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: Student High School GPA SAT Verbal SAT Math Paralegal GPA
1 3.25 480 410 3.21
2 1.80 290 270 1.68
3 2.89 420 410 3.58
4 3.81 500 600 3.92
5 3.13 500 490 3.00
6 2.81 430 460 2.82
7 2.20 320 490 1.65
8 2.14 530 480 2.30
9 2.63 469 440 2.33
Consider the following correlation matrix.
Paralegal GPA High School GPA SAT Verbal
High School GPA 0.911
SAT Verbal 0.616 0.609
SAT Math 0.487 0.636 0.599
a-1. Which variable has the strongest correlation with the dependent variable?
The strongest correlation is between .
a-2. Some of the correlations among the independent variables are strong. Does this appear to be a problem?
- with multicollinearity.
b. Consider the following output. Compute the coefficient of mulitple determination. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)
Predictor Coefficeint SE Coefficent t p
Constant -0.4111 0.7823 -.0.53 0.622
HSGPA 1.2014 0.2955 4.07 0.010
SAT_Verbal 0.001629 0.002147 0.76 0.482
SAT_Math -0.001939 0.002074 -0.94 0.393
Analysis of Variance
Source DF SS MS F p
Regression 3 4.3595 1.4532 10.33 0.01
Residual Error 5 0.7036 0.1407
Total 8 5.0631
Source DF SEQ SS
HSGPA 1 4.2061
SAT_Verbal 1 0.0303
SAT_Math 1 0.1231
Coefficient of multiple determination
Conduct a global test of hypothesis from the preceding output.
c-1. State the decision rule at the 0.05 level of significance. (Round your answer to 2 decimal places.)
Reject H0 if F >
C-2. Compute the value of F. (Round your answer to 3 decimal places.)
Value of F
C-3. Does it appear that any of the regression coefficients are not equal to zero?
regression coefficient(s) is (are)
d-1. Using 0.05 significance level conduct a test of hypothesis on each independent variable. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.
H0 is rejected in each case if t < or t >
d-2. Would you consider eliminating the variables "SAT_Verbal" and "SAT_Math"?
"SAT_Verbal" and "SAT_Math" be eliminated
The analysis has been rerun with "SAT_Verbal" and "SAT_MATH" See the following output. The regression equation is Paralegal GPA = -0.454 +1.16 HSGPA
Predictor Coefficient SE Coefficient t p
Constant -0.4542 0.5542 -0.82 0.439
HSGPA 1.1589 0.1977 5.86 0.001
Analysis of Variance
Source DF SS MS F p
Regression 1 4.2061 4.2061 34.36 0.001
Residual Error 7 0.8570 0.1224
Total 8 5.0631
e-1. Compute the coefficient of determination. (Round your answer to 4 decimal places.)
Coefficient of determination
e-2. How much has R2 changed from the previous analysis? (Round your answer to 4 decimal places.)