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 1.8 2.3 5.5 0.7 3.0 2.6 4.3 2.1 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 Source MS 841.25 5.41 DF 841.25 70.33 911.59 155.49 0.000 13 Error Total To test whether regression model exists or not using variance ratio test, what is going to be the rejection region at 0.05 significance level? O Fl 26.41 IR> 4.67 F2 6.41 IFl 6.30 F2 4.67

Explanation / Answer

The "F value'' and "Prob(F)'' statistics test the overall significance of the regression model.  Specifically, they test the null hypothesis that all of the regression coefficients are equal to zero.  This tests the full model against a model with no variables and with the estimate of the dependent variable being the mean of the values of the dependent variable.  The F value is the ratio of the mean regression sum of squares divided by the mean error sum of squares.  Its value will range from zero to an arbitrarily large number.

This is a two tailed test.

So, F> 6.41

C option

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