Description
Data Analysis 1-The Challenger
On January 28, 1986, the space shuttle Challenger disintegrated immediately
after launch (after 1 minutes and 13 seconds), killing all seven astronauts on
board (the first civilian astronaut among them). The attached data set (Challenger.txt) records data on O-rings (devices that seal the field joints of the solid
rocket motors, which boost the shuttle into orbit), on 23 space shuttle launches
prior to the accident. After each launch, the rocket motors are recovered from
the ocean for inspection and possible reuse. There were 24 launches before the
Challenger, but for one flight the motors were lost at sea. The data consist of:
temperature (of the joint) at take-o↵ in F degrees (temp); leak-check pressure
in psi (pres), that is the pressure used to test the O-rings after assembly of the
rockets1; number of O-rings that failed out of n = 6 (the total number of primary O-rings in the shuttle). Other variables in the set, which you may ignore,
count the instances of erosion, blowby, damage. Erosion is caused by excessive
heat burning up the O-ring. Blowby happens when gases rush by the O-ring.
1) Before the Challenger launch, it was suspected that the pressure used in
the leak-check test (which as you can see was increased from 50 to 200
psi) could cause some erosion and that the temperature could have an
e↵ect on the O-rings. Use these data to try to understand the probability
of failure as a function of temperature and of temperature and pressure
(which means you should compare the models as well). Use then the
fitted model to estimate the probability of failure of an O-ring when the
temperature was 31 F (the launch temperature on January 20, 1986).
2) Approach the previous problem with LDA, QDA, and KNN with K = 1.
In this case, use the ungrouped data Challengerungrouped.txt.
Data Analysis 2. Titanic
The Titanic sank when it struck an iceberg on its voyage to New York City from
Southampton. Of the 2201 known passengers and crew, only 711 survived. The
1After ignition, heat and pressure build up in the motor, the O-rings which would erode
under heat are protected by a putty which is displaced toward the O-ring under pressure
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data in the file titanic.txt classify the people on board the ship according to sex
(male/female), age in categorical form (child/adult); class (first, second, third
class passengers, crew). The data are grouped so for each age/sex/class combination totaling to the number m the number of surviving people is reported.
1) Fit a logistic regression model using sex, age, and class as predictors (they
are factors). Is the model adequate, that is, does the mean function obtained matches the data well?
2) Add now to the previous term all two-factors interactions and decide if
any can be removed. If the mean function you have obtained matches
the data well, summarize the result. For example, how does the survival
of the first class passengers di↵er from the third class passenegers? Did
children in first class survived more than children in third?
LDA and Logistic Regression. Theoretical Questions
Solve exercises 4.2 and 4.3 in the book ESL.
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