Chapter 5. Statistical aspects of regression
Statistics is a field of study based on mathematics and probability theory. However, since this book assumes you have little knowledge of these topics, a complete understanding of statistical issues in the regression model will have to await further study. What we will do instead in this chapter is to: (1) discuss what statistical methods in the regression model are designed to do; (2) show how to carry out a regression analysis using these statistical methods and interpret the results obtained; and (3) provide some graphical intuition in order to gain a little insight into where statistical results come from and why these results are interpreted in the manner that they are.
We will begin by stressing a distinction which arose in the previous chapter between the regression coefficients, α and β and the OLS estimates of the regression coefficients,
for i = 1, ..., N observations. As noted previously, α and β measure the relationship between Y and X. We pointed out that we do not know what this relationship is, i.e., what precisely α and β are. We derived so-called ordinary least squares or OLS estimates which we then labeled
These considerations ...