The quarterly sales () on five years, where denotes time, of a product are given in the following table: Year 1 2 Quarter y 1 2 3 4 I 2 3 4 I 2 3 4 1 2 3 4 1 2 31 42 HEBERRECHNER 21 13 33 45 19 15 36 52 15 37 52 22 24 40 3 50 4 23 Assume that the model that fits the data is given by equation y, = Bo + fit + fQ + BQ + BQ4+er where .. O.. and are the appropriately defined dummy variables for quarters 2, 3 and 4. Statistical softwares may give similar results, but here only use excel. (3.1) Write down the definitions of the dummy variables Q. Os and 04. (3.2) Plot y against for = 1.2..... 20. Use Excel. (3.3) What type of seasonal variation appears to exist? Explain your answer. (3.4) Fit model (E), then write down the prediction model. Use Excel. (3.5) Use the results in part (3.4) to calculate fe, and its 95% prediction interval. [6] [3] [8] [9] [30]