Question

The following multiple regression model shows the expected PRICE of a VW Passat at auction (in $) as a function of the number of MILES on the Passat, the AGE of the Passat (AGE = 2020 – Year Assembled), and whether the Passat is SILVER (Yes = 1; No = 0):

Expected Price = 16,700 – 0.06MILES – 1,233AGE + 296SILVER

a. If the level of significance equals 0.05 and 100 Passats are in the sample, determine the critical value of the associated test statistic to assess whether the coefficient for AGE is significantly negative

b. You are deciding between two Passats: Passat A has 34,600 miles, was assembled in 2016, and is silver; Passat B has 46,200 miles, was assembled in 2017, and is red. Which Passat has the higher expected PRICE and by how much?

Answer 1

Result:

The following multiple regression model shows the expected PRICE of a VW Passat at auction (in $) as a function of the number of MILES on the Passat, the AGE of the Passat (AGE = 2020 – Year Assembled), and whether the Passat is SILVER (Yes = 1; No = 0):

Expected Price = 16,700 – 0.06MILES – 1,233AGE + 296SILVER

a. If the level of significance equals 0.05 and 100 Passats are in the sample, determine the critical value of the associated test statistic to assess whether the coefficient for AGE is significantly negative

df for t distribution (100-3-1) = 96

This is one sided test, we are testing H1: β <0.

Critical value : -1.661

Rejection region: Reject Ho is calculated t < -1.661

b. You are deciding between two Passats: Passat A has 34,600 miles, was assembled in 2016, and is silver; Passat B has 46,200 miles, was assembled in 2017, and is red. Which Passat has the higher expected PRICE and by how much?

For A, AGE=2020-2016= 4 and silver = 1

Expected Price = 16700 -0.06*34600 -1233*4 + 296*1 =9988

For B, AGE=2020-2017= 3 and silver = 0

Expected Price = 16700 -0.06*46200 -1233*3 + 296*0 =10229

Passat B has the higher expected PRICE.

Passat B has 241 (10229-9988 = 241 ) more expected PRICE than Passat A.