1. Suppose 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 Atlanta. A sample of 15 recent fires in this suburb is selected. The amount of damage, y, and the distance between the fire and the nearest fire station, x, are recorded for each fire. The results are shown in Table 1. Answer the following questions:
Distance from Fire Fire Damage (y) in Distance from Fire Fire Damage (y) in
Station (x) in Miles Thousands of Dol. Station (x) in Miles Thousands of Dol.
3.4 26.2 2.6 19.6
1.8 17.8 4.3 31.3
4.6 31.3 2.1 24.0
2.3 23.1 1.1 17.3
3.1 27.5 6.1 43.2
5.5 36.0 4.8 36.4
0.7 14.1 3.8 26.1
3.0 22.3 — —
(a) Construct a regression model (least squares model) to relate fire damage, y, to the distance from the nearest fire station, x. Explain the meaning of ß0 and ß1 – the y-intercept and the slope.
(b) Test the null hypothesis that the slope is zero – that is, that there is no linear relationship between fire damage and the distance from the nearest fire station – against the alternative hypothesis that fire damage increases as the distance increases. Explain your results.
Use a = 5%.
(c) What are the values of coefficient of determination and coefficient of correlation? Explain.
(d) Suppose that the insurance company wants to predict the fire damage if a major residential fire were to occur 3.5 miles from the nearest fire station.
(e) What is a 95% confidence interval for y when x = 3.5 miles?
(f) Can we use this regression model to make predictions for homes less than 0.7 miles or more than 6.1 miles from the nearest fire station? Explain your answer.
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