(DO NOT attempt to solve.) Briefly identify/describe each decision variable, constraint and objective function. (106) 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 = 0.05 for t test and = 0.05 for F test. Notice on the following page is a plot of the residuals. DO ALL APPROPRIATE TESTS--COMPLETELY!!!! SUMMARY OUTPUT Regression Statistics Multiple R 0.938986698 R Square 0.881696019 Adjusted R Square 0.870551442 Standard Error 24568.19214 Observations 152 ANOVA df Regression Residual Total Intercept Avg Wkly Temp tp jan feb mar apr may june july aug sept oct nov SS MS F Significance F 13 6.21E+11 4.78E+10 79.11435 3.1962E-57 138 8.33E+10 6.04E+08 151 7.04E+11 CoefficientsStandard Error t Stat 310087.8302 16946.59 18.29795 -3061.992316 422.168 -7.25302 -121.7295379 48.8318 -2.49283 -9403.035399 9804.198 -0.95908 -62170.23081 9736.695 -6.38515 -96755.45052 9218.706 -10.4956 -102641.6381 10804.93 -9.49952 -84366.23824 12591.13 -6.70045 -67300.87655 15170.72 -4.43623 -50828.00036 17678.64 -2.87511 -50053.40056 17556.73 -2.85095 -30996.70032 16231.6 -1.90965 -7752.772946 13284.86 -0.58358 8454.529621 10022.2 0.84358 P-value 1.01E-38 2.66E-11 0.013855 0.339194 2.43E-09 2.63E-19 8.92E-17 4.86E-10 1.86E-05 0.00468 0.005029 0.058253 0.560456 0.400364 Lower 95% Upper 95%Lower 95.0% Upper 95.0% 276579.255 343596.4 276579.3 343596.4 -3896.747343 -2227.24 -3896.75 -2227.24 -218.284909 -25.1742 -218.285 -25.1742 -28788.92686 9982.856 -28788.9 9982.856 -81422.6488 -42917.8 -81422.6 -42917.8 -114983.6446 -78527.3 -114984 -78527.3 -124006.2813 -81277 -124006 -81277 -109262.7415 -59469.7 -109263 -59469.7 -97298.02853 -37303.7 -97298 -37303.7 -85784.06342 -15871.9 -85784.1 -15871.9 -84768.4121 -15338.4 -84768.4 -15338.4 -63091.52449 1098.124 -63091.5 1098.124 -34020.99187 18515.45 -34021 18515.45 -11362.41579 28271.48 -11362.4 28271.48 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? Highest 1 2 3 4 5 6 7 8 9 10 11 12 HIGHEST Lowest _________________ NEXT HIGHEST _________________ * * SECOND LOWEST _________________ 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). Month Jan Feb Mar Apr May Jun July Aug Sept Oct Nov Dec Jan (e). What is the model's predicted value or forecast for time period 20, which is August, and the average monthly temperature is 80