Question: Violent Crimes: Prisons Does prison really deter violent crime? Let x represent percent change in the rate of violent crime and y represent percent change rate of imprisonment in the general U.S. population.

X 6.1 5.7 3.9 5.2 6.2 6.5 11.1

Y -1.4 -4.1 -7.0 -4.0 3.6 -0.1 -4.4

Complete Parts (a) through (c) for these data, and comment on the meaning of r and r² in the context of this problem.

1. Draw a scatter diagram for the data.
2. From the scatter diagram, would you estimate the correlation coefficient r to be closest 1, 0, or –1?
3. Compute the correlation coefficient r and the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x by using the least-squares line? What percent of the variation is unexplained?

Answers may vary slightly due to the rounding

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