Sometimes it is desired to “correct for” binary, continuous, or categorical variables (“covariates”) that may also be influencing the dependent variable, or for first-order interactions between these covariates. This allows the researcher to see specifically what effects there are on the dependent variable that are strictly genetic. (See 26.10.)

To do this, first, a linear regression which includes only the dependent and the covariates is done (the “reduced model”). Then, a linear regression which includes not only the dependent and the covariates, but also the haplotype frequencies (as determined in the same way as for HTR (26.7)) (the “full model”) is done.

An F-test is then done to find the significance of including the haplotype frequencies vs. not including the haplotype frequencies. Specifically, if for n observations, regssf, errssf, regssr, and errssr are defined for the full model and the reduced model, respectively, the same way as regss and errss are for performing just HTR (26.6), then the F-test is

where df2 = n - numFull - 1, numFull = the full-model size, and numDiff = the difference in model sizes.

HelixTree also allows simply doing a regression on covariates and haplotype frequencies put together, without “correcting for” either one. Here, the F-test is the same as for performing just HTR, except that the regressors also include the covariates. (26.6).