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  1,810.5782  1  1,810.5782  38.54  
Residual  1,315.4934  28  46.9819  
Total  3,126.0716  29  
Regression output  
Variables  Coefficients  Std. Error  t(df=28) 
Intercept  14.6279  3.1572  3.178 
Distance–X  5.1603  9.252  6.21 
a1. Write out the regression equation. (Round your answers to 3 decimal places.)
y=__+__x
a2. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage?
**** The relationship between distance and damage is?____
How much damage would you estimate for a fire 9 miles from the nearest fire station? (Round your answer to the nearest dollar amount.)
1. Estimated damage=______
c1. Determine and interpret the coefficient of determination. (Round your answer to 3 decimal places.)
2. Coefficient of determination______
c2. Fill in the blank below. (Round your answer to one decimal place.)
3.____% of the variation in damage is explained by variation in distance.
d1. Determine the correlation coefficient. (Round your answer to 3 decimal places.)
4. Correlation coefficient____
d2. Choose the right option.
5.
. There is a fairly solid  link between the variables. 
d3. How did you determine the sign of the correlation coefficient?
6. 

e1. State the decision rule for 0.01 significance level: H_{0} : ? = 0; H_{1} : ? ? 0. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)
7.

e2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)
8. Value of the test statistic:
e3. Is there any significant relationship between the distance from the fire station and the amount of damage? Use the 0.01 significance level.
9.

a_1) Regression equation:
Y'= 14.6279+5.1603*Distance
a2) it's a direct relationship between two variables.
1) X=9
Y'= 14.6279+5.1603*9= 61.0706
2) Coefficient of determination:
3) 57.9186% variation explained by regression equation
4) Correlation coefficient:
5)There is a solid relationship between variables.
6) Slope is positive so, correlation coefficient sign also positive.
7)Hypothesis:
and
df= 28, significant value=0.01
Reject H0 if t< 2.76326 or t> 2.76326
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