The McKeesport Fire Department wants to know how likely it is that a truck pump

Question

The McKeesport Fire Department wants to know how likely it is that a truck pump will fail. The fire chief, George Pyro (no relation), thinks pump failure is a function of age (X1) and water hardness (X2 measured on a scale of 1 to 10). The department statistician runs a regression on a dummy variable (coded 1 for failure and 0 for no failure) for 217 pumps. She finds the following:

Y^ = .14 + .01X1 + .05X2

sb1 = .0002 sb2 = .025 Sy|x = .04 R2 = .93 Adj. R2 = .92

Write a memo explaining what the regression means. If the average water hardness is 3 and the chief would like to replace any pump with a probability of failing of .80 or more, at what age should pumps be replaced?

Explanation / Answer

given

Y^ = .14 + .01X1 + .05X2

sb1 = .0002 sb2 = .025 Sy|x = .04 R2 = .93 Adj. R2 = .92

now

The pump with a probability of failing is the dependent variable Y, that regressionconvey that the probability of failing is related about 0.14 plus 0.01 times pump ageplus 0.05 times water hardness

.In that condition, 0.8> 0.14 + 0.01 * age + 0.05 * 3,

so the pump age over 51 shouldbe replaced

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