Question

A fire insurance company wants to examine the relationship between the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. A sample of 15 recent fires in a particular city was taken. The amount of damage to the house? (in thousands of? dollars) and the distance from the burning house to the nearest fire station? (in miles) were recorded. Part of the output from a simple linear regression analysis is given below. Assume all conditions are met for simple linear regression inference. A hypothesis test is to be performed to determine if the distance from the nearest fire station is a significant predictor of amount of damage. Which of the following is the correct conclusion based on the results of the hypothesis? test?

Predictor Constant distance Coef 16.301 3.554 SE Coef 6.015 1.663 S=9.8101 R-Sq = 26.0%
A. There is strong evidence to indicate that the distance from the nearest fire station is a significant predictor of the amount of damage ?(t-statistic =?2.137,dof=?13, P-value=?0.052).
B. There is suggestive, but weak evidence to indicate that the distance a from the nearest fire station is a significant predictor of the amount of damage ?(t-statisticequals=?2.137, dofequals=?13, ?P-valueequals=?0.052).
C. There is not enough evidence to indicate that the distance from the nearest fire station is a significant predictor of the amount of damage ?(t-statisticequals=?1.403, dofequals=?14, ?P-valueequals=?0.182).
D. There is suggestive, but weak evidence to indicate that the distance a from the nearest fire station is a significant predictor of the amount of damage?(t-statisticequals=?2.137,dofequals=?14,?P-valueequals=?0.051).
E.There is suggestive evidence to indicate that the distance from the nearest fire station is a significant predictor of the amount of damage?(t-statisticequals=?2.337, dofequals=?13, P-valueequals=?0.018).

Answer 1

Check the explanation

Explanation:

Following is the completed table with p values:

Predictor Coef SE coef T P-value

Constant 16.301 6.015 16.301/6.015=2.710 0.01785

Distance 3.554 1.663 3.554/1.663=2.137 0.05218

Here degree of freedom will be dof=15-2=13

Since p-value of distance is greater than 0.05 so distance is not significant to the model.

B. There is​ suggestive, but weak evidence to indicate that the distance a from the nearest fire station is a significant predictor of the amount of damage ​(t-statisticequals=​2.137, dofequals=​13,​P-valueequals=​0.052).