Question
The O-rings in the booster rockets on the space shuttle are designed to expand when heated to seal different chambers of the rocket so that
The O-rings in the booster rockets on the space shuttle are designed to expand when heated to seal different chambers of the rocket so that solid rocket fuel is not ignited prematurely. According to engineering specifications, the O-rings expand by some amount, say at least 5%, in order to ensure a safe launch. Hypothetical data on the amount of O-ring expansion and the atmospheric temperature in Fahrenheit at the time of several different launches are given in the table below.
Temperature | % O-ring Expansion |
---|---|
93 | 22.2 |
88 | 20.9 |
87 | 20.5 |
81 | 19.8 |
73 | 18.6 |
72 | 19.1 |
68 | 17.2 |
64 | 16.3 |
55 | 15.4 |
(A) Obtain a simple linear regression model to estimate the amount of O-ring expansion as a function of atmospheric temperature. What is the estimated regression function? (Let X1 represent the temperature in Fahrenheit and Y represent the percentage of O-ring expansion. Round your numerical values to four decimal places.)
=(???)
=Interpret the R2 statistic for the model you obtained. (Enter your answer as a percent. Round your answer to two decimal places.)
(B) The R2 statistic indicates that approximately (???) % of the total variation in the percentage of O-ring expansion is accounted for by temperature.
(C) Suppose that NASA officials are considering launching a space shuttle when the temperature is 28 degrees. What amount of O-ring expansion (in %) should they expect at this temperature according to your model? (Round your answer to two decimal places.)
(???) %
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