1. 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	1,864.5782	1	1,864.5782	38.83
Residual	1,344.4934	28	48.0176
Total	3,209.0716	29

Regression output
Variables	Coefficients	Std. Error	t(df=28)
Intercept	12.3601	3.2915	3.755
Distance-X	4.7956	0.7696	6.23

a-1.	Write out the regression equation.(Round your answers to 3 decimal places.)

Y= ______+ ______X.

a-2.	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 (Click to select)directorinverse.

b.	How much damage would you estimate (in dollars) for a fire 5 miles from the nearest fire station?(Round your answer to the nearest dollar amount.)

Estimated damage

$

c-1.	Determine 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 1 decimal place.)

% of the variation in damage is explained by variation in distance.

d-1	Determine the coefficient of correlation.(Round your answer to 3 decimal places.)

Coefficient of correlation

d-2	Choose the right option.

There is a fairly solid (Click to select)inverseordirectlink between the variables.

d-3	How did you determine the sign of the correlation coefficient?

It is (Click to select)zero positive or negativebecause the slope is (Click to select)zero positive or negative.

e-1	State the decision rule for .01 significance level:H0:= 0;H1: 0.(Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

RejectH₀ift< ______ 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 .01 significance level.

(Click to select)Do not reject or RejectH₀. There is (Click to select)significant or no significantrelationship between distance and fire damage.

2.

A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.

Heater	Wattage	Area
1	1,250	267
2	1,750	101
3	2,000	186
4	1,250	106
5	1,500	283
6	1,250	115
7	750	221
8	1,000	222
9	1,000	149
10	1,000	68
11	1,000	167
12	1,500	75
13	1,000	112
14	750	223
15	750	198
16	1,000	295
17	1,000	216
18	750	163
19	1,500	252
20	1,000	254

Click here for the Excel Data File

a.	Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship?(Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.)

The correlation of Wattage and Area is _______. The link (relationship) is (Click to select)indirectordirect.

b.	Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.050 significance level.(Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.)

H0: 0;

H1: > 0.

RejectH0ift> 1.734

t=

(Click to select)Do not rejectorRejectH₀. It is (Click to select)quite reasonable or not reasonableto say the population correlation is positive.

c.	Develop the regression equation for effective heating based on wattage.(Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

The regression equation is: (Click to select)Wattage or Area=______ + ________(Click to select)Area or Wattage.

d.	Which heater looks like the best buy based on the size of the residual?(Round residual value to 2 decimal places.)

The (Click to select) fifteenth eleventh twentieth sixteenth seventeenth sixth Fourth first second fourteenth eighteenth tenth thirteenth third fifth eighth seventh ninth twelfth nineteenth heater is the "best buy." It heats an area that issquare feet larger than estimated by the regression equation.