Question

1. Suppose that a fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. The study is to be conducted in a large suburb of a major city. A sample of 14 recent fires in this suburb is selected. The amount of damage, y, and the distance between the fire and the nearest station, x, are given below. We are interested in building a regression model to predict fire damage y, given the distance from the fire x.

Distance	3.4    1.8     4.6    2.3     3.1    5.5     0.7   3.0     2.6    4.3     2.1   1.1     6.1    4.8
Damage	26.2 17.8 31.3 23.1 27.5 36.0 14.1 22.3 19.6 31.3 24.0 17.3 43.2 36.4

1. Is the predictor distance significant? What is the test statistic and p value?
2. What is the amount of variation explained in the model?
3. What is the standard error of the estimated regression line?
4. Use the final regression equation to predict the damage caused by the fire that is 6.5 miles away from the nearest station.

Answer 1

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