Chapter 8 Regression and Correlation 329
Checking the Regression Model
As in any statistical procedure, for statistical inference on a regression, you
are making some important assumptions. There are four:
- The straight-line model is correct.
- The error term e is normally distributed with mean 0.
- The errors have constant variance.
- The errors are independent of each other.
Whenever you use regression to fi t a line to data, you should consider these
assumptions. Fortunately, regression is somewhat robust, so the assumptions
do not need to be perfectly satisfi ed.
One point that cannot be emphasized too strongly is that a signifi cant re-
gression is not proof that these assumptions haven’t been violated. To verify
that your data do not violate these assumptions is to go through a series of
tests, called diagnostics.
Testing the Straight-Line Assumption
To test whether the straight-line model is correct, you should fi rst create a
scatter plot of the data to inspect visually whether the data depart from this
assumption in any way. Figure 8-14 shows a classic problem that you may
see in your data.
Figure 8-14
A curved
relationship
Another sharper way of seeing whether the data follow a straight line is
to fi t the regression line and then plot the residuals of the regression against
the values of the predictor variable. A U-shaped (or upside-down U-shaped)
pattern to the plot, as shown in Figure 8-15, is a good indication that the data
follow a curved relationship and that the straight-line assumption is wrong.
