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 = 13.985 + 5.583x
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 7 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)
Estimated damage: $ __53___.
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 coefficient: _____.
d-2. Choose the right option.
There is a fairly solid Direct or Indirect link between the variables.
d-3. How did you determine the sign of the correlation coefficient?
It is Positive or Negative because the slope is Positive or Negative.
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.)
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.
Reject or Do not reject H0. There is Significant or No significant relationship between distance and fire damage.
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