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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 16 1996 issue 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 decided to cut it down to 12 universities by throwing out odd data A scatterplot of the 12 universities data is on the following page page 2 The linear regression equation is ACCEPTANCE 2125 -134 SATSCORE R -632 R2399 I plugged in 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 RATE2475x1023SAT SCORE-7002 R -683 R2466 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 R2 which measures the fraction of the variation
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