1) The director of a national research institute believes that faculty at larger, more comprehensive institutions have lighter teaching and advisory responsibilities and more time for research and scholarly writing. The director develops a measure of institutional comprehensiveness and a measure of scholarly productivity for psychology departments. In a pilot project, the director selects 18 colleges and universities and determines the institutional comprehensiveness and scholarly productivity of the psychology departments in these institutions. The data were as follows:
| Institution | Comprehensiveness | Scholarly Productivity |
| 1 | 162 | 82 |
| 2 | 250 | 88 |
| 3 | 89 | 78 |
| 4 | 115 | 92 |
| 5 | 165 | 75 |
| 6 | 150 | 75 |
| 7 | 54 | 70 |
| 8 | 180 | 62 |
| 9 | 185 | 65 |
| 10 | 194 | 70 |
| 11 | 200 | 81 |
| 12 | 210 | 94 |
| 13 | 210 | 83 |
| 14 | 222 | 82 |
| 15 | 240 | 84 |
| 16 | 242 | 77 |
| 17 | 74 | 62 |
| 18 | 270 | 86 |
- Determine the regression equation for predicting scholarly productivity (Y) from institutional comprehensiveness (X).
- For an institution with a comprehensiveness score of 175, predict the psychology
department’s scholarly productivity score.
2) Enrollment and Courses Projection
This is a real world example. I need your help in helping the Registrar’s office in calculating how many courses should run for the Fall ’15 semester. Using enrollment and courses that ran, I need you to do two things:
- a) Identify the regression equation for the data to estimate the number of courses.
- b) If the enrollment for Fall ’15 is 7,450, how many courses should be scheduled?
The data below should help you with your recommendation.
| Fall ‘12 | Fall ‘13 | Fall ‘14 | Fall ‘15 | |
| Enrollment | 8042 | 8179 | 7651 | 7450 |
| Courses | 1322 | 1374 | 1268 | ??? |