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 $37,702,000.
Annual
Sales
($ millions),
Y
37.702
24.196
32.055
3.611
17.625
45.919
29.600
8.114
20.116
12.994
Number of
Retail
Outlets
X1
1,739
1,221
1,846
120
1,096
2,290
1,687
241
649
1,427
Number of
Automobiles
Registered
(millions),
X2
9.27
5.86
8.81
3.81
10.31
11.62
8.96
6.28
7.77
10.92
Personal
Income
($ billions),
X3
85.4
60.7
68.1
20.2
33.8
95.1
69.3
16.3
34.9
15.1
Average
Age of
Automobiles
(years),
X4
3.5
5.0
4.4
4.0
3.5
4.1
4.1
5.9
5.5
4.1
Number of
Supervisors,
X5
9.0
5.0
7.0
5.0
7.0
13.0
15.0
11.0
16.0
10.0
Conduct a global test of hypothesis to determine whether any of the regression coefficients are not zero. Use the .05 significance level.
