Question 2 (20 points) A corporation that operates a number of hotel chains in the province is interested in developing a short-term forecasting model for the number of occupied rooms in the hotels. The corporation needed the forecasts in decision making with regard to hiring personnel, ordering materials, budgeting for advertising expenditures, etc. The data consisted of the number of occupied rooms during each day for the 15 years from 2000 to 2014. The variables of the model were quarterly room averages (Yt), trend (t) over the period and the dummy variables for the 4 quarters (Qi=1 if the period is quarter i, Qi=0 otherwise, i=1, 2, 3, 4). Consider the model: Y; : o + '61t + QlQlt + 6Q2Q2t + Q3Q3t + 8t where 6t : pt_1 + at and ut N it'd N (0, 02). [8]a. Test for a positive autocorrelation at the 5% level of signicance. Interpret the results in the context of the problem. [12]b. Find the point forecast and the 95% prediction intervals of occupied rooms for the first quarter of 2015, given that Sf. = 0.09764. Interpret the results in the context of the