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	1,830.5782	1	1,830.5782		41.15
Residual	1,245.4934	28	44.4819
Total	3,076.0716	29

Regression output
Variables	Coefficients	Std. Error	t(df=28)
Intercept	14.1988	3.137	2.962
Distance–X	3.9798	0.6204	6.42

a-1. Write out the regression equation. (Round your answers to 3 decimal places.)

a-2. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage?

2. How much damage would you estimate for a fire 9 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)

c-1. Determine and interpret the coefficient of determination. (Round your answer to 3 decimal places.)

c-2. Fill in the blank below. (Round your answer to one decimal place.)

____% of the variation in damage is explained by variation in distance.

d-1. Determine the correlation coefficient. (Round your answer to 3 decimal places.)

d-3. How did you determine the sign of the correlation coefficient?

e-1. State the decision rule for 0.01 significance level: H₀ : ρ = 0; H₁ : ρ ≠ 0. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)

e-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

e-3. Is there any significant relationship between the distance from the fire station and the amount of damage? Use the 0.01 significance level.

Answer 1