A fire insurance company wants to relate the amount of fire damage in major resi

Question

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. A sample of 15 recent fires in a large suburb of a major city is selected and the amount of damage (y, in thousand dollars) and the distance (x, in miles) are given below. 4.6 31.3 A Minitab analysis gives the following output (partial output) x 3.4 2.3 3.1 5.5 0.7 3.0 2.6 4.3 6.1 4.8 3.8 y 26.2 17.8 23.1 27.5 36.3 14.1 22.3 19.6 31.3 24.0 17.3 43.2 36.4 26.1 Predictor Constant Coef 10.276 4.9178 SE Coef 1.426 0.3944 7.21 12.47 0.0000 0.0000 To test whether the regression model is significant or not, using t as our test statistic, what is going to be the rejection region at 0.05 significance level? O lt 2.1448 0 ltla 2.1604 t2 2.1604 ta 1.7709 ltla 1.7709

Explanation / Answer

To test the significance of the regression, we need to see if the coefficient of X is significant or not.

At 5% significance level, we need a two tailed test to prove it.

Hence critical value , |t|>=t(0.0975,15-1dof)=2.1448

But, the test statistic=12.47

Hence, we say that the regression is significant

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