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	1,835.5782	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	0.5178	6.36

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

How much damage would you estimate for a fire 4 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)

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

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

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

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

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.)

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

Answer 1

1)

regression equation ": y^ =13.6904+3.2931x

2)predicted damage=(13.6904+3.2931*4)*1000 =26863

3)  coefficient of determination =SSR/SST =1,835.5782/3,106.0716 =0.591

59.1% of the variation in damage is explained by variation in distance.

4)

correlation coefficient =sqrt(r²)=0.769

value of the test statistic t =6.36