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Regression Analysis

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Question;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?;and? ? 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? = 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.

 

Paper#60218 | Written in 18-Jul-2015

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