A college's economics department is attempting to determine if verbal or mathematical proficiency is more important for predicting academic success in the study of economics. The department faculty have decided to use the grade point average (GPA) in economics courses for graduates as a measure of success. Verbal proficiency is measured by the SAT verbal and the ACT English entrance examination test scores. Mathematical proficiency is measured by the SAT mathematics and the ACT mathematics entrance examination scores. The data for 112 students are available in a data file named Student GPA. The designation of the variable columns is presented in the Chapter 11 appendix. You should use your local statistical computer program to perform the analysis for this problem.
a. Prepare a graphical plot of the economics GPA versus each of the two verbal proficiency scores and each of the two mathematical proficiency scores. Which variable is a better predictor? Note any unusual patterns in the data.
b. Compute the linear model coefficients and the regression analysis statistics for the models that predict economics GPA as a function of each verbal and each mathematics score. Using both the SAT mathematics and verbal measures and the ACT mathematics and English measures, determine whether mathematical or verbal proficiency is the best predictor of economics GPA.
c. Compare the descriptive statistics-mean, standard deviation, upper and lower quartiles, and range-for the predictor variables. Note the differences and indicate how these differences affect the capability of the linear model to predict.