For the past 12 months, your real estate company has been requiring applicants for employment as sales agents to take an aptitude test, which it is hoped will predict the person's ability to sell. The results of the aptitude test have not been made available to the people who make the hiring decisions.
The applicants who have been hired have generally scored higher on the aptitude test than the applicants who have not been hired.
Now you want to know if - among the applicants who were hired - higher scores on the aptitude test are associated with better performance on the job. The following data has been collected:
| Employee |
Test Score Sales in first 6 months |
Number ($1,000,000's) |
| 1 |
46 |
2 |
| 2 |
55 |
2.7 |
| 3 |
70 |
5.9 |
| 4 |
67 |
1 |
| 5 |
64 |
2.4 |
| 6 |
60 |
1.5 |
| 7 |
64 |
3.1 |
| 8 |
58 |
6.8 |
| 9 |
58 |
3.9 |
| 10 |
67 |
1.2 |
| 11 |
52 |
21 |
| 12 |
58 |
5.6 |
| 13 |
64 |
10.6 |
| 14 |
55 |
5.9 |
| 15 |
49 |
8.4 |
| 16 |
49 |
18.3 |
| 17 |
61 |
7.1 |
| 18 |
55 |
6.4 |
| 19 |
61 |
2.7 |
| 20 |
49 |
6.3 |
| 21 |
67 |
3.2 |
| 22 |
64 |
2 |
| 23 |
64 |
4.6 |
| 24 |
67 |
4.1 |
a) Find the least squares line for the data;
b) Predict the sales performance for the first 6 months of an applicant who scores 66 on the aptitude test.