Problems

May 24, 2010

Chap 13, #5, #15, #21

5. The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asks the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information.

a. If we want to estimate crimes on the basis of the number of police, which variable is the dependent variable and which is the independent variable? Police is the independent variable, and crime is the dependent variable.

b. Draw a scatter diagram.

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c. Determine the coefficient of correlation.

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r=-231.75/8-1(5.873)(6.446)=-231.75/265= -.8744

d. Determine the coefficient of determination.

R2 = r2 = (-.8744)2=.7646

e. Interpret these statistical measures. Does it surprise you that the relationship is inverse? No, as the police numbers increase the crime decrease.

15. Bradford Electric Illuminating Company is studying the relationship between kilowatt hours (thousands) used and the number of rooms in a private single-family residence. A random sample of 10 homes yielded the following.

Number of Kilowatt-Hours Number of Kilowatt-Hours

Rooms (thousands) Rooms (thousands)

12 9 8 6

9 7 10 8

14 10 10 10

6 5 5 4

10 8 7 7

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a. Determine the regression equation.

r=44.6/10-1(2.726)(2.011)=44.6/49.31=.904

b=.904(2.011/2.7726)=.904*.737=.667

a.= 7.4-.667(9.1)=1.333

b. Determine the number of kilowatt-hours, in thousands, for a six-room house.

Yˆ= 1.33 + .667(6) =5.33

21. Refer to Exercise 13.

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a. Determine the standard error of estimate.

r=10.6/5-1(2.702)*(1.303)=10.6/43.1=.752

b=.752(1.304)/(2.701)=.752*.483=.3630

a=5.8-.3630*(5.6)=5.8-2.033=3.767

b. Suppose a large sample is selected (instead of just five)....