Suppose that a company was formed five years ago to provide meal delivery, physical therapy, and minor housekeeping services to senior citizens. The revenue data for the first five years of operation are shown here.

Revenue ($10,000s)

2011 2012 2013 2014 2015 January 23 67 72 76 81 February 34 63 64 75 72 March 45 65 64 77 71 April 48 71 77 81 83 May 46 75 79 86 85 June 49 70 72 75 77 July 60 72 71 80 79 August 65 75 77 82 84 September 67 80 79 86 91 October 60 78 78 87 86 November 71 89 87 91 94 December 76 94 92 96 99

a. Plot these data. Based on your visual observations, what time-series components are present in the data?

b. Determine the seasonal index for each month.

c. (1) Fit a linear trend model to the deseasonalized data for the years 2011–2015 and determine the MAD and MSE for forecasts for each of the months in 2016. (2) Conduct a test of hypothesis to determine if the linear trend model fits the existing data. (3) Comment on the adequacy of the linear trend model based on the measures of forecast error and the hypothesis test you conducted.

d. Use the seasonal index values computed in part b to provide seasonal adjusted forecasts for each month of the year 2016.