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# Waterbury Insurance Company wants to study the relationship

### Resolved 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 1,864.5782 1 1,864.5782 38.83
Residual 1,344.4934 28 48.0176
Total 3,209.0716 29

Regression output:
Variables Coefficients Std. Error t(df=28)
Intercept 12.3601 3.2915 3.755
Distance -X 4.7956 0.7696 6.231

a. Write out the regression equation. 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 5 miles from the nearest fire station?
c.Determine and interpret the coefficient of determnation.
d. Determine the correlation coefficient. Interpret its value. How did you determine the sign of the correlation coefficient?
Submitted: 5 years ago.
Category: Calculus and Above
Expert:  fraudpro replied 5 years ago.
1) Regression equation would be
y=12.3601+4.7956x
y is the amount of fire damage, in thousands of dollars and x is the distance from the fire station
The slope is positive so a direct relationship.
b) 36.34 (in thousands)
c) 58.1%
amount of fire damage can be explained by the relationship between distance from the fire station and the amount of fire damage
d) r=.7622
There is a positive correlation between distance from the fire station and the amount of damage. The sign of the correlation coefficient is + because there is a positive association between the two variables.
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