Two n × n matrices A and B are orthogonal if AB = BA = 0. Show that I − H and H are orthogonal. Use this result to show that as long as the intercept is in the mean function, the slope of the...

Two n × n matrices A and B are orthogonal if AB = BA = 0. Show that I − H and H are orthogonal. Use this result to show that as long as the intercept is in the mean function, the slope of the regression of ê on Ŷ is 0. What is the slope of the regression of ê on Y?

California water (Data file: water) Draw residual plots for the mean function described in for the California water data, and comment on your results. Test for curvature as a function of fitted values.