Question
2. Does prison really deter violent crimes? Let X represent percent change in the rate of violent crime and y represent percentage change in the
2.
Does prison really deter violent crimes? Let X represent percent change in the rate of violent
crime and y represent percentage change in the rate of imprisonment in the general U. S.
population. For seven recent years, the following data have been obtained.
X
6.3
6.0
3.6
5.2
6.2
6.5
11.1
Y
-
1.0
-
4.2
-
6.2
-
4.0
3.6
-
0.1
-
4.4
a.
Compute the value of the sample correlation coefficient r. (Round your value for r to be
three decimal places)
b.
Find the equation of the least-squares line
y a bx
(Round your value for a and b to
be three decimal places)
c.
Find the value of the coefficient of determination
2
r
. What percentage of the variation
in y can be explained by the corresponding variation in x and the least - squares line?
What percentage is unexplained? (Round your value for r to be three decimal places)
d.
Considering the values of r and
2
r
, does it make sense to use the least - squares line for
predictions. Explain your answers.
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