Linear regression-

only 2.31

data set: http://www.cnachtsheim-text.csom.umn.edu/Kutner/Chapter%20%201%20Data%20Sets/CH01PR28.txt

2.31. Refer to Crime rate Problem 1.28 a. Set up the ANOVA table. b. Carry out the test in Problem 2.30a by means of the F test. Show the numerical equivalence of the two test statistics and decision rules. Is the P-value for the F test the same as that for the t test? c. By how much is the total variation in crime rate reduced when percentage of high school graduates is introduced into the analysis? Is this a relatively large or small reduction? d. Obtain r. 1.28. Crime rate. A criminologist studying the relationship between level of education-and crime rate in medium-sized U.S. counties collected the following data for a random sample of 84 coun- ties; X is the percentage of individuals in the county having at least a high-school diploma, and Y is the crime rate (crimes reported per 100,000 residents) last year. Assume that first-order regression model (1.1) is appropriate. i: 1 2 3 82 83 84 X/: 74 82 81 88 83 76 8,487 8,179 8,362 8,040 6,981 7,582 a. Obtain the estimated regression function. Plot the estimated regression function and the data. Does the linear regression function appear to give a good fit here? Discuss. b. Obtain point estimates of the following: (1) the difference in the mean crime rate for two counties whose high-school graduation rates differ by one percentage point, (2) the mean crime rate last year in counties with high school graduation percentage X = 80, (3) 810, (4) 02 2.30. Refer to Crime rate Problem 1.28. a. Test whether or not there is a linear association between crime rate and percentage of high school graduates, using a t test with a = .01. State the alternatives, decision rule, and conclusion. What is the P-value of the test? b. Estimate B, with a 99 percent confidence interval. Interpret your interval estimate