13.6 - Robust Regression Examples

Quality Measurements Dataset Section

Let us look at the three robust procedures discussed earlier for the Quality Measure data set. These estimates are provided in the table below for comparison with the ordinary least squares estimate.

A comparison of M-estimators with the ordinary least squares estimator for the quality measurements data set (analysis done in R since Minitab does not include these procedures):

Method \(\boldsymbol{\beta_{0}}\) p-value \(\boldsymbol{\beta_{1}}\) p-value
OLS 29.2342 0.0276 0.5235 0.0045
Andrew's Sine 29.0080 0.0177 0.5269 0.0024
Huber's Method 29.5428 0.0204 0.5183 0.0036
Tukey's Biweight 29.1399 0.0203 0.5248 0.0030

While there is not much of a difference here, it appears that Andrew's Sine method is producing the most significant values for the regression estimates. One may wish to then proceed with residual diagnostics and weigh the pros and cons of using this method over ordinary least squares (e.g., interpretability, assumptions, etc.).