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Unformatted text preview: STAT3503 Assignment # 2 Question 1. ( Use SAS to solve this question ) A criminologist studying the relationship between level of education and crime rate in medium-size U.S. counties collected the following data for a random sample of 84 counties; 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 is appropriate.  (a) Obtain the estimated regression function.  (b) Test whether or not there is a linear association between crime rate and percentage of high school graduates, using a t test with = 0 . 01. State the alternatives, decision rule, and conclusion. What is the P-value of the test?  (c) Set up the ANOVA table.  (d) Carry out the test in part (b) by means of the F test. Show the numerical equivalence of the two test statistics and decision rules, explain it. Is the P-value for the F test the same as that for the t test, why?  (e) Obtain R 2 and r.  (f) Obtain the residuals e i and prepare a box plot of the residuals. What information is provided by your plot.  (g) Plot the residuals e i against the fitted values X i to ascertain whether any departures from the simple linear regression model. State your findings.  (h) Prepare a normal probability plot(Q-Q plot) of the residuals. Does the normality assumption appear to be reasonable here?  (i) Use the Brown-Forsythe test to determine whether or not the error variance varies with the level of X. Divide the data into the two groups, X 69 , X &gt; 69, and use = 0 . 05. State the decision rule and conclusion. Does your conclusion support your preliminary findings in part (g)? SOLUTION (a) b Y = 20518- 170 . 58 X (b) H : 1 = 0 , H : 1 = 0. 1 Since s ( 1 ) = 41 . 5743, t * =- 170 . 575- 41 . 5743 =- 4 . 1029 , because | t * | &gt; t (0 . 995;82) = 2 . 63712. Conclude H . P-value = Pr ( | T | &gt; t * ) = 0 . 000096. (c)The ANOVA tale is Source DF Sum of Squares Mean Square Model 1 93462942 93462942 Error 82 455273165 5552112 Total 83 548736108 (d) H : 1 = 0 , H : 1 6 = 0....
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This note was uploaded on 09/30/2010 for the course STAT 3503 taught by Professor Smills during the Spring '07 term at Carleton CA.
- Spring '07