Tests for heteroscedasticity, Advanced Statistics

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Lagrange Multiplier (LM) test

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 > 2094_Tests for Heteroscedasticity.png

Regression Analysis: sqresi versus sqfits

The regression equation is

sqresi = 0.00517 + 0.0196 sqfits

Predictor Coef SE Coef T P VIF

Constant 0.005173 0.001130 4.58 0.000

sqfits 0.019650 0.008395 2.34 0.019 1.000

S = 0.0112996 R-Sq = 0.4% R-Sq(adj) = 0.3%

Analysis of Variance

Source DF SS MS F P

Regression 1 0.0006996 0.0006996 5.48 0.019

Residual Error 1500 0.1915214 0.0001277

Lack of Fit 646 0.0819554 0.0001269 0.99 0.559

Pure Error 854 0.1095659 0.0001283

Total 1501 0.1922209

MTB > let k1 = 1502*0.04

MTB > print k1

Data Display

K1 60.0800

Inverse Cumulative Distribution Function

Chi-Square with 1 DF

P( X <= x ) x

0.95 3.84146

Since nR2 = (1502*0.04) 60.0800 > 3.84146 = 2094_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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