Waterbury Insurance Company wants to study the relationship between the amount o
ID: 3292812 • Letter: W
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 1,865.5782 1 1,865.5782 39.71
Residual 1,315.4934 28 46.9819
Total 3,181.0716 29
Regression output
Variables Coefficients Std. Error t(df=28)
Intercept 12.5538 3.0301 3.678
Distance-X 3.4664 8.63 6.3
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
(Click to select)
direct
inverse
.
b.
How much damage would you estimate (in dollars) for a fire 10 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)
Estimated damage $
c-1. Determine 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 1 decimal place.)
% of the variation in damage is explained by variation in distance.
d-1 Determine the coefficient of correlation. (Round your answer to 3 decimal places.)
Coefficient of correlation
d-2 Choose the right option.
There is a fairly solid
(Click to select)
inverse
direct
link between the variables.
d-3 How did you determine the sign of the correlation coefficient?
It is
(Click to select)
negative
positive
zero
because the slope is
(Click to select)
positive
zero
negative
.
e-1
State the decision rule for .01 significance level: H0 : = 0; H1 : 0. (Negative amounts 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 .01 significance level.
(Click to select)
Reject
Do not reject
H0. There is
(Click to select)
no significant
significant
relationship between distance and fire damage.
Explanation / Answer
a - 1) Y =12.554 + 3.466 X
a - 2) Direct
b) For X = 10,
Y = 12.554 + 34.66 = 47.214
So the damage is $ 47214
c - 1) 0.586
c - 2) 58.6 %
d - 1) 0.766
d - 2) Direct
d - 3) Positive; Positive
e - 1) Reject Ho if t < -2.763 or t > 2.763
e - 2) Test statistic = 6.3
e - 3) Reject; Significant
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