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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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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.

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.

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