Impact of SAT and
School Size on Graduation Rates in 31 State Universities in California
Question: The table below contains information on
graduation rates and SAT scores for large state universities and midsize state
universities in the state of California.
Estimate a regression where graduation rate is a function of SAT score
and a school size dummy variable. Are
students in midsize schools more or less likely to graduate than students in
large schools, when SAT score is held constant?
Data:
The data to analyze impact of school size and SAT measure on
odds of graduating from a public university in California are presented in the
table below.
Information on Graduation Rates, SAT Performance and School Size
for Fouryear Public Universities in California


Public Universities in California

Odds of Graduating On Time

SAT Measure

Large School Dummy

Cal Poly

2.45

620

1

UC Berkley

10.11

677.5

1

UCLA

10.11

650

1

UCSD

6.14

640

1

San Jose State

0.92

515

1

UC Davis

4.26

597.5

1

UC Irvine

6.14

565

1

SDSU

1.94

545

1

Cal State Poly

1.08

535

1

Cal State Sacramento

0.72

475

1

UCSB

4.00

607.5

1

San Francisco State University

0.85

497.5

1

Cal state Chico

1.33

507.5

1

Cal State Long Branch

1.44

510

1

Cal State Fullerton

1.08

487.5

1

Cal State Los Angeles

0.56

440

1

University of California Riverside

1.94

545

1

Cal State Northridge

0.89

460

1

Cal State San Bernadino

0.72

447.5

1

Cal State Fresno

0.92

462.5

1

UCAl Santa Cruz

2.85

547.5

1

Cal State East Bay

0.64

455

0

Cal State San Marcos

0.85

482.5

0

Sonoma State University

1.17

502.5

0

Cal State Channel Islands

1.04

477.5

0

Cal State Bakersfield

0.64

452.5

0

Cal State Dominquez Hill

0.39

425

0

Cal State Monterey Bay

0.61

485

0

Cal State Stanislaus

1.00

460

0

Humbolt State University

0.67

507.5

0

University of California Merced

1.33

510

0

The SAT measure is the average of four numbers the 25^{th}
and 75^{th} percentiles of both the math and verbal SAT score.
The large school dummy is set to 1.0 if the school has more
than 15,000 undergraduates and is set to 0 if school has between 2,000 and
15,000 undergraduates.
Regression Results: I ran a regression model where the dependent
variable is the log of the odds that a person graduates within six years of
leaving school.
The explanatory variables used in the model are the SAT
measures and the dummy variable set to 1 if the school has more than 15,000
undergraduates and 0 otherwise.
The regression results are laid out in the table below.
Regression Results for
Graduation Rate Equation


variable

Coeff.

tstat

SAT

0.005

11.9

LARGE

0.057

0.95

CONSTANT

2.53

12.1

R^{2}

86.5

Observations and
Comments:
SAT score is significantly relate to log of the odds of the
graduation rate. High SAT scores are
associated with higher levels of graduation on time.
School size is NOT significantly related to graduation rate.
The constant term is highly significant and negative. The constant term is the value of the
graduation rate for smaller schools when the SAT is zero. The SAT measure can never be zero because the
minimum value of the SAT is 200. It is
difficult to interpret the meaning of the negative constant term in the
estimated regression.
Should I remove the
constant term from the regression?
The existence of the significant constant term in this
regression suggests to me that the model is missing important variables and the
results may not be very robust.
Literature on whether regressions should be estimated
without the constant term included is mixed.
Here are some links to this topic.
Since a significant constant term indicates to me that the
model may be misspecified and in particular some variables related to the
graduation rate may have been omitted I reran the regression with the constant
term omitted. I also omitted the SIZE
variable because it was not significant in the original regression.
When I reran the model with the constant term and the size
variable omitted I got a positive but insignificant coefficient for the SAT
variable.
Concluding Thoughts: Simply glancing at the data indicates that
high SAT schools have higher graduation rates.
However, model results are not incredibly robust. I believe other variables are as important as
the SAT average including (1) the socioeconomic status of the students at the
school and (2) the percent of students who attend part time.
Also, the sample size used to construct this model is really
small.
More work will follow probably in August of 2016.
Authors Note: I have created a new blog devoted to the
creation and explanation of policy proposals that will help improve our
world. My first policy proposal
examines whether allowing private course providers to teach courses inside
public schools will help improve educational outcomes.
My post identifies three possible improvements that might be
realized by this policy change.
First, the available experience to date suggests that it is
very difficult to close poorly performing public schools. It is more economically and politically
feasible to offer a private alternative to the math or reading departments of a
school when student math and reading scores are low inside a district.
Second, many school departments offer relatively few foreign
language courses. The expansion of
foreign language courses to many school districts is likely to prove to be more
cost effective when courses are offered through a private firm rather than
through each school district separately.
Third, most school systems lack rigorous courses in computer
programming. Many young people from
affluent families are learning computer programming in summer camps. As a result there is a growing STEM
knowledge gap between children from affluent families and the rest of
society. It would be very difficult for
most school systems to offer advanced programming classes. Private companies have proven they can offer
good classes and should be allowed to offer these classes inside the public
schools.
PLEASE READ MY POST ON THIS TOPIC
COMPETITION AMONG COURSE PROVIDERS IN PUBLIC SCHOOLS
THANKS !!!!
I think the intercept is meaningless in this case, but it is important for the mathematical arranges of the regression. Indeed, SAT scores look like good predictors of graduation rates. Socio economic status can be important to, but this is a public universities universe, which would contain homogeneous groups of students from a social status perspective.
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