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

yn = -1,205 11.032

+ 45.36 14802 x1 + 3,325 14862 x2 - 1,881 19492 x3 + 3,054 17382 x4

+ 1,969 17382 x5 R2 = 0.89 where yn = 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.