Garish Motors sells new and used automobiles. Sales of new cars over the past 50 weeks are given in the following table (week 50 is the most recent).

a. Compute a forecast for sales next week by using a 4-week moving average. What is the forecast? What is the MSE for the last five observations?
b. Can you reduce the MSE for the last five observations by changing the moving-average window? (Try 5- to 10-week windows.)
c. Compute a forecast for sales next week by using exponential smoothing with α = 0.25. What is the forecast? What is the MSE for the last five observations?
d. Can you improve the MSE for the last five observations by changing the smoothing constant α?

Week Sales Week Sales 36 26 42 27 50 28 59 29 49 72 30 58 54 31 52 49 37 59 34 41 35 53 36 42 37 13 52 38 14 55 39 15 45 40 51 16 41 17 42 18 44 43 19 64 44 20 59 45 21 55 46 22 30 47 23 60 48 24 53 25 47