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 (). The MegaStat output is reported here: ANOVA table Source Regression Residual Total SS 1,805.5782 1,275.4934 3,081.0716 df 1 28 29 MS 1,895.5782 39.64 45.5533 Regression output Variables Coefficients Intercept 1,381, 345 Distance-X 300, 415 Std. Error 3.0963 47,717.0465 t(df=28) 3.475 6.3 Click here for the Excel Data File a-1. Determine the regression equation. (Round your answers to 3 decimal places.) y =

Answer 1

a-1

Here the regression line

y = 1381345 + 300415 x

a-2

Here the distance between fire station and the amount of fire damage have a direct relationship.

b. Here x = 7 miles

y = 1381345 + 300415 * 7 = 3484250

c-1

Here coefficient of determination = r² = SSR/SST = 1805.5782/3081.0716 = 0.586

c-2

Here 58.60% in the variation in damage is explained by the variation in distance.

d-1

Here the correlation coefficient = r = sqrt(0.586) = 0.7655

d-2

There is fairly solid positive link between the variables.

d-3 Here the coefficient of slope is positive so coefficient is positive.

e-1 t_critical = TINV(0.01, 28) = 2.7633

e-2 test statistic

T = 6.3

e-3 Here we will reject the null hypothesis if t < -2.7633 and t > 2.7633