The administrator of a new paralegal program at Seagate Technical College wants
ID: 3040847 • Letter: T
Question
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:
Consider the following correlation matrix.
a-1. Which variable has the strongest correlation with the dependent variable?
a-2. 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 mulitple determination. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)
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 3 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"?
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
e-1. Compute the coefficient of determination. (Round your answer to 4 decimal places.)
e-2. How much has R2 changed from the previous analysis? (Round your answer to 4 decimal places.)
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 2.33Explanation / Answer
a1) High school GPA has the strongest correlation with the dependent variable. The strongest correlation is between High School GPA and Paralegal GPA ie. 0.911.
a2) No as the values in correlation matrix is near unity so we can say that there is no multicollinearity among the data.
b) coefficient of multiple determination R2 =[RSS/(n-2)]/[TSS/(n-1)] = [4.3595*7]/[5.0631*1] = 6.027
c1) the pvalue is 0.01 which is less than 0.05 so we accept the null hypothesis. (from table)
c2) value of F(calculated) = MSS/MSE = 10.33 , F (critical) is 4.07.
c3) No the regression coefficients are not equal to zero, some are negative and some are near to zero but not equal to zero.
d1) Ho is rejected in case t < 15.7225 and /or t > 15.1923.
d2) SAT_Verbal and SAT_Math are not significant (pvalues) so we can eliminate them it would not affect the model.
e1) coefficient of determination R2 =[RSS/(n-2)]/[TSS/(n-1)] = [4.2061*7]/[5.0631*1] = 5.815
e2) R2 has only been reduced by 0.212 ie. 21.2% only.
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