Econometrics Exam 2 || with 100% Error-free Solutions.
holding x2 constant, a 1 unit increase in x1 is associated with 𝜷1 unit increase in y correct
answers Interpretation of Beta 1 in a 2 variable regression
1-(( SSR / n - k - 1 )/ ( TSS / n -1 )) correct answers Formula for Adjusted R^2
- provides correction for number of independent variables (k)
decreases correct answers As K (the number of indepednent variables) increases, adjusted R^2
linear in parameters, random sampling correct answers MLR 1 and 2 (same as SLR)
No perfect collinearity (need variation in x that is not explained by the other x variables) correct
answers MLR 3
zero conditional mean (but with more variables!); E[ e | x1, x2.... ] = 0 correct answers MLR 4
increases R^2, increase svariance (if variables are irrelevant), doesn't affect bias correct answers
What does adding more independent variables do to a regression (that may be irrelevant too)
Homoskedasticity, uncorrelated erros correct answers MLR 5 and 6 (same as SLR)
σ^2 / TSS(1-Rj^2) correct answers Variance of 𝜷j in MLR
R^2 from a regression where xj is dependent variable and all the other x variables are the
independent variables correct answers Rj^2
SSR / n -k - 1 correct answers σ^2 estimator
statistically insignificant doesn't indicate zero effect! (must use logic and econcomic reasoning to
think about what variables to add) correct answers Why do we not just only add statistically
significant variables
- speaking to the bias-variance tradeoff and which variables to add
𝜷j^ - 𝜷j / SE(𝜷j^) correct answers Test Statistics for a single 𝜷j
√var(𝜷j^) correct answers SE of 𝜷j^
(R^2unrestricted - R^2restricted / q) / (1-R^2unrestricted)(n-k-1) correct answers F statistic (test
for multiple 𝜷j)
# of restrictions in the null correct answers q in the F statistic formula
, initial R^2 from the model (including all the 𝜷) correct answers R^2unrestricted
R^2 if null is true (adding in zeroes for the 𝜷 in the null) correct answers R^2 restricted
E[y(1)|D=1] - E[y(0)|D=0] correct answers Two group treatment problem: what stata measures
as the 𝜷1
- y are the groups, D is indicator for treatment
E[y(1)|D=1] - E[y(0)|D=1] correct answers Two treatment Group problem: What we would
ideally measure to get the 'true effect'
E[Y(0)|D=1] - E[Y(0)|D=0) correct answers Selection bias term in the two treatment group
problem
E[y(1)|D=1] - E[y(0)|D=1] + E[Y(0)|D=1] - E[Y(0)|D=0) correct answers Total formula for 𝜷1^
in the treatment problem
categorical variable correct answers variable with 2 or more categories but the categories have no
intrinsic ordering (like region)
ordinal variable correct answers A variable that expresses rank but not necessarily relative size
Create a bunch of indicators for each rank, leaving one out! correct answers Transforming
categorical variables
captures omitted group - avg happiness of left out region correct answers in MLR with a bunch
of indicator variables (with one left out), interpretation of 𝜷0
- working ex is happiness by region
difference in happiness between group 1 and omitted group, controlling for x variable correct
answers in MLR with a bunch of indicator variables (with one left out), interpretation of 𝜷1
- working ex is happiness by region
Pres. Approval = 𝜷0 + 𝜷1*democrat + 𝜷2*republican + 𝜷3*gas + 𝜷4(republican*gas)
(𝜷0-𝜷2 are three y int, 𝜷3 is slope for Dem + Ind, 𝜷3+𝜷4 is slope for republican) correct answers
write equation that allows for y int across 3 political parties (repub, democrat, other), and tests if
republicans internalize gas prices different when internalizing presidential approval (y variable)
Linear probability model correct answers OLS w/ indicator dependent variable
- E[Y | x1, x12] = Pr(y=1 | x1,x2)
∆ probability of y=1 associated with a 1 unit increase in x
holding x2 constant, a 1 unit increase in x1 is associated with 𝜷1 unit increase in y correct
answers Interpretation of Beta 1 in a 2 variable regression
1-(( SSR / n - k - 1 )/ ( TSS / n -1 )) correct answers Formula for Adjusted R^2
- provides correction for number of independent variables (k)
decreases correct answers As K (the number of indepednent variables) increases, adjusted R^2
linear in parameters, random sampling correct answers MLR 1 and 2 (same as SLR)
No perfect collinearity (need variation in x that is not explained by the other x variables) correct
answers MLR 3
zero conditional mean (but with more variables!); E[ e | x1, x2.... ] = 0 correct answers MLR 4
increases R^2, increase svariance (if variables are irrelevant), doesn't affect bias correct answers
What does adding more independent variables do to a regression (that may be irrelevant too)
Homoskedasticity, uncorrelated erros correct answers MLR 5 and 6 (same as SLR)
σ^2 / TSS(1-Rj^2) correct answers Variance of 𝜷j in MLR
R^2 from a regression where xj is dependent variable and all the other x variables are the
independent variables correct answers Rj^2
SSR / n -k - 1 correct answers σ^2 estimator
statistically insignificant doesn't indicate zero effect! (must use logic and econcomic reasoning to
think about what variables to add) correct answers Why do we not just only add statistically
significant variables
- speaking to the bias-variance tradeoff and which variables to add
𝜷j^ - 𝜷j / SE(𝜷j^) correct answers Test Statistics for a single 𝜷j
√var(𝜷j^) correct answers SE of 𝜷j^
(R^2unrestricted - R^2restricted / q) / (1-R^2unrestricted)(n-k-1) correct answers F statistic (test
for multiple 𝜷j)
# of restrictions in the null correct answers q in the F statistic formula
, initial R^2 from the model (including all the 𝜷) correct answers R^2unrestricted
R^2 if null is true (adding in zeroes for the 𝜷 in the null) correct answers R^2 restricted
E[y(1)|D=1] - E[y(0)|D=0] correct answers Two group treatment problem: what stata measures
as the 𝜷1
- y are the groups, D is indicator for treatment
E[y(1)|D=1] - E[y(0)|D=1] correct answers Two treatment Group problem: What we would
ideally measure to get the 'true effect'
E[Y(0)|D=1] - E[Y(0)|D=0) correct answers Selection bias term in the two treatment group
problem
E[y(1)|D=1] - E[y(0)|D=1] + E[Y(0)|D=1] - E[Y(0)|D=0) correct answers Total formula for 𝜷1^
in the treatment problem
categorical variable correct answers variable with 2 or more categories but the categories have no
intrinsic ordering (like region)
ordinal variable correct answers A variable that expresses rank but not necessarily relative size
Create a bunch of indicators for each rank, leaving one out! correct answers Transforming
categorical variables
captures omitted group - avg happiness of left out region correct answers in MLR with a bunch
of indicator variables (with one left out), interpretation of 𝜷0
- working ex is happiness by region
difference in happiness between group 1 and omitted group, controlling for x variable correct
answers in MLR with a bunch of indicator variables (with one left out), interpretation of 𝜷1
- working ex is happiness by region
Pres. Approval = 𝜷0 + 𝜷1*democrat + 𝜷2*republican + 𝜷3*gas + 𝜷4(republican*gas)
(𝜷0-𝜷2 are three y int, 𝜷3 is slope for Dem + Ind, 𝜷3+𝜷4 is slope for republican) correct answers
write equation that allows for y int across 3 political parties (repub, democrat, other), and tests if
republicans internalize gas prices different when internalizing presidential approval (y variable)
Linear probability model correct answers OLS w/ indicator dependent variable
- E[Y | x1, x12] = Pr(y=1 | x1,x2)
∆ probability of y=1 associated with a 1 unit increase in x
