For the 23 space shuttle flights before the Challenger mission disaster in 1986, The following table shows the temperature (◦F) at the time of the flight and whether at least one primary O-ring suffered thermal distress.Use logistic regression to model the effect of temperature on the probability of thermal distress. Interpret the effect.Estimate the probability of thermal distress at 31◦F, the temperature at the time of the Challenger flight.At what temperature does the estimated probability equal 0.50? At that temperature, give a linear approximation for the change in the estimated probability per degree increase in temperature.Interpret the effect of temperature on the odds of thermal distress.Test the hypothesis that temperature has no effect, using (i) the Wald test, (ii) the likelihood-ratio test. FtI23456789Temperature667069686772737057637078TD00000000Ft1314151617181920212223Temperature6753671011120Note: Ft= flight no., TD = thermal distress (1 = yes, 0 = no).7570817679757658TD0111

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 51E

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For the 23 space shuttle flights before the Challenger mission disaster in 1986, The following table shows the temperature (◦F) at the time of the flight and whether at least one primary O-ring suffered thermal distress.

Use logistic regression to model the effect of temperature on the probability of thermal distress. Interpret the effect.
Estimate the probability of thermal distress at 31◦F, the temperature at the time of the Challenger flight.
At what temperature does the estimated probability equal 0.50? At that temperature, give a linear approximation for the change in the estimated probability per degree increase in temperature.
Interpret the effect of temperature on the odds of thermal distress.
Test the hypothesis that temperature has no effect, using (i) the Wald test, (ii) the likelihood-ratio test.

Ft
I
2
3
4
5
6
7
8
9
Temperature
66
70
69
68
67
72
73
70
57
63
70
78
TD
00000000
Ft
13
14
15
16
17
18
19
20
21
22
23
Temperature
67
53
67
10
11
12
0
Note: Ft= flight no., TD = thermal distress (1 = yes, 0 = no).
75
70
81
76
79
75
76
58
TD
0
1
1
1

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Interpret the effect of temperature on the odds of thermal distress.
Test the hypothesis that temperature has no effect, using (i) the Wald test, (ii) the likelihood-ratio test.

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