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ps4sol - Stat 203 HW 4 Solution 1 Some students may treat...

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Stat 203 HW 4 Solution 1. Some students may treat any number > 0 as 1, but this will cause a lost of information. So they can get at most 8 points. A sample of R code is attached in the end. (a) The fitted result is: Call: glm(formula = Y ~ T, family = binomial) Deviance Residuals: Min 1Q Median 3Q Max -0.95227 -0.78299 -0.54117 -0.04379 2.65152 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 5.08498 3.05247 1.666 0.0957 . T -0.11560 0.04702 -2.458 0.0140 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 24.230 on 22 degrees of freedom Residual deviance: 18.086 on 21 degrees of freedom AIC: 35.647 Number of Fisher Scoring iterations: 5 We can see that the temperature has a coefficient of -0.1156, meaning what when temperature decreases by 1, the log odds ratio of O-ring failure will increase by 0.1156 (or the odds ratio of O-ring failure will increase to exp(0.1156) times). (b) The fitted result is: Call: glm(formula = Y[-18, ] ~ T[-18], family = binomial) Deviance Residuals:
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Min 1Q Median 3Q Max -0.7608 -0.5742 -0.3320 -0.1861 1.5204 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 8.66157 3.63441 2.383 0.01716 * T[-18] -0.17680 0.05869 -3.013 0.00259 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 20.0667 on 21 degrees of freedom Residual deviance: 9.4096 on 20 degrees of freedom AIC: 24.748 Number of Fisher Scoring iterations: 6 We can see that the temperature has a coefficient of -0.1768, meaning what when temperature decreases by 1, the log odds ratio of O-ring failure will increase by 0.1768 (or the odds ratio of O-ring failure will increase to exp(0.1768) times). (c) The probability is 0.96. (d) The probability that at least one out of six O-rings fails is . The probability that all six O-rings fail is . Our judgment should be based on one of the above two percentage, which are both too high. So I would not advise that; launching at so low temperature was obviously unwise. (Students will get full credit if only they make right judgment.
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