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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. x 6.5 6.5 5.2 6.2 5.4 3.9 1.6 -4.4 -6.6 -4.0 3.6 -0.1 -4.4 y LAUSE SALT Complete parts (a) through (e), given Ex=44.8, y=-17.5, x2 = 317.56, y2 = 113.81, Exy=-107.87, and r-0.0889. (a) Draw a scatter diagram displaying the data. # x(percent change in the rate of violent crime) xpercent change in the rate of violent crime x(percent change in the rate of violent crime xpercent change in the rate of violent crime) (b) Verify the given sums x, y, x, y2, xy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex= Ey= Sy= (c) Find x, and y. Then find the equation of the least-squares line;= a + bx. (Round your answer to four decimal places.) x= y= 9TH ܐܨܕ

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 6.5 5.2 6.2 5.4 3.9 1.6 -4.4 -6.6 -4.0 3.6 -0.1 -4.4 y LAUSE SALT Complete parts (a) through (e), given Ex=44.8, y=-17.5, x2 = 317.56, y2 = 113.81, Exy=-107.87, and r-0.0889. (a) Draw a scatter diagram displaying the data. # x(percent change in the rate of violent crime) xpercent change in the rate of violent crime x(percent change in the rate of violent crime xpercent change in the rate of violent crime) (b) Verify the given sums x, y, x, y2, xy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex= Ey= Sy= (c) Find x, and y. Then find the equation of the least-squares line;= a + bx. (Round your answer to four decimal places.) x= y= 9TH ܐܨܕ

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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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. x y 6.5 5.4 1.6 -4.4 -6.6 5.2 6.2 6.5 11.1 -4.0 3.6 -4.4 LAUSE SALT Complete parts (a) through (e), given Ex= 44.8, Ey=-17.5, x2 = 317.56, xy2 = 113.81, Exy=-107.87, and r = 0.0889. (a) Draw a scatter diagram displaying the data. JE -2 x (percent change in the rate of violent crime) x(percent change in the rate of violent crime) x(percent change in the rate of violent crime) x(percent change in the rate of violent crime) (b) Verify the given sums Ex, y, x2, xy2, xy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ey= Ex2- v2. Exy = r= (c) Find x, and y. Then find the equation of the least-squares line;= a + bx. (Round your answer to four decimal places.) 9- X
Transcribed Image Text: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 y 6.5 5.4 1.6 -4.4 -6.6 5.2 6.2 6.5 11.1 -4.0 3.6 -4.4 LAUSE SALT Complete parts (a) through (e), given Ex= 44.8, Ey=-17.5, x2 = 317.56, xy2 = 113.81, Exy=-107.87, and r = 0.0889. (a) Draw a scatter diagram displaying the data. JE -2 x (percent change in the rate of violent crime) x(percent change in the rate of violent crime) x(percent change in the rate of violent crime) x(percent change in the rate of violent crime) (b) Verify the given sums Ex, y, x2, xy2, xy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ey= Ex2- v2. Exy = r= (c) Find x, and y. Then find the equation of the least-squares line;= a + bx. (Round your answer to four decimal places.) 9- X
(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 10 x (percent change in the rate of violent crime) x(percent change in the rate of violent crime) x(percent change in the rate of violent crime) x(percent change in the rate of violent crime) (e) Find the value of the coefficient of determination 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? (Round your answer for 2 to four decimal places. Round your answers for the percentages to two decimal place.) 2- % explained unexplained (f) Considering the values of r and r2, does it make sense to use the least-squares line for prediction? Explain your answer. The correlation between the variables is so low that it does not make 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 makes sense to use the least-squares line for prediction. The correlation between the variables is so high that it makes sense to use the least-squares line for prediction.
Transcribed Image Text:(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 10 x (percent change in the rate of violent crime) x(percent change in the rate of violent crime) x(percent change in the rate of violent crime) x(percent change in the rate of violent crime) (e) Find the value of the coefficient of determination 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? (Round your answer for 2 to four decimal places. Round your answers for the percentages to two decimal place.) 2- % explained unexplained (f) Considering the values of r and r2, does it make sense to use the least-squares line for prediction? Explain your answer. The correlation between the variables is so low that it does not make 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 makes sense to use the least-squares line for prediction. The correlation between the variables is so high that it makes sense to use the least-squares line for prediction.
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