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, x (km), between the fire and the nearest fire station are given in the following table. 3.1 y 26.2 17.8 31.3 23.1 27.5 36.0 14.1 22.3 6.1 3.4 1.8 4.6 2.3 5.5 0.7 3.0 2.6 4.3 2.1 1.1 4.8 3.8 y 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 give any reason to doubt the usual assumptions of the model. (b) Write a short report giving your conclusions. You do not need to upload the output from R. Include a possible interpretation of the intercept and slope parameters.
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, x (km), between the fire and the nearest fire station are given in the following table. 3.1 y 26.2 17.8 31.3 23.1 27.5 36.0 14.1 22.3 6.1 3.4 1.8 4.6 2.3 5.5 0.7 3.0 2.6 4.3 2.1 1.1 4.8 3.8 y 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 give any reason to doubt the usual assumptions of the model. (b) Write a short report giving your conclusions. You do not need to upload the output from R. Include a possible interpretation of the intercept and slope parameters.
Chapter4: Linear Functions
Section4.3: Fitting Linear Models To Data
Problem 19SE: For the following exercises, draw a best-fit line for the plotted data.
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Transcribed Image Text: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.
3.4
1.8
4.6
2.3
3.1
5.5
0.7
3.0
y 26.2 17.8 31.3 23.1 27.5 36.0
2.1
y 19.6 31.3 24.0 17.3 43.2 36.4 26.1
14.1 22.3
2.6
4.3
1.1
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.
(b) Write a short report giving your conclusions. You do not need to upload the output
from R. Include a possible interpretation of the intercept and slope parameters.
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