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The analysts in the operating division of ABC Hotel were asked to develop a model that could be used to forecast the room demands in its hotels operated in Hong Kong. The available historical data consist of the monthly average number of occupied rooms during each month from 2001 to 2014. Thus, a total of 168 observations are obtained. The logarithm of these observations were then tted to the model 11 y1=o+1t+2,j2,.+s,; r =1,..., 168; j=l where for j = 1 (January), 2 (February), . . . , 11 (November); Z 1 if the observation yI is frommonth j J" 0 otherwise Source DF Sum of Squares Mean Square Model 12 6.06828 0. 505 69 Error 15 5 0.06957 0.00045 Variable DF Estimate Standard error t-statistic Intercept 1 6.2876 000642727 978 .262 T 1 0.0027 0.00003379 80.653 Z1 1 -0.0416 000801629 -5.190 Z2 1 -0.1121 0.00801479 -13.984 Z3 1 -0.0845 0.00801344 -10.540 Z4 1 0.0398 0.00801223 4.972 Z5 1 0.0020 0.00801116 0.255 Z6 1 0.1469 000801023 18.340 Z7 1 0.2890 000800945 36.085 Z8 1 0.3112 000800880 38.85? Z9 1 0.0559 000800831 6.991 Z10 1 0.03 95 000800795 4 .938 Z11 1 -0.1122 000800774 -14.013 Durbin-Watson statistics = 1.19; First order auto-correlation = 0.791 a Based on these estimation results, comment on the goodness-of-t of this model. Based on the nature of these data and the above results, discuss whether there is any violation of assumption. Give reason(s). (5 marks) b. Are the \"room demand\" models of April and May the same? Discuss. (4 marks) c. Outline a procedure based on the idea of regression sum of squares to test whether the monthly effects 'om April to September are the same. Give the test statistics, degrees of -eedom and the decision rule