We can now proceed to check whether a
regression model still produces trustworthy results in
this scenario of non-normal predictor and response
variables, but normal errors. Firstly, we will briefly
check that regression via ordinary least squares
provides coefficients that are unbiased. We will do this
by running a simulation in which we generate a large
number of samples (10,000), each sample having a total
of 30 cases, or 15 cases in each subsample formed by
the dichotomous predictor variable. A linear regression
model is then fit in each sample, the coefficient for the
effect of X on Y is estimated, and summary statistics
are calculated for the coefficients. The results are
displayed in Table 1.