Question

# Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the...

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 13.985 3.1125 2.34 Distance–X 5.5828 0.8778 6.36

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 ...................................

b )How much damage would you estimate for a fire 7 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.)

Coefficient of determination..................................

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.)

Correlation Coffecient.................

d-2. Choose the right option.

There is a fairly solid....................................link between the variables.

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

ıt is ...................................because the slope is .........................

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.)

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.

.....................H0.There is ......................................relationship between distance and fire damage.

a-1.

Y=13.985 + 5.5828 X.

a-2.

The relationship between distance and damage is direct .

b.

Estimated damage is Y=13.985 + 5.5828*7 = 53.0646

c-1.

Coefficient of determination is 1835.5782/3106.0716 = 0.59096

c-2.

59.096 % of the variation in damage is explained by variation in distance.

d-1.

Correlation Coffecient is 0.7687

d-2.

There is a fairly solid direct link between the variables.

d-3.

ıt is Positive because the slope is Positive.

e-1.

Using table of critical vaues for t-distribution we get critical values as -2.763 and 2.763.

Reject H0 if t < -2.763 or t > 2.763

e-2.

value of the test statistic 6.36

e-3.

Reject Ho There is significantrelationship between distance and fire damage.

Let me know in the comment section if anything is not clear. I will reply ASAP!
If you liked the answer, please give a thumbs-up. This will be quite encouraging for me.Thank-you!