Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (X) and the amount of fire damage, in thousands of dollars (Y). The MegaStat output is reported below. (You can find the actual data in the data set on the CD as prb13-56.)

Answer the following questions.

a. Write out the regression equation. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage?

b. How much damage would you estimate for a fire 5 miles from the nearest fire station?

c. Determine and interpret the coefficient of determination.

d. Determine the coefficient of correlation. Interpret its value. How did you determine the sign of the correlation coefficient?

e. Conduct a test of hypothesis to determine if there is a significant relationship between the distance from the fire station and the amount of damage. Use the .01 significance level and a two-tailed test.

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ANOVA table Source SS df MS Regression 1,864.5782 1 Residual 1,344.4934 28 1,864.5782 48.0176 F 38.83 Total 3,209.0716 29 Regression output Variables Coefficients Std. Error t (df = 28) Intercept Distance-X 12.3601 4.7956 3.2915 3.755 0.7696 6.231