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. x 6.5 5.5 3.5 5.2 6.2 6.5 11.1 y −1.5 −4.5 −6.2 −4.0 3.6 −0.1 −4.4 given Σx = 44.5, Σy = −17.1, Σx2 = 315.69, Σy2 = 109.27, Σxy = −104.17, and r ≈ 0.0964. a) 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? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.) r2 = explained % unexplained % b) Considering the values of r and r2, does it make sense to use the least-squares line for prediction? Explain your answer. choose one: The correlation between the variables is so high that it makes sense to use the least-squares line for prediction. The correlation between the variables is so low that it makes sense to use the least-squares line for prediction. The correlation between the variables is so high that it does not make sense to use the least-squares line for prediction. The correlation between the variables is so low that it does not make sense to use the least-squares line for prediction.
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.
x | 6.5 | 5.5 | 3.5 | 5.2 | 6.2 | 6.5 | 11.1 |
y |
−1.5
|
−4.5
|
−6.2
|
−4.0
|
3.6 |
−0.1
|
−4.4
|
given Σx = 44.5, Σy = −17.1, Σx2 = 315.69, Σy2 = 109.27, Σxy = −104.17,
and r ≈ 0.0964.
a) 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? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.)
r2 = | |
explained | % |
unexplained | % |
b) Considering the values of r and r2, does it make sense to use the least-squares line for prediction? Explain your answer. choose one:
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