hw3fall11 - (c Test whether there is a linear relationship...

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STAT5044: Regression and ANOVA Homework #3 Problem# 1. (Sales growth data) A marketing researcher studies annual sales of a product that had been introducted 10 years ago. The data are as follows, where X is the year (coded) and Y is sales in thousands of units: i 1 2 3 4 5 6 7 8 9 10 x i 0 1 2 3 4 5 6 7 8 9 y i 98 135 162 178 221 232 283 300 374 395 Does a linear relation appear adequate here? Do you also believe that all the assump- tions about a simple linear normal regression model are correct for this data? If not, what is the problem ? Justify your claim. Problem# 2. Without using R commends such as “lm”, “bptest”, and “conf”, you program for each problem and solve the problem. Refer to Airfreight breakage (Prob- lem 1 in hw2). (a) Fit the simple linear regression and estimate parameters. (b) Obtain confidence interval under normality assumption of error
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Unformatted text preview: (c) Test whether there is a linear relationship between x and y. Problem# 3. Refer to Airfreight breakage (Problem 1 in hw2). Without normality assumption, create the distribution of β 1 using bootstrap method and then obtain a 95% confidence interval of β 1 . Compare your confidence interval with the one which obtained under normality assumption. Why different? or why similar? NOTE: use the following R commend, “sample(x,n,replace=TRUE)” and “quan-tile(x,probs=c(0.025,0.975)”) Problem# 4. Refer to Sales growth data (Problem 1) Check all assumptions. Perform Brown-Forsy test. Consider 5 or 6 different two groups and calculate how many times you obtain constant variance. Compare this result with Brunsch-Pagan test 1...
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