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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 Oring failure will increase by 0.1156 (or the odds ratio of
Oring 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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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 Oring failure will increase by 0.1768 (or the odds ratio of
Oring failure will increase to exp(0.1768) times).
(c) The probability is 0.96.
(d) The probability that at least one out of six Orings fails is
. The
probability that all six Orings 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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This note was uploaded on 04/25/2010 for the course MATH 30 taught by Professor Karaali during the Spring '08 term at Pomona College.
 Spring '08
 KARAALI

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