QSAR Nightmare—No More

In Chapter 5, when discussing the use of co-linear descriptors in regression analysis, we mentioned the instability of regression equations. Here we will illustrate the Nightmare of QSAR on a regression using four connectivity indices % of 

Observe that the statistical data, the coefQdent of the regressions and the standard errors, are the same in Tables A20.1 and A20.2, but the regressions in Table A20.2 are stable, and the coefficients of descriptors already used do not change when a new orthogonal descriptor is added into the next stepwise regression. Hence, the relative contributions of individual descriptors in the regression are constant 

It is very interesting to compare the coefQcients in Tables A20.1 and A20.2. Look at the entries along the diagonal in the two tables  

They are the same. The constant terms in Table A20.2 are all the same and eqnal to the constant term in the first equation. Because of this, from Table A20.1 alone (which is based on regressions using non-orthogonal connectivity indices x  

Illustration of the QSAR Nightmare Stepwise Regressions for the Hosoya Z Topological Index Using the /- z Connectivity 

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