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.