Anon

Robust Regressions 165

When we examined the diagonal of the hat matrix, we found the fol-
lowing results:

Maximum leverage = 0.0189

Mean leverage = 4.0783e–004

suggesting that there is no dangerous point. Robust regression can be
applied; that is, there is no need to change the regression design. We applied
robust regression using the Huber and Tukey weighting functions with the
following parameters:

Huber (k = 1.345 × standard deviation)

and

Tukey (k = 4.685 × standard deviation)

The robust regression estimate with Huber weighting functions yields the
following results:

R^2 = 0.1324

Adjusted R^2 = 0.1322

Weight parameter = 0.0287

Number of iterations = 39

Beta t-Statistic Change in p-Value

β 0 –0.000706 –0.767860 0.442607

β 1 0.405633 7.128768 0.000000

The robust regression estimate with Tukey weighting functions yields
the following results:

R^2 = 0.1315

Adjusted R^2 = 0.1313

Weight parameter = 0.0998

Number of iterations = 88

Beta t-Statistic Change in p-Value

β 0 –0.000879 –0.632619 0.527012

β 1 0.400825 4.852742 0.000001