(Solution) - Does prison really deter violent crime Let x represent percent -(2025 Original AI-Free Solution)

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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):

Complete parts (a) through (e), given ?x = 44.7, ?y = ?17.4, ?x2 = 315.85, ?y2 = 116.1, ?xy = ?107.18, and r ? 0.084.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums ?x, ?y, ?x2, ?y2, and ?xy and the value of the sample correlation coefficient r.
(c) Find x, y, a, and b. Then find the equation of the least-squares line ? = ? + bx.
(e) Find the value of the coefficient of determination r2. 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?
(f) Considering the values of r and r2, does it make sense to use the least-squares line for prediction? Explain.