Math_Problems

Week 5 Individual Assignment 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. [pic] c. Determine the coefficient of correlation. [pic] 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 [pic] 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. [pic] 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). About 68 percent of the predictions would be between what two values' Y’=3.767 +..3630(7)=3.767 + 2.541=6.308 Chap 14, #1, #3, 1. The director of marketing at Reeves Wholesale Products is studying the monthly sales. Three independent variables were selected as estimators of sales: regional population, per-capita income and regional unemployment rate. The regression equation was computed to be (in pounds). Y' = 64,100 + 0.394X1 + 9.6X2 + 11,600X3 a) What is the full name of the equation' Multiple regression b) Interpret the number 64,100. It is the Y intercept c) What are the estimated monthly sales for a particular region with a population of 796,000, per-capita income of 6,940 and an unemployment rate of 6.0%' Y’= 64,100 + .394(796000) + 9.6(6940) - 11600(6) = 64100 + 313624+ 66624- 69600= $374748 3. A sample of General Mills employees was studied to determine their degree of satisfaction with their present life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied, namely, age at the time of first marriage (X1), annual income (X2), number of children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the average number of social activities per week—such as bowling and dancing (X6). Suppose the multiple regression equation is: Yˆ= 16.24+ 0.017X1 + 0.0028X2 + 42X3 + 0.0012X4 + 0.19X5 + 26.8X6 a. What is the estimated index of satisfaction for a person who first married at 18, has an annual income of $26,500, has three children living, has assets of $156,000, has an index of health status of 141, and has 2.5 social activities a week on the average' Yˆ= 16.24+ .017(18) + .0028(26500) + 42(3) + .0012(156000) + 0.19(141) + 26.8(2.5) 497.736=16.24 + .306 + 74.2 + 126 + 187.2 + 26.79 + 67 b. Which would add more to satisfaction, an additional income of $10,000 a year or two more social activities a week' Social activities Chap 16 #5 5. The following table lists the annual amounts of glass cullet produced by Kimble GlassWorks, Inc. ScrapYear Code (tons) 2002 1 2.0 2003 2 4.0 2004 3 3.0 2005 4 5.0 2006 5 6.0 Determine the least squares trend equation. Estimate the amount of scrap for the year 2008. [pic] b = 0.9*(1.5811/1.5811) = 0.9 a = 4 – 0.9*3 = 1.3 [pic]= 1.3 + 0.9 t [pic]= 1.3 + 0.9*7 = 7.6