Manuel Gutierrez correctly predicted the increasing need for home health care services due to the country’s aging population. Five years ago, he started a company offering meal delivery, physical therapy, and minor housekeeping services in the Galveston area. Since that time he has opened offices in seven additional Gulf State cities.

Manuel is currently analyzing the revenue data from his first location for the first five years of operation.

Revenue ($10,000s)
2005 2006 2007 2008 2009 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 2005–2009 and determine the MAD and MSE for forecasts for each of the months in 2010. (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. Manuel had hoped to reach $2,000,000 in revenue by the time he had been in business for 10 years.
From the results in part

c, is this a feasible goal based on the historical data provided? Consider and comment on the size of the standard error for this prediction. What makes this value so large? How does it affect your conclusion?

e. Use the seasonal index values computed in part b to provide seasonal adjusted forecasts for each month of the year 2010.