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).
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 |
Standard Error |
t(df=28) |
|---|
Intercept |
14.62785 |
3.1572 |
3.178 |
Distance–X |
5.1603 |
0.8312 |
6.21 |
Click here for the Excel Data File
a-1. Determine 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?
b. How much damage would you estimate for a fire 9 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)
c-1. Determine the coefficient of determination.(Round your answer to 3 decimal places.)
c-2. Interpret the coefficient of determination.(Round your answer to one decimal place.)
d-1. Determine the correlation coefficient.(Round your answer to 3 decimal places.)
d-2. Evaluate the correlation between the variables.
d-3. How did you determine the sign of the correlation coefficient?
e-1. State the decision rule for 0.01 significance level:H
0 :ρ = 0;H
1 :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.