a. Consider the data in Exercise 20. Suppose that instead of the least squares line passing through the points (x1, y1),..., (xn, yn), we wish the least squares line passing through (x1 x2, y1) ,..., (xn - x̅, yn). Construct a scatter-plot of the (xi, yi) points and then of the (xi - x̅, yi) points. Use the plots to explain intuitively how the two least squares lines are related to one another.
b. Suppose that instead of the model Yi = β0 + β1xi +εi (i = 1,..., n), we wish to fit a model of the form Yi = β*0 + β*1 (xi - x̅) + εi (i = 1, ...., n). What are the least squares estimators of β*0 and β*1, and how do they relate to 0 and 1?