SAT Scores vs. acceptance ratesThe experiment must meet two objectives: (1) produce a professional report of the experiment and (2) 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 the average SAT scores of incoming freshmen and the acceptance rate of applicants to the top universities in the country. The cases used cover 12 of the top 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 scatter plot and decided to narrow it down to 12 colleges by eliminating the odd data. A scatterplot of data from the 12 universities can be found on the following page (page 2). The linear regression equation is: ACCEPTANCE = 212.5 + -.134 * SAT_SCORER= -.632 R^2=.399 I plugged the data into my calculator and ran the various regressions. I saw that power regression had the best correlation of the 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= -.683 R^2=.466 The 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 -.632 and the R in the power transformation is -.683. Based on R^2 measuring the fraction of the variation in y values ​​explained by least squares regression of y on x, the power transformation model has a higher R^2 of 0.466 versus 0.399. The residuals plot for linear regression is on page 5 and the residuals plot for power regression is on page 6. The two residuals plots look very similar to each other and no useful observations can be made from them. 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 outlier in both models was the University of Chicago. In this experiment he had an unusually high acceptance rate among universities. This school is an excellent school academically, which means that the average SAT scores are