Suppose that the sales manager of a large automotive parts distributor wants to estimate 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 reasonably 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 following table 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 $37,702,000.
R2
Number of Average
Annual Number of Automobiles Personal Age of
Sales Retail Registered Income Automobiles Number of ($ millions), Outlets, (millions), ($ billions), (years), Supervisors,
Y X1 X2 X3 X4 X5
37.702 1,739 9.27 85.4 3.5 9.0
24.196 1,221 5.86 60.7 5.0 5.0
32.055 1,846 8.81 68.1 4.4 7.0
3.61 120 3.81 20.2 4.0 5.0
17.625 1,096 10.31 33.8 3.5 7.0
45.919 2,290 11.62 95.1 4.1 13.0
29.600 1,687 8.96 69.3 4.1 15.0
8.114 241 6.28 16.3 5.9 11.0
20.116 649 7.77 34.9 5.5 16.0
12.994 1,427 10.92 15.1 4.1 10.0
Conduct a global test of hypothesis to determine whether any of the regression coefficients are not zero. Use the .05 significance level.