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SAT Scores Vs. Acceptance Rates - Papers Online

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 ...

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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 ...

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SAT Scores Vs. Acceptance Rates. (2004, November 11). Retrieved January 20, 2026, from http://www.essayworld.com/essays/SAT-Scores-Vs-Acceptance-Rates/17337

"SAT Scores Vs. Acceptance Rates." Essayworld.com. Essayworld.com, 11 Nov. 2004. Web. 20 Jan. 2026. <http://www.essayworld.com/essays/SAT-Scores-Vs-Acceptance-Rates/17337>

"SAT Scores Vs. Acceptance Rates." Essayworld.com. November 11, 2004. Accessed January 20, 2026. http://www.essayworld.com/essays/SAT-Scores-Vs-Acceptance-Rates/17337.

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PAPER DETAILS

Added: 11/11/2004 03:48:05 PM
Category: Education
Type: Premium Paper
Words: 767
Pages: 3

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