Sebastian Tello
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Quiz 4

  1. We are looking to assess the effect of gas mileage (Miles per gallon (mpg)) on price (measure in $) accounting for a car’s country of origin (Foreign or domestic) and repair record (Rep78 (Number of repairs since). Which of the following best represents the theoretical regression which would answer that question?
    1. Price=β1Foreign+β2MPG+β3Rep78\text{Price}=\beta_1\text{Foreign}+\beta_2\text{MPG}+\beta_3\text{Rep78}Price=β1​Foreign+β2​MPG+β3​Rep78
    2. Price=β0+β1Foreign+β2MPG+β3Rep78+β4Price+ϵ\text{Price}=\beta_0+\beta_1\text{Foreign}+\beta_2\text{MPG}+\beta_3\text{Rep78}+\beta_4Price+\epsilonPrice=β0​+β1​Foreign+β2​MPG+β3​Rep78+β4​Price+ϵ
    3. Price=β0+β1Foreign+β2MPG+β3Rep78+ϵ\text{Price}=\beta_0+\beta_1\text{Foreign}+\beta_2\text{MPG}+\beta_3\text{Rep78}+\epsilonPrice=β0​+β1​Foreign+β2​MPG+β3​Rep78+ϵ
    4. MPG=β0+β1Foreign+β2Price+β3Rep78+ϵ\text{MPG}=\beta_0+\beta_1\text{Foreign}+\beta_2\text{Price}+\beta_3\text{Rep78}+\epsilonMPG=β0​+β1​Foreign+β2​Price+β3​Rep78+ϵ
      5. ‣
      Answer

      C

  2. Now you use STATA to estimate the results of the regression. Using the regression below, which of the following provides the best interpretation of the coefficient on foreign?
      3. image
    1. There is no economical effect of foreign on price since the p-value is greater than 0.05.
    2. For cars with the same mpg and rep78 (i.e. holding all else constant), the foreign car cost $1023.21 more than the domestic car.
    3. For cars with the same foreign and rep78 (i.e. holding all else constant), the marginal effect of mpg is -292.43 per mpg.
    4. For cars with the same mpg and rep78 (i.e. holding all else constant), the foreign car costs between $706.48 less and $2752.90 more than the domestic car.
      5. ‣
      Answer

      B

  3. Using the same regression output as above, select all that are true:
    1. The average price of a car that has no repair record, is domestic and has an MPG of 30 is 10,586.48 (not right)
    2. As the mpg increases the price of the car decreases (true)
    3. The more repairs the car has, the more expensive it is (true)
    4. Having 3 repairs increases the price of the car by 1289.4 approximately (true) (true)
    5. All of the coefficient’s have confidence intervals that cross zero (not true)
      6. ‣
      Answer

      B, C, D

  4. We now study the correlation between weight (lbs) and mpg, and weight and price, the output is below. If we were to include weight into the regression above, which of the following will be true:
      5. image
      image
    1. The new coefficient on MPG will be more negative than without controlling for weight
    2. The new coefficient on MPG will be more positive than without controlling for weight
    3. The standard errors will be larger
    4. The coefficient on MPG will not change
      5. ‣
      Answer

      b. The coefficient on MPG will be more positive than without controlling for weight

  5. Now, we add “weight” to the regression and take out mpg, and we get the following output. Which of the following is true of this regression? Select all that apply.
    1. It has a local minimum
    2. It has a local maximum
    3. The direction of the marginal effect of weight on price changes after 1770.66 pounds
    4. The marginal effect of weight on price is -4.33 approximately
      5. image