Question 3 Asuss Airline would like to forecast the number of passengers who will y from Singapore to Shanghai in 2013. The data is given in Table 31. The consultant rst developed a time series regression model, using time as the independent variable and the number of passengers as the dependent variable to :t the data. The tted line is shown in Figure 31, and the autocorrelation function for the residuals obtained from the regression model is shown in Figure 32. Table 3]: Number of passengers ying from Singapore to Shanghai Numberof Numberof 1tear passengers [1,0005] 1tear passengers [1,0005] 1993 22.3 20116 69.9 1994 26.1 290? 7'93 1995 29.4 20113 96.3 1996 34.5 2009 105-0 1992 32.6 2010 110-1:I 1993 40.3 2011 1117. 1999 39.5 2912 114-9 2000 45.4 2013 135-5 2001 46.3 2014 144.3 2002 45.3 2015 1415 2003 43.0 2016 150- 1 2004 54.5 291? 151-57I 2005 61.9 I] 5 [El 15 2'0 2'5 Time Figure 31: Fitted line plot Autocorrelation Function for Residuals 1.0. 0.6- 0.4 - 0.2 Autocorrelation 0.0 -0.Z -0.4- -0.6 - -0.6- -1.0- 2 3 5 Lag Figure 3-2: Autocorrelation function for residuals (a) Write down the regression model with the unknown coefficients. (3 marks) (b) Examine whether the assumption of independent errors for this model is violated. Justify your answer. (4 marks) (c) After applying another two models, the fitted models are specified as follow: log(Passenger,) = 3.123 + 0.083t Passenger, = 22.716 * 1.086 Based on these two models, forecast the number of passengers for 2018. (Note: log is short for logarithm.) (10 marks) (d) In general, how should the consultant decide which model to use for forecasting