Sat Scores Vs. Acceptance Rates :: essays research papers

sit Scores vs. Acceptance Rates     The look into must fulfill two goals (1) to produce a professional get across of your experiment, and (2) to show your understanding of the topicsrelated to least squares reverse as expound in Moore & McCabe, Chapter 2.In this experiment, I will determine whether or non on that point is a relationshipbetween number SAT dozens of incoming freshmen versus the acceptance rate ofapplicants at top universities in the country. The cases being used are 12 ofthe in truth best universities in the country according to US News & World Report.The average SAT scores of incoming freshmen are the explanatory varyings. Theresponse variable is the acceptance rate of the universities.     I used September 16, 1996 issue of US News & World Report as my source.I started come forth by choosing the top fourteen "Best National Universities". Next,I graphed the fourteen schools using a scatterplot and dec ided to cut it down to12 universities by throwing out odd data.A scatterplot of the 12 universities data is on the chase page (page 2)The linear regression equation isACCEPTANCE = 212.5 + -.134 * SAT_SCORER= -.632 R2=.399I plugged in the data into my calculator, and did the various regressions. Isaw that the power regression had the best correlation of the non-linear chemises.A scatterplot of the transformation can be seen on page 4.The Power Regression compare isACCEPTANCE RATE=(2.475x1023)(SAT SCORE)-7.002R= -.683 R2=.466The power regression seems to be the better model for the experiment that I havechosen. in that respect is a higher(prenominal) 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 model ha s 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 one another(prenominal) and no helpful observations can be seenfrom them. The outliers in both models was not a factor in choosing the bestmodel. In both models, there was one distinct outlier which appeared in thegraphs.     The one outlier in both models was University of Chicago. It had an outstandingly high acceptance rate among the universities in this experiment. Thisschool is a very good school academically which means the average SAT scores of