Residual Standard Error and R2
Summary
•
We want to measure how useful a linear model is for predicting the response
variable.
•The residual standard error is the standard deviation of the residuals
–Smaller residual standard error means predictions are better
•The R2is the square of the correlation coefficient r
–Larger R2means the model is better
–
Can also be interpreted as “proportion of variation in the response variable
accounted for by the linear model” - see later statistics classes or the book
for why.
Example data set
We have a data set with observations of four variables measuring advertising budgets
and sales for a product in each of 200 markets:
•sales is a measure of sales volume in thousands of units
•TV is TV advertising budget in thousands of dollars
•radio is radio advertising budget in thousands of dollars
•newspaper is newspaper advertising budget in thousands of dollars
Below are plots displaying three separate simple linear regression fits to the data. In all
three plots/models,
sales
is the response variable; the explanatory variable is different
for each model.
10
20
0 100 200 300
TV
sales
10
20
0 10 20 30 40 50
radio
sales
10
20
0 30 60 90
newspaper
sales
1
