Sebastian Tello
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Quiz 3

  1. A city evaluates the effects of a voluntary after-school tutoring program on math test scores with the following regression: Scorei=γ0  +  γ1Tutoringi  +  ϵiScore_i = \gamma_0\;+\;\gamma_1Tutoring_i\;+\;\epsilon_iScorei​=γ0​+γ1​Tutoringi​+ϵi​. Which of the following must be true for γ^1\hat\gamma_1γ^​1​ to be unbiased?
    1. Corr(Scorei,  Tutoringi)=0Corr(Score_i,\;Tutoring_i)=0Corr(Scorei​,Tutoringi​)=0
    2. Corr(Scorei,  ϵi)=0Corr(Score_i,\;\epsilon_i)=0Corr(Scorei​,ϵi​)=0
    3. Corr(Tutoringi,  ϵi)=0Corr(Tutoring_i,\;\epsilon_i)=0Corr(Tutoringi​,ϵi​)=0
    4. Var(Tutoringi)=0Var(Tutoring_i) = 0Var(Tutoringi​)=0
      5. ‣
      Answer

      C

  2. If Var(Tutoringi)=0Var(Tutoring_i) = 0Var(Tutoringi​)=0 were true, this would imply that γ1=0\gamma_1=0γ1​=0
    1. True
    2. False
      3. ‣
      Answer

      False, no because it couldn’t be estimated.

  3. If Corr(Scorei,  Tutoringi)=0Corr(Score_i,\;Tutoring_i)=0Corr(Scorei​,Tutoringi​)=0 were true, this would imply that γ1=0\gamma_1=0γ1​=0
    1. True
    2. False
      3. ‣
      Answer

      True.

  4. You are running a regression on the relationship between sleep hours as a proxy for sleep quality (measured during the night before the given exam) and exam scores using the following model: Scorei=β0  +  β1HoursSlepti  +  ϵiScore_i = \beta_0\;+\;\beta_1 HoursSlept_i\;+\;\epsilon_iScorei​=β0​+β1​HoursSlepti​+ϵi​. Assuming you have reliable measurements, which of the following should you not include as a control variable?
    1. Previous exam scores
    2. Anxiety level on the morning of the exam
    3. Average hours studied per day in the 7 days before the exam
    4. Stress level in the week prior to the exam
‣
Answer

b) Anxiety level on the morning of the exam, as this is likely an outcome of hours slept and also likely affects exam scores.

  1. You're estimating the effect of a voluntary financial counseling program on credit scores using the following regression. Credit score is measured as FICA score that ranges from 250 to 850, and counseling is a binary variable, measured if you attended the counseling program or not: CreditScorei=β0  +  β1FinancialCounselingi  +  ϵiCreditScore_i = \beta_0\;+\;\beta_1 FinancialCounseling_i\;+\;\epsilon_iCreditScorei​=β0​+β1​FinancialCounselingi​+ϵi​. Which of the following potential covariates is most likely to reduce the most bias?
    1. Credit score after counseling
    2. Whether your parents are athletes or not
    3. Number of credit cards opened in the past 3 years
    4. Number of staff in your closest financial counseling center
‣
Answer

c)