Waterbury Insurance Company wants to study the relationship between the amount o

Question

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 1,815.5782 1 1,815.5782 39.7 Residual 1,280.4934 28 45.7319 Total 3,096.0716 29 Regression output Variables Coefficients Std. Error t(df=28) Intercept 14.7532 3.118 3.508 Distance-X 3.4332 8.611 6.3 a-1. Write out the regression equation. (Round your answers to 3 decimal places.) Y = + X. a-2. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage? The relationship between distance and damage is . b. How much damage would you estimate (in dollars) for a fire 5 miles from the nearest fire station? (Round your answer to the nearest dollar amount.) Estimated damage $ c-1. Determine the coefficient of determination. (Round your answer to 3 decimal places.) Coefficient of determination c-2. Fill in the blank below. (Round your answer to 1 decimal place.) % of the variation in damage is explained by variation in distance. d-1 Determine the coefficient of correlation. (Round your answer to 3 decimal places.) Coefficient of correlation d-2 Choose the right option. There is a fairly solid link between the variables. d-3 How did you determine the sign of the correlation coefficient? It is because the slope is . e-1 State the decision rule for .01 significance level: H0 : = 0; H1 : 0. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject H0 if t < or t > e-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic e-3. Is there any significant relationship between the distance from the fire station and the amount of damage? Use the .01 significance level. H0. There is relationship between distance and fire damage.

Explanation / Answer

a-1. The regression equation is, y = 14.7532 + 3.4332 x, where y is the amount of fire damage and x is the distance to the fire station.

a-2. The relationship between the damage and distance is direct since the slope (coefficient of X) is positive.

b. For a fire 5 miles away from the fire station, x = 5.

So y = 14.7532 + 3.4332 x 5 = 31.9192

c-1. Coefficient of determination = 1815.5782/3096.0716=0.5864

c-2. 58.64% of the variation in damage is explained by variation in distance.

d-1. Coefficient of correlation = sqrt(0.5864)=0.7658

d-2. Question seems incomplete.

d-3. Sign of the correlation coefficient is positive because the slope is positive.

e-2. Critical statistic = 2.756 from t-table corresponding to 0.01 level of significance with 29 degrees of freedom.

e-3. t = 0.7658 x sqrt(29-2) / sqrt (1-0.7658^2) = 6.187

This is higher than the critical statistic of 2.756

So we can reject the Null hypothesis and conclude that there is a significant relationship between distance from fire station and the amount of damage.

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