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The administrator of a new paralegal program at a community college wants to predict the GPA in the new program. He believes that the high school GPA, the verbal score on the Scdholastic Aptitude Test (SAT), and the mathematics score on the SAT would be good predictors of paralegal GPA. The data on nine students are:

The administrator of a new paralegal program at a community college wants to predict the GPA in the new program. He believes that the high school GPA, the verbal score on the Scdholastic Aptitude Test (SAT), and the mathematics score on the SAT would be good predictors of paralegal GPA. The data on nine students are:

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The administrator of a new paralegal program at a community college wants to predict the GPA in the new program. He believes that the high school GPA, the verbal score on the Sedholastic Aptitude Test (SAT), and the mathematics score on the SAT would be good predictors of paralegal GPA. The data on nine students are: 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. Student 1. 2 3 4 5 Predictor Constant дра verbal math 6 7 8 High school GPA Error Total 410 270 420 410 500 600 500 490 430 460 320 490 530 480 9 2.63 469 440 Source: Plan Administrator, Community and Technical College, University of Toledo, Ohio. дра verbal math 3.25 1.80 2.89 3.81 3.13 2.81 2.20 2.14 legal 0.911 The regression equation is legal =-0.411 1.20 gpa The MINITAB software system was used to generate the following output. The following correlation matrix was obtained. 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? 0.616 0.487 CAT SAT verbal math Coef -0.4111 1.2014 480 290 0.001629 -0.001939 gpa 0.609 0.636 Paralegal GPA b. Consider the following output. Compute the coefficient of multiple determination. 3.21 1.68 3.58 3.92 0.002147 0.002074 Analysis of Variance SOURCE DF SS MS Regression 3 4.3595 1.4532 5 0.7036 0.1407 8 5.0631 3.00 2.82 1.65 2.30 2.33 verbal 0.599 0.00163 verbal -0.00194 math Stdev 0.7823 0.2955 t-ratio -0.53 4.07 0.76 -0.94
Transcribed Image Text:The administrator of a new paralegal program at a community college wants to predict the GPA in the new program. He believes that the high school GPA, the verbal score on the Sedholastic Aptitude Test (SAT), and the mathematics score on the SAT would be good predictors of paralegal GPA. The data on nine students are: 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. Student 1. 2 3 4 5 Predictor Constant дра verbal math 6 7 8 High school GPA Error Total 410 270 420 410 500 600 500 490 430 460 320 490 530 480 9 2.63 469 440 Source: Plan Administrator, Community and Technical College, University of Toledo, Ohio. дра verbal math 3.25 1.80 2.89 3.81 3.13 2.81 2.20 2.14 legal 0.911 The regression equation is legal =-0.411 1.20 gpa The MINITAB software system was used to generate the following output. The following correlation matrix was obtained. 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? 0.616 0.487 CAT SAT verbal math Coef -0.4111 1.2014 480 290 0.001629 -0.001939 gpa 0.609 0.636 Paralegal GPA b. Consider the following output. Compute the coefficient of multiple determination. 3.21 1.68 3.58 3.92 0.002147 0.002074 Analysis of Variance SOURCE DF SS MS Regression 3 4.3595 1.4532 5 0.7036 0.1407 8 5.0631 3.00 2.82 1.65 2.30 2.33 verbal 0.599 0.00163 verbal -0.00194 math Stdev 0.7823 0.2955 t-ratio -0.53 4.07 0.76 -0.94
f. 9. C. d. 0. Conduct a global test of hypothesis from the preceding output. Does it appear that any of the regression coefficients are not equal to zero? Conduct a test of hypothesis on each independent variable. Would you consider eliminating the variables "verbal" and "math"? Let a .05. The regression equation is legal -0.454 1.16 gpa Error Total 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 analusis? Predictor Coef Constant -0.4542 gpa 1.1589 Analysis of Variance SOURCE DF SS Regression. 1 4.2061 7 8 Residuals (Y-Y') Following are a histogram and a ster-and-leaf diagram of the residuals. Does the normality assumption for the residuals seem reasonable? 1 2 (3) 4 2 1 1 Histogram of residual N = 9 Midpoint Count -0.4 -0.2 0.0 0.2 0.4 0.6 -04 -02 0.8570 5.0631 -0 110 0 00 02 0 06 Stdev 0.5542 0.1977 Stem-and-leaf of residual N = 9 Leaf Unit 0.10 0.70 0.35 E 0.00 -0.35 MS 4.2061 0.1224 1. 3 3 1 0 1 . t-ratio -0.82 5.86 Following is a plot of the residuals and the Y' values. Do you see any violation of the assumptions? 1 1.50 2.00 2.50 3.00 3.50 4.00 Y'
Transcribed Image Text:f. 9. C. d. 0. Conduct a global test of hypothesis from the preceding output. Does it appear that any of the regression coefficients are not equal to zero? Conduct a test of hypothesis on each independent variable. Would you consider eliminating the variables "verbal" and "math"? Let a .05. The regression equation is legal -0.454 1.16 gpa Error Total 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 analusis? Predictor Coef Constant -0.4542 gpa 1.1589 Analysis of Variance SOURCE DF SS Regression. 1 4.2061 7 8 Residuals (Y-Y') Following are a histogram and a ster-and-leaf diagram of the residuals. Does the normality assumption for the residuals seem reasonable? 1 2 (3) 4 2 1 1 Histogram of residual N = 9 Midpoint Count -0.4 -0.2 0.0 0.2 0.4 0.6 -04 -02 0.8570 5.0631 -0 110 0 00 02 0 06 Stdev 0.5542 0.1977 Stem-and-leaf of residual N = 9 Leaf Unit 0.10 0.70 0.35 E 0.00 -0.35 MS 4.2061 0.1224 1. 3 3 1 0 1 . t-ratio -0.82 5.86 Following is a plot of the residuals and the Y' values. Do you see any violation of the assumptions? 1 1.50 2.00 2.50 3.00 3.50 4.00 Y'
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