A researcher wishes to investigate the relationship amongst the distance between a house and the closest fire station in kilometers X (independent variable) and the damage that fire caused to them in thousand dollars as a dependent variable Y

A sample of houses from different parts of the city is randomly selected and the results are summarized in the ANOVA table below:

Degrees of Freedom SS

Regression 1 841.77

Residual 13 69.75

Total 14 911.52

Coefficients Standard Error t Stat p-value

Intercept 10.28 1.42 7.24 0.006

X variable 4.92 0.39 12.53 0.001

a. What is the estimated regression equation that relates the fire damage (Y) to the distance from the fire station (X)?

b. If a property is 5.8 kilometers away from the closest fire station what is the estimated damage in thousands of dollars?

c. Is the regression relationship significant? Use the p-value approach and 1% level of significance.

d. Compute the coefficient of determination between distance and the fire damage. Interpret the result in the context of the problem.