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2. Graduation rate - the percentage of entering freshman attending full time and graduating

within 5 years - and what influences it is a concern in U.S. colleges and universities. U.S. New

and World Report's "College Guide" provides data on graduation rates for colleges and

universities as a function of the percentage of freshmen in the top 10% of their high school

class, total spending per student, and student-to-faculty ratio. A random sample of 10

universities gave the following data on student-to-faculty ratio (S/F ratio) and graduation rate

(grad rate).

S/F ratio, x

16

20

17

19

22

17

17

17

10

18

Graduation rate, y

45

55

70

50

47

46

50

66

26

60

a. Draw a scatterplot for this set of data.

b. Determine the linear correlation coefficient, r.

c. Based on the value of r, is there sufficient evidence to conclude that there is a relationship

between the student/faculty ratio and graduation rate? Explain.

d. Determine the line of best fit.

e. Predict the graduation rate given a student/faculty ratio of 20.

f. What is the residual for a student/faculty ratio score of 20?

g. What is the coefficient of determination?

h. Is the data point (10, 26) an influential observation? Explain.

3. With a set of 8 data points, suppose that you have computed: ) = 2 + 7x, y = 17,r = .305.

Predict the value of y for a value of x = 6