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	1,810.5782	1	1,810.5782		38.54
Residual	1,315.4934	28	46.9819
Total	3,126.0716	29

Regression output
Variables	Coefficients	Std. Error	t(df=28)
Intercept	14.6279	3.1572	3.178
Distance–X	5.1603	9.252	6.21

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?____

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

1. Estimated damage=______

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

2. Coefficient of determination______

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

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

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

4. Correlation coefficient____

d-2. Choose the right option.

5.

. There is a fairly solid

link between the variables.

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

6.

It is

because the slope is

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

7.

Reject H0 if t <

or t >

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

8. 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 0.01 significance level.

9.

H0. There is______

relationship between distance and fire damage.

Answer 1

a_1) Regression equation:

Y'= 14.6279+5.1603*Distance

a-2) it's a direct relationship between two variables.

1) X=9

Y'= 14.6279+5.1603*9= 61.0706

2) Coefficient of determination:

3) 57.9186% variation explained by regression equation

4) Correlation coefficient:

5)There is a solid relationship between variables.

6) Slope is positive so, correlation coefficient sign also positive.

7)Hypothesis:

and

df= 28, significant value=0.01

Reject H0 if t< -2.76326 or t> 2.76326