BUSN 5000 FINAL STUDY GUIDE 2026
QUESTIONS WITH SOLUTIONS GRADED A+
⩥ What problem do the population regression coefficients solve?.
Answer: - population least squares problem, minimize the mean squared
errors between the outcome and its regression approximation: min E [(y-
B0-B1x)^2]
⩥ solutions to population least squares problem?.
Answer: 1. B0 = E(y)-B1E(x)
2. B1 = cov(x,y)/var(x)
solutions to the first order conditions
⩥ How do you use the plug in principle to estimate the population
coefficients?.
Answer: B0 and B1 can be estimated by replacing E(x) and E(y) with
sample averages. The estimators, B hat 0 and B hat 1 are called the
ordinary least squares (OLS) estimators bcs they solve sample analog to
the least squares problem.
⩥ What is the main implication of the Frisch-Waugh-Lovell theorem?.
Answer: formal definition for what hold constant other factors in a
multiple regression means. A residualized x is that part of the variable
left over after you take into account the other XS. r hat = x(i) - x hat(i)
,⩥ Under what condition is the OLS estimator unbiased?.
Answer: Only under the conditional mean assumption (CMA), which
requires that the error terms are mean independent of the explanatory
variables
⩥ What is omitted variable bias and how would you determine its
direction?.
Answer: Omitted Variable Bias occurs when a confounding variable is
left out of the model. Directions determined by formula.
E(β~1)=β1+β2δ~,
β1 is the true effect.
β2 is the effect of the omitted variable on y.
δ~ is the correlation between the included and omitted variables. For
example, if education and experience are negatively correlated and
experience positively affects wages, omitting experience will bias the
education coefficient downward
⩥ How does classical measurement error affect the estimated regression
coefficients?.
Answer: in an explanatory variable, this typically leads to attenuation
bias, drives estimated coefficient downward toward zero.
⩥ What does R2 tell you?.
,Answer: Coeff of determination; tells you the fraction of the total
variation in y that is accounted for by the variation in the fitted values (y
hat).
⩥ What is the sampling distribution of the OLS estimator?.
Answer: CLT tells us OLS estimator is asymptotically normal, sample
distribution can be approximated by a normal distribution in large
samples.
⩥ What is the right standard error to use in cross-section regression
analysis?.
Answer: Heteroscedasticity-ROBUST standard error
⩥ How do you test the significance of an estimated regression
coefficient?.
Answer: Use asymptotically valid t-test, H0: Bk = 0 si rejected if
absolute value of t stat = Bk/se(bk) is greater than 1.96 at 5 %
significance level
⩥ How do you test the joint significance of several estimated regression
coefficients?.
Answer: Use f test to compare the fit of a long regression containing all
variables against a short regression that omits the variables. being tested.
, ⩥ How do you balance economic and statistical significance in
interpreting regression results?.
Answer: hile statistical significance is determined by p-values and t-
statistics, economic significance is about the magnitude and practical
importance of the coefficient estimate. Balancing them involves
recognizing that a result can be statistically significant but economically
trivial, or vice versa depending on the sample size
⩥ If we say 𝐸(𝑦|𝑥)=𝛽0+𝛽1𝑥, where 𝛽0 and 𝛽1 are population regression
_____ and solve the population _____ problem.. Answer:
coefficients, least squares
⩥ The population regression function provides the best ______ to the
CEF..
Answer: linear approximation
⩥ 𝑦𝑖=𝛽0+𝛽1𝑥𝑖1+𝑢𝑖,𝑖=1,...,𝑁.(1)
The coefficient 𝛽1 measures the _____ in 𝑦 associated with a unit _____
in 𝑥1, holding all of the unobservables constant. Ans
wer: change, change
⩥ If 𝛽0 and 𝛽1 solve the population least-squares problem their values
______ the expected value of the _____ difference between the
dependent variable and the CEF. An
swer: minimize, squared
QUESTIONS WITH SOLUTIONS GRADED A+
⩥ What problem do the population regression coefficients solve?.
Answer: - population least squares problem, minimize the mean squared
errors between the outcome and its regression approximation: min E [(y-
B0-B1x)^2]
⩥ solutions to population least squares problem?.
Answer: 1. B0 = E(y)-B1E(x)
2. B1 = cov(x,y)/var(x)
solutions to the first order conditions
⩥ How do you use the plug in principle to estimate the population
coefficients?.
Answer: B0 and B1 can be estimated by replacing E(x) and E(y) with
sample averages. The estimators, B hat 0 and B hat 1 are called the
ordinary least squares (OLS) estimators bcs they solve sample analog to
the least squares problem.
⩥ What is the main implication of the Frisch-Waugh-Lovell theorem?.
Answer: formal definition for what hold constant other factors in a
multiple regression means. A residualized x is that part of the variable
left over after you take into account the other XS. r hat = x(i) - x hat(i)
,⩥ Under what condition is the OLS estimator unbiased?.
Answer: Only under the conditional mean assumption (CMA), which
requires that the error terms are mean independent of the explanatory
variables
⩥ What is omitted variable bias and how would you determine its
direction?.
Answer: Omitted Variable Bias occurs when a confounding variable is
left out of the model. Directions determined by formula.
E(β~1)=β1+β2δ~,
β1 is the true effect.
β2 is the effect of the omitted variable on y.
δ~ is the correlation between the included and omitted variables. For
example, if education and experience are negatively correlated and
experience positively affects wages, omitting experience will bias the
education coefficient downward
⩥ How does classical measurement error affect the estimated regression
coefficients?.
Answer: in an explanatory variable, this typically leads to attenuation
bias, drives estimated coefficient downward toward zero.
⩥ What does R2 tell you?.
,Answer: Coeff of determination; tells you the fraction of the total
variation in y that is accounted for by the variation in the fitted values (y
hat).
⩥ What is the sampling distribution of the OLS estimator?.
Answer: CLT tells us OLS estimator is asymptotically normal, sample
distribution can be approximated by a normal distribution in large
samples.
⩥ What is the right standard error to use in cross-section regression
analysis?.
Answer: Heteroscedasticity-ROBUST standard error
⩥ How do you test the significance of an estimated regression
coefficient?.
Answer: Use asymptotically valid t-test, H0: Bk = 0 si rejected if
absolute value of t stat = Bk/se(bk) is greater than 1.96 at 5 %
significance level
⩥ How do you test the joint significance of several estimated regression
coefficients?.
Answer: Use f test to compare the fit of a long regression containing all
variables against a short regression that omits the variables. being tested.
, ⩥ How do you balance economic and statistical significance in
interpreting regression results?.
Answer: hile statistical significance is determined by p-values and t-
statistics, economic significance is about the magnitude and practical
importance of the coefficient estimate. Balancing them involves
recognizing that a result can be statistically significant but economically
trivial, or vice versa depending on the sample size
⩥ If we say 𝐸(𝑦|𝑥)=𝛽0+𝛽1𝑥, where 𝛽0 and 𝛽1 are population regression
_____ and solve the population _____ problem.. Answer:
coefficients, least squares
⩥ The population regression function provides the best ______ to the
CEF..
Answer: linear approximation
⩥ 𝑦𝑖=𝛽0+𝛽1𝑥𝑖1+𝑢𝑖,𝑖=1,...,𝑁.(1)
The coefficient 𝛽1 measures the _____ in 𝑦 associated with a unit _____
in 𝑥1, holding all of the unobservables constant. Ans
wer: change, change
⩥ If 𝛽0 and 𝛽1 solve the population least-squares problem their values
______ the expected value of the _____ difference between the
dependent variable and the CEF. An
swer: minimize, squared
