Matching standardized scores refer to the previous two

Question

Question - Matching standardized scores. Refer to the previous two exercises. An alternative to the least-squares method is based on matching standardized scores. Specifically, we set

x-y^-/s_y = x-x^-/s_x

and solve for y. Let's use the notation y = a0 + a1x for this line. The slope is a1 = sy/sx and the intercept is a₀ = y^- - a₁x^-. Compare these expressions with the formulas for the least-squares slope and intercept.

(a) Using the data in the previous exercise, find the values of a0 and a1.

(b) Plot the data with the least-squares line and the new prediction line.

(c) Use the new line to find predicted ACT scores. Find the mean and the standard deviation of these scores. How do they compare with the mean and standard deviation of the actual ACT scores?