Waterbury Insurance Company wants to study the relationship between the amount o
ID: 3292790 • 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).
a-1. Write out 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?
How much damage would you estimate for a fire 5 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)
c-1. Determine and interpret the coefficient of determination. (Round your answer to 3 decimal places.)
c-2. Fill in the blank below. (Round your answer to one decimal place.)
d-1. Determine the correlation coefficient. (Round your answer to 3 decimal places.)
d-2. Choose the right option.
d-3. How did you determine the sign of the correlation coefficient?
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.)
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.
ANOVA table Source SS df MS F Regression 1,850.5782 1 1,850.5782 39.69 Residual 1,305.4934 28 46.6248 Total 3,156.0716 29Explanation / Answer
Question a-1)
Answer: y^ = 12.688 + 5.121x
Question a-2)
Answer: The value of the slope (5.211) is positive so we can conclude that there may be a direct relationship between these two variables.
y^ = 12.688 + 5.121x
= 12.688 + (5.121*5)
= 38.293 (in 1000$)
Answer: $38293
Question c-1)
Coefficient of determination = SSR / SST = 1850.5782/3156.0716 = 0.586
Answer: coefficient of determination = 0.586
Answer: We can conclude that 58.6% of the amount of fire damage is going to be explained by the variable the distance from the fire station.
Question c-2)
Correlation coefficient = sqrt (1850.5782/3156.0716) = 0.766
Answer: Correlation coefficient = 0.766
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