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 | 1,850.5782 | 1 | 1,850.5782 | 39.69 | ||
Residual | 1,305.4934 | 28 | 46.6248 | |||
Total | 3,156.0716 | 29 | ||||
Regression output | |||
Variables | Coefficients | Std. Error | t(df=28) |
Intercept | 12.6882 | 3.1699 | 2.82 |
Distance–X | 5.121 | 8.504 | 6.3 |
a-1. Write out the regression equation. (Round your answers to 3 decimal places.)
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 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-3. How did you determine the sign of the correlation coefficient?
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.)
e-2. Compute the value of the test statistic for the hypothesis of β_{1}. (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.
a-1) Y^ =12.6882+5.121x
b) estimated value =12.6882+5.121*5 =38.29
c-1)coefficient of determination =SSR/SST =1850.5782/3156.0716 =0.586
58.6% of variation can be explained by this model
d-1)
correlation coefficient =sqrt(R^{2})=0.766
d-3)correlation coefficient has same sign as slope which is positive here
e-1)
0.01 level,two tail test and n-2= 28 df, critical t= | 2.7633 | ||
Decision rule: reject Ho if absolute value of test statistic |t|>2.763 or if t<-2.763 or t>2.763 |
e-2)
value of the test statistic for the hypothesis of β1= 6.30
e-3)
yes
there is a signiificant evidence,,,,
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