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
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2CYU
Related questions
Question
Help me answer all parts except A&D
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
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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