Question: Does prison really deter violent crime? Let \(x\) represent percent change in the rate of violent crime and \(y\) represent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained (Source: The Crime Drop in America, edited by Blumstein and Wallman, Cambridge University Press).

1. Draw a scatter diagram displaying the data.
2. Verify the given sums \(\Sigma x, \Sigma y, \Sigma x^{2}, \Sigma y^{2}\), and \(\Sigma x y\) and the value of the sample correlation coefficient \(r\) .
3. Find \(\bar{x}, \bar{y}, a\), and \(b\). Then find the equation of the least-squares line \(\hat{y}=a+b x\)
4. Graph the least-squares line on your scatter diagram. Be sure to use the point \((\vec{x}, \bar{y})\) as one of the points on the line.
5. Find the value of the coefficient of determination \(r^{2}\). 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? Answers may vary slightly due to rounding.
   Complete parts (a) through (e), given \(\Sigma x=44.7, \Sigma y=-17.4, \Sigma x^{2}=315.85\) \(\Sigma y^{2}=116.1, \Sigma x y=-107.18\), and \(r \approx 0.084\)
6. Considering the values of \(r\) and \(r^{2}\), does it make sense to use the least-squares line for prediction? Explain.

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