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 >

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 = , 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.