4.  HBK, a food industry company wants to build a forecasting model to predict the sales of its hot-beverage.  HBK had the last weekly sales for the past 152 weeks.  Using the time series components for trend (variable called tp) and seasonal--monthly dummy variables (using Dec as a baseline) and the causal variable of average weekly temperature HBK management build the model on the following page.  

Note the average hot-beverage weekly sales is $91,500. 

a.  Evaluate the model on the following page, i.e., is it a good model?  If so, why, or if not, why?   Consider all the appropriate tests, use α = 0.05 for t test and α = 0.05 for F test.   Notice on the following page is a plot of the residuals.

DO ALL APPROPRIATE TESTS--COMPLETELY!!!!

b. If you believe the model is OKAY, provide at least two reasons to justify your belief.  On the other hand, if you believe the model is not OKAY, provide suggestions on how you would improve the model.

c.  Ranking the order of the months in terms of their impact on weekly sales, i.e., which month has the highest expected weekly sales, next highest, and which are the lowest and second lowest?

(d).   Show how you will code the dummy variables in this model, in other words fill in 13 rows with your dummy variables in the table below. (the first column, Month, tells you what month it is).

(e).  What is the model’s predicted value or forecast for time period 20, which is August, and the average monthly temperature is 80?