The analysis of covariance emphasizes the use of regression to fix a problem with the two-sample -test that has a confounding variable. You can also think of the use of a dummy variable as a way to...

The analysis of covariance emphasizes the use of regression to fix a problem with the two-sample
-test that has a confounding variable. You can also think of the use of a dummy variable as a way to fix a problem in the regression of
 on
. Take a look at this scatter-plot:

(a) If we fit parallel slopes to these data, with one line for the red and another for the green points, what do you think the slope will be?

(b) What happens if we estimate the slope while ignoring the presence of two clear groups? That is, if we fit a simple regression of
 on
 using all of the data?