Term Papers on SAT Scores Vs. Acceptance Rates

Term Paper Title	SAT Scores Vs. Acceptance Rates
# of Words	784
# of Pages (250 words per page double spaced)	3.14

SAT Scores vs. Acceptance Rates

     The experiment must fulfill two goals: (1) to produce a professional
report of your experiment, and (2) to show your understanding of the topics
related to least squares regression as described in Moore & McCabe, Chapter 2.
In this experiment, I will determine whether or not there is a relationship
between average SAT scores of incoming freshmen versus the acceptance rate of
applicants at top universities in the country. The cases being used are 12 of
the very best universities in the country according to US News & World Report.
The average SAT scores of incoming freshmen are the explanatory variables.  The
response variable is the acceptance rate of the universities.

     I used September 16, 1996 issue of US News & World Report as my source.
I started out by choosing the top fourteen "Best National Universities".  Next,
I graphed the fourteen schools using a scatterplot and decided to cut it down to
12 universities by throwing out odd data.

A scatterplot of the 12 universities data is on the following page (page 2)

The linear regression equation is:
                           ACCEPTANCE =  212.5  + -.134 * SAT_SCORE
                           R= -.632       R^2=.399

I plugged in the data into my calculator, and did the various regressions.  I
saw that the power regression had the best correlation of the non-linear
transformations.

A scatterplot of the transformation can be seen on page 4.

The Power Regression Equation is
         ACCEPTANCE RATE=(2.475x10^23)(SAT SCORE)^-7.002
         R= -.683   R^2=.466

The power regression seems to be the better model for the experiment that I have
chosen.  There is a higher correlation in the power transformation than there is
in the linear regression model. The R for the linear model is -.632 and the R in
the power transformation is -.683. Based on R^2 which measures the fraction of
the variation in the values of y that is explained by the least-squares
regression of y on x, the power transformation model has a higher R^2 which is .
466 compared to .399.  The residual plot for the linear regression is on page 5
and the residual plot for the power regression is on page 6. The two residuals
plots seem very similar to one another and no helpful observations can be seen
from them.  The outliers in both models was not a factor in choosing the best
model.  In both models, there was one distinct outlier which appeared in the
graphs....

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