Problem 2 (20 points) 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 ofces in seven additional Gulf State cities. Manuel is currently analyzing the revenue data (in $10,000s) from his first location for the first ve years of operation. (See Manuel_Revenue.xlsx.) (a) Plot these data. Based on your visual observations, what time series components are present in the data? (b) Determine the multiplicative seasonal index for each month. (0) Fit a linear trend model to the deseasonalized data for the years 20052009 and determine the MSE and MAE for the future forecasts. ((1) Conduct a test of hypothesis to determine if the linear trend model ts the existing data. (e) Comment on the adequacy of the linear trend model based on the measures of forecast error and the hypothesis test you conducted. (f) Use the seasonal index values computed in part (b) to provide seasonal adjusted forecasts for each month of the year 2010