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 A sample of 6 recent fires in some suburb of a major city is selected. The amount of damage and the distance between the fire and the nearest fire station are recorded for each fire in the table below: Distance from fire station(miles)2.91.34.41.82.65.1Fire damage ($ thousands)26.116.830.322.825.135Find the least squares line for the given data.Test the null hypothesis ?0: ?1= 0 against ??: ?1 ≠ 0. Use ? = 0.05. Interpret the result.Find coefficient of correlation ? and interpret its its value.Predict possible amount of the fire damage for the house that is ?? = 3.5 miles from the nearest station. Use a 90% prediction interval.

As per the Bartleby guildlines we are supposed to do only first question Given that Let X denotes…

Answered: Distance from fire station (miles)…

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 26PFA

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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 A sample of 6 recent fires in some suburb of a major city is selected. The amount of damage and the distance between the fire and the nearest fire station are recorded for each fire in the table below:

Distance from fire station

(miles)

2.9

1.3

4.4

1.8

2.6

5.1

Fire damage ($ thousands)

26.1

16.8

30.3

22.8

25.1

Find the least squares line for the given data.
Test the null hypothesis ?0: ?1= 0 against ??: ?1 ≠ 0. Use ? = 0.05. Interpret the result.
Find coefficient of correlation ? and interpret its its value.
Predict possible amount of the fire damage for the house that is ?? = 3.5 miles from the nearest station. Use a 90% prediction interval.

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