Enrollment (thousands) 53 28 27 36 42 Burglaries 86 57 32 131
157
For the following problems, use the sample data in the table
above consisting of numbers of enrolled students (in thousands) and
numbers of burglaries for randomly selected large colleges.
Enrollment (thousands)
53
28
27
36
42
Burglaries
86
57
32
131
157
1. Find the linear correlation coefficient r and the critical
values for a 0.05 significance level. What can be determined from
this?
2. Which of the following change if the two variables of
enrollment and burglaries are switched: the value of r, the
critical values?
3. Does the value of r change from what was found in question 1
if the actual enrollment numbers of 53,000, 28,000, 27,000, 36,000
and 42,000 are used instead of 53, 28, 27, 36 and 42?
4. If you had calculated the value of the linear correlation
coefficient to be 1.247, what should you conclude?
5. Find the regression equation for the sample data. What is the
best-predicted number of burglaries, given an enrollment of 50
(thousand) and how did you find it?
6. Repeat the previous question, assuming that the linear
correlation coefficient is r = 0.997.
7. Using the original linear correlation coefficient r that you
found in question 1, what is the proportion of the variation in
numbers of burglaries that is explained bu the linear relationship
between enrollment and the number of burglaries?
8. True or false: If there is no linear correlation between
enrollment and the number of burglaries, then those two variables
are not related in any way.