SAT Scores vs. Acceptance Rates The experience should serve two purposes: (1) produce a professional report of your experience and (2) show your understanding of regression-related topics least squares as described in Moore & McCabe, Chapter 2. In this experiment, I will determine whether or not there is a relationship between the average SAT scores of freshmen and the acceptance rate of applicants to top universities of the country. The cases used concern 12 of the 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 university acceptance rate. I used the September 16, 1996 issue of US News & World Report as my source. I started by choosing the top fourteen “best national universities.” Next, I graphed the fourteen schools using a scatterplot and decided to narrow it down to 12 universities by discarding odd data. A scatterplot of data from the 12 universities can be found on the next page (page 2). The linear regression equation is: ACCEPTANCE = 212.5 + -.134 * SAT_SCORER= -.632 R^2=.399I plugged the data into my calculator and ran the various regressions. I saw that power regression had the best correlation of nonlinear transformations. A scatterplot of the transformation can be seen on page 4. The power regression equation is ACCEPTANCE RATE = (2.475x10^23)(SAT SCORE)^-7.002R = -0.683 R^2 = 0.466 Power regression seems to be the best model for the experiment I chose. There is a higher correlation in the power transformation than in the linear regression model. The R for the linear model is -0.632 and the R in the power transformation is -0.683. Based on R^2 which measures the fraction of the variation in y values ​​that is explained by the least squares regression of y on x, the power transformation model has a higher R^2 which is 0.466 compared to 0.399. The residual plot for linear regression is on page 5 and the residual plot for power regression is on page 6. The two residual plots look very similar to each other and no useful observations cannot be derived from it. Outliers in both models were not a factor in choosing the best model. In both models, a distinct outlier appeared in the graphs. The only exception in both models was the University of Chicago. The acceptance rate was unusually high among the universities participating in this experiment. This school is a very good school academically, meaning the average SAT scores are