS F P
Regression 1 1.050 1.050 0.23 0.634
Residual Error 1517 7021.693 4.629
Total 1518 7022.743
Since β_{1 }≠ 0 and is 0.070, H1 would be accepted suggesting that there are no homoscedasticity errors but there is indication that there is heteroscedasticity.
Regression Analysis: lnsqres versus lnage
The regression equation is
lnsqres = - 7.23 + 0.315 lnage
Predictor Coef SE Coef T P
Constant -7.2276 0.9125 -7.92 0.000
lnage 0.3155 0.2563 1.23 0.219
S = 2.15052 R-Sq = 0.1% R-Sq(adj) = 0.0%
Analysis of Variance
Source DF SS MS F P
Regression 1 7.007 7.007 1.52 0.219
Residual Error 1517 7015.736 4.625
Total 1518 7022.743
Since β_{1 }≠ 0 and is 0.315, H1 would be accepted suggesting that there are no homoscedasticity errors but there is indication that there is heteroscedasticity.
Regression Analysis: lnsqres versus lnnk
The regression equation is
lnsqres = - 5.99 - 0.281 lnnk
Predictor Coef SE Coef T P
Constant -5.98771 0.08819 -67.89 0.000
lnnk -0.2812 0.1631 -1.72 0.085
S = 2.14949 R-Sq = 0.2% R-Sq(adj) = 0.1%
Analysis of Variance
Source DF SS MS F P
Regression 1 13.738 13.738 2.97 0.085
Residual Error 1517 7009.004 4.620
Total 1518 7022.743
Since β_{1 }≠ 0 and is 0.281, H1 would be accepted suggesting that there are no homoscedasticity errors but there is indication that there is heteroscedasticity.
MTB > # lntotexp is significant and estimate of beta/2 is -0.155/2 or -0.775