# Simple Linear Regression

In this chapter you are introduced to the simple linear regression model, which is estimated using the principle of least squares.

2.1 Simple Linear Regression Model

The simple linear regression model is

food-expt = ві + в2incomet + et t = 1, 2,…, T (2.1)

where food-expt is your dependent variable, incomet is the independent variable, et is random error, and в1 and в2 are the parameters you want to estimate. The errors of the model, et, have an average value of zero for each value of incomet; each has the same variance, a2, and are uncorrelated with one another. The independent variable, incomet, has to take on at least two different values in your dataset. If not, you won’t be able to estimate a slope! The error assumptions can be summarized as etlincomet iid N(0,a2). The expression iid stands for independently and identically distributed and means that the errors are statistically independent from one another (and therefore uncorrelated) and that each has the same probability distribution. Taking a random sample from a single population accomplishes this.