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
Use statistical software to replicate 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
pictureClick here for the Excel Data File.
a-1. Which variable has the strongest correlation with the dependent variable?
b. Use statistical software to replicate the following regression analysis with all the independent variables. Compute the coefficient of multiple determination. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)
The regression equation is Paralegal GPA = −0.411 + 1.20 HSGPA + 0.00163 SAT_Verbal − 0.00194 SAT_Math
Predictor Coefficient SE Coefficient 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 0.014
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
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.)
c-2. Compute the value of F. (Round your answer to 2 decimal places.)
c-3. Does it appear that any of the regression coefficients are not equal to zero?
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.)
d-2. Would you consider eliminating the variables "SAT_Verbal" and "SAT_Math"?
After eliminating the insignificant variables, the analysis was rerun. See the following output.
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 34.35 0.001
Residual Error 7 0.8570 0.1224
Total 8 5.0631
e-1. Writeout the regression equation. (Negative amounts should be indicated by a minus sign. Round your answer to 4 decimal places.)
e-2. Compute the coefficient of determination. (Round your answer to 4 decimal places.)
e-3. How much has R2 changed from the previous analysis? (Round your answer to 4 decimal places.)
g. Following is a plot of the residuals and the yˆ values. Do you see any violation of the assumptions?
A scatter plot. The vertical axis plot residual (y - Å·) ranging from -0.35 to 0.7 in increments of 0.35. The horizontal axis plots fitted Å· ranging from 1.50 to 4.00 in increments of 0.50. The values are as follow: (1.50, 0.6), (2.00, 0.35), (2.10, -0.35), (2.75, 0.00), (2.8, 0.71), (3.2, -0.2), (3.3, -0.05), (3.9, -0.05). All values approximated.