A fire insurance company wants to relate the amount of fire damage in major residentialfires to the distance between the residence and the nearest fire station. The study wasconducted in a large suburb of a major city; a sample of fifteen recent fires in the suburbwas selected. The amount of damage, y (£000), and the distance, x (km), between thefire and the nearest fire station are given in the following table.3.1y 26.2 17.8 31.3 23.1 27.5 36.0 14.1 22.36.13.41.84.62.35.50.73.02.64.32.11.14.83.8y 19.6 31.3 24.0 17.3 43.2 36.4 26.1(a) Fit a simple linear regression model to these data. Check if the residual plots giveany reason to doubt the usual assumptions of the model.

A fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the residence and the nearest fire station. The study was conducted in a large suburb of a major city; a sample of fifteen recent fires in the suburb was selected. The amount of damage, y (£000), and the distance, r (km), between the fire and the nearest fire station are given in the following table. 2.3 3.1 y 26.2 17.8 31.3 23.1 27.5 36.0 14.1 22.3 1.1 y 19.6 31.3 24.0 17.3 43.2 36.4 26.1 * 3.4 1.8 4.6 5.5 0.7 3.0 2.6 4.3 2.1 6.1 4.8 3.8 (a) Fit a simple linear regression model to these data. Check if the residual plots give any reason to doubt the usual assumptions of the model.