Page 94 - Applied Statistics with R

94 CHAPTER 7. SIMPLE LINEAR REGRESSION

Stopping Distance vs Speed

120 100
Stopping Distance (in Feet) 80 60 40

0 20
5 10 15 20 25

Speed (in Miles Per Hour)

With this in mind, we would like to restrict our choice of ( ) to linear functions
of . We will write our model using for the slope, and for the intercept,
0
1
= + + .
1
0
7.1.1 Simple Linear Regression Model

We now define what we will call the simple linear regression model,

= + +
0

1
where

2
∼ (0, ).

That is, the are independent and identically distributed (iid) normal random

2
variables with mean 0 and variance . This model has three parameters to be
2
estimated: , , and , which are fixed, but unknown constants.
0
1
We have slightly modified our notation here. We are now using and , since

we will be fitting this model to a set of data points, for = 1, 2, … .