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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