Question

2.   Suppose a fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. A random sample of 15 fires in a large suburb is selected. The amount of damage (thousands of dollars) and the distance (miles) between the fire and the nearest fire station are recorded for each fire. The following simple linear regression model was used:

Fire Damage_i=B₀+B₁(Distance from Fire Station)_i+E_i

Coefficients Std. Error
Intercept     10.2779    1.4203
Distance           4.9193 0.3927

a)   The response variable is:   

b)   The explanatory variable is:   

c)   The least squares regression line is:

d)   Find the predicted fire damage when a residential home is located 6 miles from the fire station.   

e)   Suppose the researchers tests the hypotheses:                      
H₀: p=0 versus H_a: p>0

The value of the t statistic for this test is:

f)   The P-value for the t statistic found in part (e) is:

g)   Based on parts (e) & (f) state your conclusion regarding the significance of
h) Give the interpretation of B₁

i) Give the interpretation of B₀

Answer 1

a)   The response variable is:
fire damage

b)   The explanatory variable is:
distance from fire station

c)   The least squares regression line is:
y^ = 10.2779 + 4.9193 x

d)   Find the predicted fire damage when a residential home is located 6 miles from the fire station.

y^ = 10.2779 + 4.9193 *6
= 39.7937

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