Suppose that the sales manager of a large automotive parts distributor wants to estimates as early as April the total annual sales of a region. On the basis of regional sales, the total sales for the company can also be estimated. If, based on past experience, it is found that the April estimates of annual sales are reasonable accurate, then in future years the April forecast could be used to revise production schedules and maintain the correct inventory at the retail outlets.
Several factors appear to be related to sales, including the number of retail outlets in the region stocking the company’s parts, the number of automobiles in the region registered as of April 1, and the total personal income for the first quarter of the year. Five independent variables were finally selected as being the most important (according to the sales manager). Then the data were gathered for a recent year. The total annual sales for that year for each region were also recorded. Note in the Exam Data One that for region 1 there were 1,739 retail outlets stocking the company’s automotive parts, there were 9,270,000 registered automobiles in the region as of April 1 and so on. The sales for that year were$37,702,000.
Please check the Exam Data One on Moodle, and answer the following questions:
1. What percent of the variation is explained by the regression equation
2. Compute the elasticity for each variable. On this basis, discuss the relative impact that each variable has on demand. (For computing elasticity, you can use the first row of the data from Exam Data One. Which are: Number of retail outlets=1739, Number of automobiles registered(Millions)=9.27, Personal income($billions)=85.4, Average age of automobiles(years)=3.5, Number of supervisors=9
3. Conduct a t-test for the statistical significance of each variable. Discuss the results of the t-tests in lights of the policy implications.
Teton Village, Wyoming, near Grand Teton Park and Yellowstone Park, contains shops, restaurants, and motels. The village has two peak seasons—winter, for skiing on the 10,000-foot slopes, and summer, for tourists visiting the parks. The number of visitors(in thousands) by quarter for five years can be found in Exam Data Two on Moodle.
a) Develop the typical seasonal pattern for Teton Village
b) Determine the seasonally adjusted number of visitors for winter 2011.