Tests for heteroscedasticity, Advanced Statistics

The Null Hypothesis - H0: There is no heteroscedasticity i.e. β1 = 0

The Alternative Hypothesis - H1:  There is heteroscedasticity i.e. β1 0

Reject H0 if nR2 > 1640_Tests for Heteroscedasticity.png

MTB > let c20 = c11*c11 

MTB > let c21 = c15*c15

C20 = sqres

C21 = sqrfits

C11 = RESI1

C15 = FITS1

Regression Analysis: sqres versus sqfits

The regression equation is

sqres = 0.00597 + 0.0168 sqfits

Predictor      Coef   SE Coef     T      P

Constant   0.005967  0.001281  4.66  0.000

sqfits     0.016760  0.009539  1.76  0.079

S = 0.0125463   R-Sq = 0.2%   R-Sq(adj) = 0.1%

Analysis of Variance

Source            DF         SS         MS     F      P

Regression         1  0.0004859  0.0004859  3.09  0.079

Residual Error  1517  0.2387891  0.0001574

Total           1518  0.2392750

MTB > let k1 = 1519*0.02

MTB > print k1

Data Display

K1    30.3800

Inverse Cumulative Distribution Function

Chi-Square with 1 DF

P( X <= x )        x

       0.95  3.84146

MTB > # Since nrsq = 1519*0.02 > chi = 3.8415, we have hetero from LM test

Since nR2 = 30.380 > 3.8415 = 1640_Tests for Heteroscedasticity.png, there is sufficient evidence to reject H0 which suggest that there is heteroscedasticity from the Lagrange Multiplier (LM) test at 5% significance level which means that one or more slopes are not zero.

Posted Date: 3/4/2013 5:44:54 AM | Location : United States

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