In an attempt to quantify a possible relationship between the amount of ?re damage caused by residential ?res and the distance from the residence to the closest ?re station, the following data were acquired from a random sample of 12 recent ?res.
|
Distance from Fire Station
|
Fire damage
|
Distance from Fire Station
|
Fire damage
|
|
x (miles)
|
y ($103 )
|
x (miles)
|
y ($103 )
|
|
1.8
|
17.8
|
5.5
|
36.0
|
|
4.6
|
31.3
|
3.0
|
22.3
|
|
0.7
|
14.1
|
4.3
|
31.3
|
|
3.4
|
26.2
|
1.1
|
17.3
|
|
2.3
|
23.1
|
3.1
|
27.5
|
|
2.6
|
19.6
|
2.1
|
24.0
|
(i) Postulate an appropriate model, estimate the model parameters and evaluate the model ?t.
(ii) An insurance company wishes to use this model to estimate the expected ?re damage to two new houses, house A that is being built at a distance of 5 miles from the nearest ?re station, and house B, 3 miles from the same ?re station. Determine these estimates along with appropriate uncertainty intervals.
(iii) Is it "safe" to use this model to predict the ?re damage to a house C that is being built 6 miles from the nearest ?re station? Regardless of your answer, provide a prediction and an appropriate uncertainty interval.