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. ANOVA table
Source SS df MS F
Regression 1,835.5782 1 1,835.5782 40.45
Residual 1,270.4934 28 45.3748
Total 3,106.0716 29
Regression output
Variables Coefficients Std. Error t(df=28)
Intercept 13.6904 3.0467 2.427
Distance-X 3.2931 6.318 6.36
1a. Write out the regression equation.
2a. 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 (in dollars) for a fire 4 miles from the nearest fire station?
3. Determine the coefficient of determination.
4a. Determine the coefficient of correlation.
b. Choose the right option.
c. How did you determine the sign of the correlation coefficient?
5a. State the decision rule for .01 significance level: H0 : ? = 0; H1 : ? ? 0.
b. Compute the value of the test statistic.
c. Is there any significant relationship between the distance from the fire station and the amount of damage? Use the .01 significance level.