Regression Analysis: Simple and multiple linear regressions, understanding the Ordinary Least Squares (OLS) estimator, assumptions of the Classical Linear Regression Model (CLRM), and how to interpret coefficients.
Hypothesis Testing: Null and alternative hypotheses, t-tests, F-tests, p-values, an...
Multiple Choice (2.5 points each = 22.5 points total)
1) When there is simultaneous causality that can be modeled as Yi = β0 +β1 Xi +ui and Xi = γ0 +γ1 Yi +vi ,
when would Xi have a negative correlation with the error term, ui ?
a) β1 < 0
b) β1 > 0
c) γ1 < 0 ✓
d) γ1 × β1 < 0
2) Which of the following statements is FALSE? A high R2 or R̄2
a) does not necessarily mean that you have the best set of regressors
b) does not mean that there is no omitted variable bias
c) does not mean that the regressors are a true cause of the dependent variable
d) means that an added variable is statistically significant ✓
3) You can avoid the dummy variable trap by all of the following methods EXCEPT
a) including an interaction term ✓
b) having a reference group
c) not estimating an intercept
d) allowing some observations to fall into more than one category of your group of dummy variables
4) Changing the units of measurement for the dependent variable in a model does not cause a change in
a) the standard error of the regression
b) the confidence intervals for the slope terms
c) the goodness of fit of the regression ✓
d) the sum of squared residuals
5) The reason for including control variables in multiple regressions is to
a) increase the R2
b) reduce heteroskedasticity in the error term
c) reduce imperfect multicollinearity
d) make the variables of interest no longer correlated with the error term after holding the control
variables constant ✓
6) You want to estimate the risk (on a scale of 1-1000 with larger numbers indicating higher risk) of
someone developing heart disease in a population over 40 years old. The time someone wakes up in
the morning is negatively correlated with the risk of heart disease, but the relationship is not causal.
Age does have a causal effect because older people are at higher risk because their hearts are not as
resilient. There is a strong, negative correlation between the time someone wakes up and their age.
Which of the following specifications is subject to omitted variable bias?
a) risk = β0 + β1 age + β2 wake time + ui
b) risk = β0 + β1 age + ui
c) risk = β0 + β1 wake time + ui ✓
d) risk = β1 age + β2 wake time + ui
7) Which of the following is NOT an assumption of OLS multiple regression?
a) random sample
b) there is homoskedasticity
c) large outliers are unlikely
d) there is no multicollinearity of any kind ✓
e) your regressors are not correlated with the error term
f) the error term follows a normal distribution, centered on 0
8) Which of the following circumstances would increase the standard error of the coefficient, βj , for a
variable, Xj ?
a) There is very little variation in Xj ✓
b) There is very little predictive power (the R2 is low) in the regression of all the other X variables on
Xj
c) The R2 of the regression for Y including all K of the X-variables is high
d) The Xj variable was scaled up by a factor of 3
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