We begin by looking at a simple way to predict a quantitative response, Y, with one predictor variable, x, assuming that Y has a linear relationship with x. The model for this can be written as follows:
We can state it as the expected value of Y is a function of the parameters 
(the intercept) plus 
(the slope) times x, plus an error term e. The least squares approach chooses the model parameters that minimize the Residual Sum of Squares (RSS) of the predicted y values versus the actual Y values. For a simple example, let's say we have the actual values of Y1 and Y2 equal to 10 and 20 respectively, along with the predictions of y1 and y2 as 12 and 18. To calculate RSS, we add the squared differences:
This, with simple substitution, yields the following:
Before we begin with an application, I want to point out that if you read the headlines...
