Question: a. What is so special about the least-squares line that distinguishes it from all other lines?
b. How does the least-squares line "know" that it is predicting Y from X instead of the other way around?
c. It is reasonable to summarize the "most typical" data value as having X as its X value and Y as its Y value. Show that the least-squares line passes through this most typical point.
d. Suppose the standard deviations of X and of Y are held fixed while the correlation decreases from one positive number to a smaller one. What happens to the slope coefficient, b?