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Unformatted text preview: ORIE 312 — Final Exam Spring 2008 Professors Peter Jackson and David Ruppert This exam is closed book. Time yourself carefully. Do the problems first that you find easiest. You do not need to complete all numerical calculations. For example, an answer in the form (0.1)(157) + (0.9)(123) would be just as acceptable as 126.4. The point value of each subquestion is in square brackets, for example, [4]. Good luck. 1. In the analysis of an industrial experiment, Y is 1 if an item is defective (and 0 otherwise) and X is the rate of gas flow during the heating step in the manufacturing process. The logistic regression model used was P ( Y = 1  X ) = L ( β + β 1 X + β 2 X 1 ) where L is the logistic function. The estimated coefficients were b β = 25, b β 1 = 1 . 5, and b β 2 = 0 . 6. (a) What is the probability that an item is defective given that gas flow rate was 10.5 during the heating step? [5] (b) If it is desired to set the gas flow rate to minimize the probability of the item being defective, then what rate would you recommend? [5] 2. To study the problem of high variation in a manufacturing process, five batches were sampled from the production line. Each batch had four items. The batches were sampled four hours apart, and the items within a batch were sampled within one minute of each other. A fixed effects analysis was done in R with the default constraint. The results are below. Call: lm(formula = y ~ batch) Coefficients: Estimate Std. Error t value Pr(>t) (Intercept) 10.02846 0.08268 121.293 < 2e16 *** batch2 0.08069 0.11693 0.690 0.50066 batch3 3.03873 0.11693 25.988 6.89e14 *** batch4 0.19822 0.11693 1.695 0.11068 batch5 0.57697 0.11693 4.935 0.00018 *** Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 Residual standard error: 0.1654 on 15 degrees of freedom Multiple RSquared: 0.9847, Adjusted Rsquared: 0.9806 Fstatistic: 240.6 on 4 and 15 DF, pvalue: 2.082e13 (a) What was the sample mean for batch 2? [3] (b) What is the constraint used by...
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 Spring '09
 JACKSON
 Forecasting, Linear Regression, Regression Analysis, Errors and residuals in statistics, normal QQ plot

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