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

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 β₁ ≠ 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 β₁ ≠ 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 β₁ ≠ 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 β₁ ≠ 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