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	1,870.5782	1	1,870.5782		41.23
Residual	1,270.4934	28	45.3748
Total	3,141.0716	29

Regression output
Variables	Coefficients	Std. Error	t(df=28)
Intercept	13.4867	3.1191	2.21
Distance–X	5.2717	0.8211	6.42

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

( y= .... + .....x)

a.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 direct/indirect)

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

(estimated damage)

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-2.Choose the right option

There is a fairly solid direct/indirect link between the variables

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

It is positive/negative because the slope is positive/negative

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.)

  Reject h0 if t>..... or t<......

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.

(ps:please highlight the answers.thank you)

Answer 1

y=13.4867+5.2717x

a)

direct  relationship

b)

predicted damage =(13.4867+5.2717*4)*1000 =34574

c-1) coefficient of determination=SSR/SST =1870.5782/3141.0716 =0.596

c-2) 59.6 % of the variation in damage is explained by variation in distance

d-1) correlation coefficient =sqrt(R²) =0.772

d-2) There is a fairly solid direct link between the variables

d-3)It is positive because the slope is positive

e-1)

Reject h0 if t> 2.763 or t <-2.763

e-2) value of the test statistic =6.42

e-3)

Yes