Page 91 - Applied Statistics with R

7.1. MODELING 91

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)

Let’s now define some terminology. We have pairs of data, ( , ), for =

1, 2, … , where is the sample size of the dataset.
We use as an index, simply for notation. We use as the predictor (ex-

planatory) variable. The predictor variable is used to help predict or explain
the response (target, outcome) variable, .

Other texts may use the term independent variable instead of predictor and
dependent variable in place of response. However, those monikers imply math-
ematical characteristics that might not be true. While these other terms are
not incorrect, independence is already a strictly defined concept in probability.
For example, when trying to predict a person’s weight given their height, would
it be accurate to say that height is independent of weight? Certainly not, but
that is an unintended implication of saying “independent variable.” We prefer
to stay away from this nomenclature.

In the cars example, we are interested in using the predictor variable speed to
predict and explain the response variable dist.
Broadly speaking, we would like to model the relationship between and
using the form

= ( ) + .

The function describes the functional relationship between the two variables,
and the term is used to account for error. This indicates that if we plug in a