The Null Hypothesis - H0: β1 = 0 i.e. there is homoscedasticity errors and no heteroscedasticity exists
The Alternative Hypothesis - H1: β1 ≠ 0 i.e. there is no homoscedasticity error and there is heteroscedasticity
Regression Analysis: lnsqresi versus lntotexp
The regression equation is
lnsqresi = - 4.82 - 0.301 lntotexp
Predictor Coef SE Coef T P VIF
Constant -4.8198 0.6893 -6.99 0.000
lntotexp -0.3009 0.1523 -1.98 0.048 1.000
S = 2.26403 R-Sq = 0.3% R-Sq(adj) = 0.2%
Analysis of Variance
Source DF SS MS F P
Regression 1 20.015 20.015 3.90 0.048
Residual Error 1500 7688.739 5.126
Lack of Fit 28 160.408 5.729 1.12 0.304
Pure Error 1472 7528.331 5.114
Total 1501 7708.754
Since β1 ≠ 0 and is -0.301, H1 would be accepted suggesting that there are no homoscedasticity errors but there is indication that there is heteroscedasticity.
Regression Analysis: lnsqresi versus lnage
The regression equation is
lnsqresi = - 7.75 + 0.442 lnage
Predictor Coef SE Coef T P VIF
Constant -7.7468 0.9747 -7.95 0.000
lnage 0.4419 0.2739 1.61 0.107 1.000
S = 2.26501 R-Sq = 0.2% R-Sq(adj) = 0.1%
Analysis of Variance
Source DF SS MS F P
Regression 1 13.355 13.355 2.60 0.107
Residual Error 1500 7695.399 5.130
Lack of Fit 40 131.348 3.284 0.63 0.964
Pure Error 1460 7564.051 5.181
Total 1501 7708.754
Since β1 ≠ 0 and is 0.442, H1 would be accepted suggesting that there are no homoscedasticity errors but there is indication that there is heteroscedasticity.