Isa 291 - Descriptive Analysis of the Data

ISA 291 FINAL PROJECT REPORT

Kevin Leonhardt, Yaozhong Fan, George Wang, Rocco Vienhage

DESCRIPTIVE ANALYSIS OF THE DATA

Our model was built from a training data set containing observations of 1266 four-year degree granting universities across the United States, and 500  additional randomly selected observations were used for validation. The data includes key indicators about the cost and value of universities and higher-education institutions across the United States. The information that can be extracted from the data is meant to help students choose a school that is well-suited to meet their needs, priced affordably, and consistent with their educational and career goals. We utilized this dataset to predict retention rates for first-time, full-time students at four-year institutions with the primary goal of identifying key predictors.

To arrive at our final model, we decided to use the institution’s (1) state, (2) control, (3), latitude, (4) admission rate, (5) 25th percentile ACT score, (6) 25th percentile SAT score in the critical reading section, (7) percentage of undergraduates older than 25, (8) percentage of white undergraduates, (9) percentage of degrees awarded in Liberal Arts And Sciences, General Studies And Humanities, (10) number of undergraduate degree-seeking students, (11)  percent of all federal undergraduate students receiving a federal student loan, and (12) average family income of dependent students along with a number of squared and interaction terms.

The pie chart below shows a percentage of institutions that fall into each of the three control types, public, private nonprofit, and private for-profit. As you can see from the chart, the majority of schools in the United States are private nonprofit. The bar chart shows retention rates for universities across a number of states accounted for in our model. Lastly, the table at the bottom of the page shows means, standard deviations, and five number summaries for each of our remaining dependent variables included in the model (excluding squared and interaction terms) as well as our independent variable.

[pic 1][pic 2][pic 3]

OUR FINAL MODEL

[pic 4]

[pic 5]

[pic 6]

MODEL FIT

Our final model had an r-square value of 0.7686 and an adjusted r-square of 0.7605. With more variables, we were able to get a higher r-square value, but the model was much more difficult to interpret. Since our primary goal was to understand our predictors’ relationships with retention rate, we decided to simplify to make our model more useful for our purposes.

INTERPRETING OUR QUALITATIVE VARIABLES (2)

State

• On average, the first-time, full-time student retention rate at four year institutions in CA is 0.08241 higher than OH when holding all other variables constant.
• On average, the first-time, full-time student retention rate at four year institutions in CO is 0.05044 less than OH when holding all other variables constant.
• On average, the first-time, full-time student retention rate at four year institutions in PA is 0.02316 higher than OH when holding all other variables constant.
• On average, the first-time, full-time student retention rate at four year institutions in TX is 0.02879 less than OH when holding all other variables constant.
• On average, the first-time, full-time student retention rate at four year institutions in WV is 0.05759 less than OH when holding all other variables constant.

Control

• On average, the first-time, full-time student retention rate at four-year, private nonprofit institutions is 0.01117 less than public institutions when holding all other variables constant.
• On average, the first-time, full-time student retention rate at four year private for-profit institutions is 0.13805 less than public institutions when holding all other variables constant.

INTERPRETING OUR QUANTITATIVE VARIABLES

Latitude

On average, the first-time, full-time student retention rate at four year institutions increases by 0.00239 for every one-degree increase above its mean of 38.1433750 degrees when holding all other variables constant.

Admission Rate

On average, the first-time, full-time student retention rate at four year institutions increases by 0.0088 for every one-percent increase above its mean of 64.12665% when holding all other variables constant.

Top 25% of Average Critical Reading SAT Scores

On average, the first-time, full-time student retention rate at four year institutions increases by 0.00079472 for every one-point increase above its mean of 471.3910951 points when holding all other variables constant.

Top 25% of Average ACT Scores

On average, the first-time, full-time student retention rate at four year institutions increases by 0.00591 for every one-point increase above its mean of 20.6189918 points when holding all other variables constant.

Percentage of Students Pursuing Liberal Arts Degrees

On average, the first-time, full-time student retention rate at four year institutions decreases by 0.09488 for every one-percent increase above its mean of 0.0487322 points when holding all other variables constant.