CLT and regression

Hello,

Can someone explain how the central limit theorem is related to
regression analysis? I understand the basics of the CLT, but don't
understand its relationship with regression analyis. I am conducting
an analysis with approx. 1000 subjects. These subjects have a score
between 0-100 on a certain physical functioning (PF) scale. PF is the
dependent variable in my analysis. The distribution of these scores are
highly skewed. Can I still use linear regression analysis? Or should I
go for non-parametric or bootstrapping techniques?

Thanks

.