The following model was fitted to explain the selling prices of automobiles in a sample of 106 sales:

where
ŷ = selling price of an automobile, in euros
x₁ = the size of the car
x₂ = number of seats in the car
x₃ = age of car, in years
x₄ = dummy variable taking the value 1 if the car has a airbag and 0 otherwise
x₅ = dummy variable taking the value 1 if the car has a sunroof and 0 if it is a convertible
a. Interpret the estimated coefficient of x₄.
b. Interpret the estimated coefficient of x₅.
c. Find a 95% confidence interval for the impact of an airbag on selling price, all other things being equal.
d. Test the null hypothesis that type of roof has no impact on selling price against the alternative that, all other things equal, cars with sunroofs have a higher selling price than those with a convertible.

Transcribed Image Text:

ŷ -1,205 + 45.36x₁ +3,325x21,881x3 + 3,054x4 (1.03) (480) (738) + 1,969 x5 (738) R² = 0.89 (486) (949)