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homework_3_solution

homework_3_solution - LINEAR REGRESSION MODELS W4315...

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LINEAR REGRESSION MODELS W4315 HOMEWORK 3 ANSWERS February 20, 2010 Instructor: Frank Wood 1. (50 points) 1 Refer to Copier maintenance Problem 1.20. a. Estimate the change in the mean service time when the number of copiers serviced increases by one. Use a 90 percent confidence interval. Interpret your confidence interval. b. Conduct a t test to determine whether or not there is a linear association between X and Y here; control the α risk at .10. State the alternatives, decision rule, and conclusion. What is the P -value of your test? c. Are your results in parts (a) and (b) consistent? Explain. d. The manufacturer has suggested hat the mean required time should not increase by more than 14 minutes for each additional copier that is serviced on a service call. Conduct a test to decide whether this standard is being satisfied by Tri-City. Control the risk of a Type I error at .05. State the alternatives, decision rule, and conclusion. What is the P -value of the test? e. Does b 0 give any relevant information here about the ”start-up” time on calls-i.e., about the time required before service work is begun on the copiers at a customer location? Answer: a. First read the data into Matlab and estimate the coefficients of the regression line pr1=textread(’CH01PR20.txt’); X=pr1(:,2); Y=pr1(:,1); avgX = mean(X); avgY = mean(Y); SXX = sum (( X - avgX ) . 2 ); SXY = sum((X-avgX).*(Y-avgY)); b1 = SXY/SXX; b0 = avgY- b1*avgX; 1 This is problem 2.5 in ”Applied Linear Regression Models(4th edition)” by Kutner etc.
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