Tests for heteroscedasticity, Advanced Statistics

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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.

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