The Statistical Sleuth Chapter 22, Problem 23 Space Shuttle O-Ring Failure On Ja

Question

The Statistical Sleuth

Chapter 22, Problem 23

Space Shuttle O-Ring Failure On January 27, 1986, the night before the space shuttle Chal- lenger exploded, an engineer recommended to the National Aeronautics and Space Administration (NASA) that the shuttle not be launched in the cold weather. The forecasted temperature for the Challenger launch was 31F—the coldest launch ever. After an intense 3-hour telephone conference, officials decided to proceed with the launch. Shown in Display 22.15 are the launch temperatures and the number of O-ring problems in 24 shuttle launches prior to the Challenger (Chapter 4). Do these

data offer evidence that the number of incidents increases with decreasing temperature?

Data set in R:

library(Sleuth3)

ex2223

(Please also include R code)

My approach:

model1 <- glm(Incidents ~ Temp, data = ex2223, family = poisson)
summary(model1)
pchisq(model1$deviance, df = model1$df.residual, lower.tail = FALSE)

(I don't know what to do next.)

Explanation / Answer

Here we estimate the Poisson Regression model to predict the no. of incidents (discrete variable) based on temp (continuous variable).

library(Sleuth3)
ex2223
str(ex2223)
plot(ex2223)

model1 <- glm(Incidents ~ Temp, data = ex2223, family = poisson)
summary(model1)

We find the equation:

ln(Incidents) = 6.39 - 0.1089*Temp

Inferences:

1) Variable Temp is significant to predict the no. of incidents, since p-value<0.05.

2) Temp is inversely related to the no. of incidents since coefficient sign is negative.

3) Unit decrease in temp increase the no. of incidents by 1.12 times.

[R code: exp(-model1$coefficients[2]) ]

Thus, the data offers evidence that the number of incidents increases with decreasing temperature.

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