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   1,875.5782   1   1,875.5782      42.33
Residual   1,240.4934   28   44.3033        
Total   3,116.0716   29           

Regression output
Variables   Coefficients   Std. Error   t(df=28)
Intercept   12.5907   3.1151   3.547
Distance–X   2.6223   0.403   6.51

Click here for the Excel Data File

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?

How much damage would you estimate for a fire 6 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.)

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

d-2. Choose the right option.

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.

i need answeres for e

Answer 1

X:distance from the fire station

Y:amount of fire damage in thousands of dollars.

a-1)From the given information ,the regression equation is given by,

E(Y)= 12.591+ 2.622 * X

a-2) There is a direct relationship between the distance from the fire station and the amount of damage in thousands of dollars, since if the distance from the fire station is more ,then it would take more time for the fire engine to reach the emergency spot. So the damge due to the fire will be more .

If the emergency spot is situated 6 miles away from the nearest fire station ,then X=6 miles. So the estimated damage is given ,E(Y) = 12.591+ 2.622 * 6=28.323 which is approximately 28 thousand dollars.

c-1)From the ANOVA table, the coefficient of determination is given by,

=

=0.602

This means that 60.2% of the variance in Y (damage in thousands of dollars) is explained by this regression equation.

d-1)The correlation coefficient is given by,

=0.776

d-3) From the regression output we see that the sign of the slope coefficient is positive. And the sign of the correlation coefficient is the same as that of the slope coefficient.So the correlation coefficient also has a positive value.

e-1) To test against

the test statistic is given by, ,under

Here n=30.

We reject if > ,where is the level of significance.

Otherwise we accept .

Here =0.01

So,

e-2)

=6.51

e-3) Here . So we reject the null hypothesis at 0.01 level of significance and conclude that the correlation coefficient is significantly different from zero. This suggests that there is a significant relationship between the distance from the fire station and the amount of damage.