Problem Set 6:  Regression Analysis of Iowa State Enrollment

Background
You are asked to develop a statistical model of  nonresident enrollment demand for Iowa State University, based on data collected over the period 1973-1993.  You can download the Excel spreadsheet from the Economics 532 Web Page.  The data set is listed under the Data Set heading.  Click on the and save the data set called enroll.xls.  

You can conduct the analysis using whatever package you wish, but it is possible to run regressions in Excel.  First, Make sure you can access the regression program by clicking on Tools, and then on Add-Ins (Figure 1).  Make sure that the Analysis Tool Pack is checked (Figure2).  Thereafter, when you click on tools, select the Data Analysis option (Figure 1), and then click on regression.  You will be able to specify the dependent and independent variables by choosing ranges for the variables as in Figure 3.  You may also need to get sample means if you wish to compute elasticities.  You can generate sample means by accessing the Descriptive Statistics package in the Data Analysis Package, as in Figure 4.

Variable Definitions and Sources
The data set is taken from,  Darin Wohlgemuth, "An Economic Analysis of College Enrollment." Unpublished MS thesis, Iowa State University, 1993.  The data set contains information on Iowa State nonresident first-time freshman enrollments for several states in the Midwest and West over the period 1973-1993.  The  data set also contains several additional variables which may help you predict enrollment from each state in each year.  The variables include:

STATE:  A numerical identifier for each state in the sample.  The codes are:
4	Arkansas
6	Colorado
13	Illinois
14	Indiana
16	Kansas
18	Louisiana
22	Michigan
23	Minnesota
25	Missouri
27	Nebraska
32	New Mexico
34	North Dakota
35	Ohio
36	Oklahoma
38	Pennsylvania
41	South Dakota
43	Texas
49	Wisconsin

YEAR:  Year of observation.

ISU-FTS:  Number of new ISU fall freshman enrollees from each state.  Source: Iowa State University Enrollment Services Annual Statistical Report.

In State ENR:  Number of undergraduate enrollees in all public and private colleges and universities in the home state.  Source: Digest of Educational Statistics, by the United States Department of Education, National Center for Educational Statistics.  

ISU Tuition: Annual nonresident tuition and fees at Iowa State.  Source: Iowa State 
University Enrollment Services Annual Statistical Report.   

ALUMNI:  Number of Iowa State alumni living in each state.  Source:  ISU Alumni 
Association and the Iowa State Fact Book. 

COL Salary: National mean annual salary of all males 25 and over, who have completed four or more years of college.  Source:  Current Population Survey.

HS Salary:  National mean annual salary of all males 25 and over, who have completed exactly 4 years of high school.  Source: Current Population Survey.

HSGRAD:  Size of the public high school graduating class in each state. 
Source:  Digest of Educational Statistics.  

In State Tuition:  Resident tuition and fees at public universities in the home state.  Sources:  Digest of Educational Statistics, Barron's Profiles of American Colleges and The College Blue Book. 

CPI_83:  Consumer Price Index in 1983 dollars.  Source: Bureau of Labor Statistics, reported in Statistical Abstract.

PC Income:  Per capita personal income in the state.  Source: U.S. Bureau of Economic Analysis, published in the Statistical Abstract.

DISTANCE:  Distance from the closest border of the home state to Ames, Iowa.

Note that you may want to transform some of these variables before using them in regression.  Also, not all variables need to be used in the analysis, and some may not be appropriate theoretically.

Assigned Tasks
1)	Write out the specification of the demand equation in the form 

 	ISUENR = a + b1*X1 + b2*X2 + ... + bk*Xk

where a, b1, b2, ..., bk are the parameters to be estimated.  Explain why you selected the explanatory variables, X1, X2, ..., Xk.

2)	How does your model perform in terms of  R-square and  t-statistics of coefficients?
 
3)	What is the own-price elasticity of demand, based on your model?  If the University wants to maximize tuition revenue, should they raise tuition, lower tuition, or leave tuition unchanged?  Explain.

4)	What is the income elasticity of demand?  Is nonresident enrollment at ISU a luxury, a necessity, or an inferior good.

5)	Are other state universities complements or substitutes with ISU?

6)	Besides prices and income, what else explains nonresident enrollments?

7)	Using the observations  for Wisconsin in 1993, what does your model predict nonresident enrollment from Wisconsin would be in 1993?   How close is your prediction to the actual figure?

8)	Besides the variables you used in your model, what other information do you think you should include in an equation explaining nonresident enrollment at ISU?  Explain your answer.