Chapter 7 Simple Linear Regression

Suppose you have two homes that are the same in every way except for size. Our intuition would suggest that bigger homes cost more (all else equal) so we would expect that there is a positive relationship between house size and house price.

Saying bigger homes cost more is a qualitative statement because all we are saying is that the relationship between house size and house price is positive. What if we want to make a quantitative statement? In other words, while we are fairly confident that the actual house price (say, in dollars) will increase for every unit increase in house size (say, an additional square foot) - we want to know exactly what this average-price-per-square-foot is.

A Regression can measure the relationship between the mean value of one variable and corresponding values of other variables. In other words, it is a statistical technique used to explain average movements of one (dependent) variable, as a function of movements in a set of other (independent) variables.

This chapter will discuss the estimation, interpretation, and statistical inference of a simple linear regression model, which means that we will attempt to explain the movements in a dependent variable by considering one independent variable. This is the simplest regression model we can consider in order to understand what is going on under the hood of a regression. The next chapter will extend this analysis to multiple regression models where the only real difference is that the number of independent variables are greater than one.