The quarterly sales of the TRK-50 mountain bike for the previous four years by a bicycle shop in Switzerland is presented in the following table. Year 1 2 3 Quarter 1 2 3 4 1 2 3 4 1 2 3 st 4 1 2 3 4 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Yt 10 31 43 16 11 33 45 17 13 34 48 19 15 37 51 21 (a) By using a software of your choice, plot the time series (b) What kind of trend appears to exist? (c) What type of seasonal variation appears to exist? (d) Is a transformation needed to obtain a series that displays constant variation? (e) Fit a proper model with trend and seasonal variations terms. (f) Do all the independent variables seem to be important? Justify your answer statistically. (g) Write out the definitions of the dummy variables Q2, Q3, and Q4 (h) Predict the bike sales in year 5. Find point estimation and 95% confidence and prediction interval. (i) Write the prediction equation for the model, and use it to calculate y17 and y18