Introduction to Regression & Correlation
, we explore the possible relationship between a quantitative
vari- able and one (or more)
variables. The explanatory variable(s) can be a
quantitative or qualitative random variable, but for now we will only consider quantitative variables.
When we have one explanatory variable:
When we have more than one explanatory variable:
Regression analysis allows us to describe the relationship between
The Linear Regression Model
To motivate our regression model, reconsider the following example which we first saw when we intro-
duced the idea of correlation:
(Adapted from Question 13, page 675 in
Canadian Ed. (2014). Sharpe, N.R., DeVeaux, R.D.,
Velleman, P.F., Wright, D. Pearson Toronto).
Data on the number of sales associates working, and the number of
sales (in $1000s), were recorded for 10 randomly selected small book stores. The objective of the study
was to determine if there was a linear relationship between the number of sales associates on the floor
(explanatory variable) and the amount of business done in sales (response variable). A partial table of
the data is presented below.