The Null Hypothesis - H0: γ_{1} = γ_{2 = ... = }0 i.e. there is no heteroscedasticity in the model
The Alternative Hypothesis - H1: at least one of the γ_{i}'s are not equal to zero i.e. the squared residuals are related to one of the independent variables.
Reject H0 if nR^{2} >
MTB > let c23 = c7*c7
MTB > let c24 = c8*c8
MTB > let c25 = c9*c9
MTB > let c26 = c10*c10
MTB > let c27 = c7*c8
MTB > let c28 = c7*c9
MTB > let c29 = c7*c10
MTB > let c30 = c8*c9
MTB > let c31 = c8*c10
MTB > let c32 = c9*c10
C7 = totexp
C8 = income
C9 = age
C10 = nk
C23 = sqtotexp
C24 = sqincome
C25 = sqage
C26 = sqnk
C27 = totexpincome
C28 = totexpage
C29 = totexpnk
C30 = incomeage
C31 = incomenk
C32 = agenk
Regression Analysis: sqres versus totexp, income, ...
* sqnk is highly correlated with other X variables
* sqnk has been removed from the equation.
The regression equation is
sqres = 0.0178 - 0.000232 totexp + 0.000023 income + 0.000298 age - 0.00555 nk
+ 0.000001 sqtotexp + 0.000000 sqincome - 0.000005 sqage
- 0.000000 totexpincome + 0.000003 totexpage + 0.000015 totexpnk
- 0.000001 incomeage + 0.000035 incomenk - 0.000021 agenk
Predictor Coef SE Coef T P
Constant 0.017804 0.007900 2.25 0.024
totexp -0.00023207 0.00005370 -4.32 0.000
income 0.00002344 0.00003865 0.61 0.544
age 0.0002978 0.0003511 0.85 0.396
nk -0.005551 0.003233 -1.72 0.086
sqtotexp 0.00000060 0.00000011 5.65 0.000
sqincome 0.00000004 0.00000002 1.79 0.074
sqage -0.00000464 0.00000427 -1.09 0.277
totexpincome -0.00000041 0.00000013 -3.27 0.001
totexpage 0.00000259 0.00000110 2.36 0.018
totexpnk 0.00001477 0.00001740 0.85 0.396
incomeage -0.00000110 0.00000090 -1.22 0.223
incomenk 0.00003506 0.00001355 2.59 0.010
agenk -0.00002146 0.00008647 -0.25 0.804
S = 0.0123952 R-Sq = 3.4% R-Sq(adj) = 2.5%
Analysis of Variance
Source DF SS MS F P
Regression 13 0.0080446 0.0006188 4.03 0.000
Residual Error 1505 0.2312304 0.0001536
Total 1518 0.2392750
Source DF Seq SS
totexp 1 0.0003007
income 1 0.0000070
age 1 0.0000053
nk 1 0.0000429
sqtotexp 1 0.0037616
sqincome 1 0.0000507
sqage 1 0.0001055
totexpincome 1 0.0010903
totexpage 1 0.0005678
totexpnk 1 0.0009260
incomeage 1 0.0001557
incomenk 1 0.0010217
agenk 1 0.0000095
MTB > let k4=1519*0.034
MTB > print k4
Data Display
K4 51.6460
MTB > InvCDF 0.95;
SUBC> ChiSquare 13.
Inverse Cumulative Distribution Function
Chi-Square with 13 DF
P( X <= x ) x
0.95 22.3620
MTB > # Since nrsq = 1519*0.034= 51.6460 > chi=22.360 we have hetero from white test# Also both B-P and White test seem to indicate that totexp is the culprit
Since nrsq = 51.6460 > 22.360 = , there is sufficient evidence to reject H0 which suggests that there is heteroscedasticity in the model from White's general heteroscedasticity test at the 5% significance level. Both Breusch Pagan test and White's general heteroscedasticity test seem to indicate that totexp is the culprit as the T value is significant and the P-value is 0.000.