Tony Lin's Virtual Statistics 153 page.
Regression is a method by which a line is fit to data.
The Classical Linear Model in regression assumes that the Y's are independent random variables, that the expected value of Y given x is a linear function of x, that the x's are fixed, that the variance of Y given x is constant, and that the distribution of Y given x is normal. Under these assumptions, certain distributional results follow. On the other hand, if the assumptions of the Classical Linear Model don't hold, then neither do the conclusions. An important task when doing regression is detecting failures in the assumptions . However, if certain fundamental assumptions do not hold, then there are no fixes, such as in the case of ecological regression .