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
|
160
|
82
|
|
2
|
252
|
88
|
|
3
|
89
|
78
|
|
4
|
110
|
92
|
|
5
|
170
|
75
|
|
6
|
154
|
75
|
|
7
|
50
|
70
|
|
8
|
185
|
62
|
|
9
|
185
|
65
|
|
10
|
194
|
70
|
|
11
|
205
|
81
|
|
12
|
210
|
94
|
|
13
|
210
|
83
|
|
14
|
220
|
82
|
|
15
|
240
|
84
|
|
16
|
244
|
77
|
|
17
|
70
|
62
|
|
18
|
274
|
86
|
a. Determine the regression equation for predicting scholarly productivity (Y) from institutional comprehensiveness (X).
b. 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
|
???
|
|
|
|
|
|
|