It is usually normal to find a strong correlation between slopes and intercepts in regressions. This is usually seen in every method comparison analysis. For the very same reason also the two linear parameter Alpha and Beta that model the variance variation for the heteroscedastic linear method show correlation. Where a correlation should not be found is between the crossed pairs Alpha (and Beta) with slope (and intercept). For this reason a pairs plot is a very important diagnostic tool to validate the overall result.

As shown in the picture the pairs Alpha/slope, Alpha/intercept, Beta/slope and Beta/intercept do not show a manifest correlation. This pair plot has been generated with the data and the regression reported in the previous post.

Worth noting is the fact that the credibility intervals CI for Beta do not contain the zero. This could be interpreted as a confirmation for fact that the error term is not homoscedastic.

The heteroscedastic linear model could become an important tool for method comparison. As previously reported in arxiv.org (pag. 24-31), using an homogeneous error term in an heteroscedastic situation leads to an important power loss of the test.