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

4

.2

6

.2

6.5

8

.1

Y

-

1.0

-

4.2

-

6.2

-

4.0

-

3.6

-

2

.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.