Using Python,

The Space Shuttle Challenger disaster occurred on January 28, 1986, when it

broke apart 73 seconds into its flight, leading to the deaths of its seven crew

members. The spacecraft disintegrated over the Atlantic Ocean, off the coast

of central Florida at 11:38 EST. Disintegration of the entire vehicle began after

an O-ring seal in its right solid rocket booster failed at liftoff. Subsequently, a

special commission was appointed to investigate the accident. The commission

found that NASA disregarded warnings from engineers about the dangers of

launching posed by the low temperatures of that morning, claiming that en-

gineers could not provide a convincing argument against the launch (source:

Wikipedia, Applied Probability for Engineers).

File Oring.csv provides data on launch temperature and O-ring failure for

the 24-space shuttle launches prior to the Challenger disaster. There are six

O-rings used to seal field joints on the rocket motor assembly. A +1 in the

O-rings indicates that at least one O-ring failure had occurred on that launch

and a 0 indicates that no failure had occurred.

1. Normalize the launch temperature using the expression

(x)/

2. Create a logistic regression model using the gradient decent technique to

predict the probability of O-ring failure based on the launch temperature.

Provide the equation for your model.

dataset:

Temp Failure 0 53 1 1 56 1 2 57 1 3 63 0 4 66 0 5 67 0 6 67 0 7 67 0 8 68 0 9 69 0 10 70 0 11 70 1 12 70 1 13 70 1 14 72 0 15 73 0 16 75 0 17 75 1 18 76 0 19 76 0 20 78 0 21 79 0 22 80 0 23 81 0