Alex is a street vendor selling T-shirts in New York City. His sales in past ten weeks are listed as below. Weeks Sales (1, 33) (2, 31) (3, 31) (4, 37) (5, 40) (6, 33) (7, 50) (8, 45) (9, 55) (10, 60)
(1) Alex wants to prepare for future sales. Please make forecast, based on historical data, for sales in week 11 and 12, using the following methods: moving average (3), moving average (4), moving average (5), exponential smoothing (0.1), exponential smoothing (0.4), exponential smoothing (0.8). Compare “the mean absolution deviation (MAD)” and “Forecast error” among these methods.
(2) Please make forecast using the simple linear regression. What is the model? Is the model valid (residual analysis)? What is the significance of the regression model (R2, p-value of the slope)?
(3) Compare the smoothing methods with the regression. Which method would you recommend? Why?