Does prison really deter violent crime? Letxrepresent percent change in the rate of violent crime andyrepresent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained.x6.35.94.15.26.26.511.1y1.2

4.0

7.4

4.0

3.60.1

4.4

Complete parts (a) through (e), givenx=45.3,y=17.5,

x²=322.25,y²=120.53,xy=109.47,

andr0.0800.(a) Draw a scatter diagram displaying the data.

(b) Verify the given sumsx,y,x²,y²,xy, and the value of the sample correlation coefficientr. (Round your value forrto four decimal places.)x=y=x²=y²=xy=r=

(c) Findx, andy. Then find the equation of the least-squares line=a+bx. (Round your answer to four decimal places.)x=y==+x

(d) Graph the least-squares line. Be sure to plot the point (x,y) as a point on the line.

(e) Find the value of the coefficient of determinationr². What percentage of the variation inycan beexplainedby the corresponding variation inxand the least-squares line? What percentage isunexplained? (Round your answer forr²to four decimal places. Round your answers for the percentages to two decimal place.)r²=explained%unexplained%

(f) Considering the values ofrandr², does it make sense to use the least-squares line for prediction? Explain your answer.

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 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.