The administrator of a new paralegal program at Seagate Technical College wants to estimate the grade point average in the new program. He thought that high school GPA, the verbal score on the Scholastic Aptitude Test (SAT), and the mathematics score on the SAT would be good predictors of paralegal GPA. The data on nine students are:

a. Consider the following correlation matrix. Which variable has the strongest correlation with the dependent variable? Some of the correlations among the independent variables are strong. Does this appear to be a problem?

b. Consider the following output. Compute the coefficient of multiple determinations.

c. Conduct a global test of hypothesis from the preceding output. Does it appear that any of the regression coefficients are not equal to zero?
d. Conduct a test of hypothesis on each independent variable. Would you consider eliminating the variables “verbal” and “math”? Let α = .05.
e. The analysis has been rerun without “verbal” and “math.” See the following output. Compute the coefficient of determination. How much has R2 changed from the previous analysis?

f. Following is a histogram of the residuals. Does the normality assumption for the residuals seem reasonable?

g. Following is a plot of the residuals and the yˆ values. Do you see any violation of theassumptions?

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A-18820250 IP-26590863 ra | 313332122 T th 0 0 0 M-42464444 Se-42455 354 A-50913104 28881821 IG-312332222 aud 123456789 070 0.35- 0.00- * 1.50 2.00 2.50 3.00 3.50 4.00 The regression equation is Legal =-0.411 + 1.20 GPA + 0.00163 Verbal -0.00194 Math Predictor Constant GPA Verbal Math Coef -0.411l 1.2014 0.001629 -0.001939 SE Coef 0.7823 0.2955 0.002147 0.002074 -0 53 4.07 0.76 -0.94 0.622 0.010 0.482 0.393 Analysis of Variance SOURCE Regression Reaidual Error Total MS 1.4532 0.1407 DF 0.014 4 359S 0.7036 5.0631 10.33 SOURCE GPA Verbal Maヒh DF Seq ss 1 4.2061 0 0303 0.1231 The regression equation is Legal0.454 + 1.16 GPA Predictor Constant GPA Coef -0.4542 1.1589 SE Coef 0.5542 0.1377 -0.82 5.86 0.439 0.001 Analysis of Variance SOURCE Regression Residual Error Total DF S8 MS 1 4.2061 4.2061 34.35 .001 7 0.857001224 8 5.0631 0.4 Residuals