#8

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.x6.25.84.25.26.26.511.1y?1.8

?4.0

?7.4

?4.0

3.6?0.1

?4.4

Complete parts (a) through (e), given?x=45.2,?y=?18.1,

?x²=320.66,?y²=122.33,?xy=?113.41,

andr?0.074.

(a) Draw a scatter diagram displaying the data.

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

(c) Findx, andy. Then find the equation of the least-squares line=a+bx. (Round your answers forxandyto two decimal places. Round your answers foraandbto three 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 three decimal places. Round your answers for the percentages to one 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 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.

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. 6.2 5.8 4.2 5.2 6.2 6.5 11.1 1.8 4.0 7.4 4.0 3.6 o.1 4.4 Complete parts (a) through (e), given 2x = 45.2, 2y = 18.1,2x2 = 320.66, 2y2 = 122.33, by = 113.41, and r a: 0.074. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums 2x, 2y, 2x2, Zyz, Exy, and the value of the sample correlation coefcient r. (Round your value for r to three decimal places.) 2x = 2y = 2x2 = 23y2 = zxy = r: HUHUUU (c) Find )7, and F. Then nd the equation of the least-squares line 9 = a + bx. (Round your answers for)? and F to two decimal places. Round your answers for a and b to three decimal places.) =: E + X ' '