Least-Squares Method and Coefficient of Determination
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The director of graduate studies at a large college of business would like to predict the grade point average (gpa) of students in an MBA program based on Graduate Management admission test (GMAT) scores. A sample of 20 students who had completed 2 years in the program is selected. The results are as follows:
Observation GMAT Score GPA
1 688 3.72
2 647 3.44
3 652 3.21
4 608 3.29
5 680 3.91
6 617 3.28
7 557 3.02
8 599 3.13
9 616 3.45
10 594 3.33
11 567 3.07
12 542 2.86
13 551 2.91
14 573 2.79
15 536 3.00
16 639 3.55
17 619 3.47
18 694 3.60
19 718 3.88
20 759 3.76
(Hint: First, determine which are the independent and dependendent variables)
a.Construct a scatter plot and, assuming a linear relationship, use the least-squares method to compute the regression coeffients b(0) and b(1)
b. Interpret the meaning of the y-intercept, b(0), and the slope, b(1), in this problem.
c. Use the prediction line developed in (a) to predict the GPA for a student a GMAT score of 600
d. Determine the coefficient of determination, r^2, and interpret its meaning in this problem
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Solution Summary
This solutions contains a graphical display of the data to determine the regression equation and the coefficient of determination. It also interprets the y-intercept and predicts the GPA for a GMAT score of 600.
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