Sat Scores Vs. Acceptance Rates :: essays research papers

sit Scores vs. Acceptance pass judgment     The experiment must fulfill two goals (1) to produce a proreport of your experiment, and (2) to show your understanding of the bindingicsrelated to least squares reversion as described in Moore & McCabe, Chapter 2.In this experiment, I will posit whether or not there is a relationshipbetween mediocre SAT scores of incoming freshmen versus the acceptance rate ofapplicants at top universities in the country. The cases being used are 12 ofthe very go around universities in the country according to US News & valet de chambre Report.The average SAT scores of incoming freshmen are the explanatory variables. The repartee variable is the acceptance rate of the universities.     I used September 16, 1996 hack 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 decid ed to cut it down to12 universities by throwing out odd data.A scatterplot of the 12 universities data is on the following page (page 2)The linear turnabout equation isACCEPTANCE = 212.5 + -.134 * SAT_SCORER= -.632 R2=.399I plugged in the data into my calculator, and did the non-homogeneous regressions. Isaw that the actor regression had the best correlation of the non-linear changes.A scatterplot of the transformation can be seen on page 4.The Power statistical regression Equation isACCEPTANCE RATE=(2.475x1023)(SAT SCORE)-7.002R= -.683 R2=.466The power regression seems to be the better mannikin for the experiment that I holdchosen. There is a higher correlation in the power transformation than there isin the linear regression model. The R for the linear model is -.632 and the R inthe power transformation is -.683. Based on R2 which measures the fraction ofthe variation in the values of y that is explained by the least-squaresregression of y on x, the power transformation mode l has a higher R2 which is .466 compared to .399. The residual plot for the linear regression is on page 5and the residual plot for the power regression is on page 6. The two residualsplots seem very similar to i another and no helpful observations can be seenfrom them. The outliers in some(prenominal) models was not a factor in choosing the bestmodel. In some(prenominal) models, there was one distinct outlier which appeared in thegraphs.     The one outlier in twain models was University of Chicago. It had anunusually high acceptance rate among the universities in this experiment. Thisschool is a very good school academically which means the average SAT scores of