Reg review

Question 1

what is the standard error?

Answer 1

The estimated standard deviation of the sampling distribution of the slope parameter, which tells us how precise our estimate is.

Question 2

what is the p-value?

Answer 2

The smallest significance level at which we would reject the null hypothesis.

Question 3

What is a confidence interval?

Answer 3

Over repeated sampling, we would expect 95% of confidence intervals constructed in this manner to contain the true population parameter.

Question 4

What does it mean for a coefficient to be unbiased?

Answer 4

If an estimator is unbiased, then the mean of the sampling distribution of the estimate should be centered on the true population parameter (E(beta1_hat) = beta1_population)

Question 5

Definition of beta1 coefficient?

Answer 5

Beta1_hat is the slope of y with respect to x when all other regressors are held constant, or fixed, a one-unit change in X is associated with a beta1_hat change in Y, holding all else constant.

Question 6

What is an endogenous regressor?

Answer 6

correlated with the error term, or correlated with Y through the error term

Question 7

What is an exogenous regressor?

Answer 7

uncorrelated with error and has a direct impact on Y, should be included to avoid OVB.

Question 8

What is consistency?

Answer 8

Betahat is a consistent estimator of betapop, as N approaches infinity, betahat converges in probability to betapop (a.k.a. asymptotic unbiasedness, large samples property)

Question 9

What is the law of large numbers?

Answer 9

Our estimates of the population mean and variance will converge in probability to the true population parameters.

Question 10

What is the CLT?

Answer 10

As N approaches infinity, the sampling distribution will be normally distributed.

Question 11

What are the Guass-markov assumptions for MLR and which are needed for unbiasedness and consistency? Which are needed to be BLUE?

Answer 11

Gauss Markov Assumptions for MLR: (1 – 4 for unbiasedness, 1 – 5 for BLUEs (best linear unbiased estimators))

1. Linear in parameters
2. Random sampling (independent and identically distributed random variables)
3. No perfect collinearity (between any of the predictors, r < 1 between all regressors)
4. Zero conditional mean (the expected value of U conditional on all Xs is equal to zero)
5. Homoskedasticity (the variance of U conditional on all Xs is equal to the variance of U, sigma-squared)

Question 12

Probability of type 1 error?

Answer 12

alpha

Question 13

Probability of type 2 error?

Answer 13

beta

Question 14

What is r-squared?

Answer 14

Proportion of the sample variation in Y that is explained by X

Question 15

Factors affecting sampling variances of OLS slope estimators

Answer 15

1) Error Variance: Take more stuff out of the error (make σ2 smaller); add more explanatory variables. As error variance in pop decreases, Var((β_j ) ̂) gets smaller.
2) Total Sample Variation: It is easier to estimate how xj affects y if we see more variation in xj (increase SSTj); increase SSTj by increasing the sample size.
3) As Rj2 gets bigger so does Var(b1). If xj is unrelated to all other independent variables, it is easier to estimate its ceteris paribus effect on y.

Question 16

What happens when you have heteroskedasticity?

Answer 16

Variance formulas for OLS invalid, does not affect beta coefficients; cannot perform F/t-tests.

Question 17

In small samples ^B1 = (B1 + ^cov(x,u)/^var(u))

What can we do to show that zero conditional mean assumption holds here?

Answer 17

the cov of x and u is equal to 0 in our sample.

Question 18

Formula for B1 coefficient?

Answer 18

cov(x,y)/var(x)

Question 19

Formula for B0 coefficient?

Answer 19

E(y)-B1*E(x)

Question 20

Formula for SST?

Answer 20

∑(actual xj – x ̅j)2)/n

Question 21

Formula for var(Bj), SLR?

Answer 21

σ^2/SSTx

Question 22

Formula for var(Bj), MLR? (expressed in terms of sigma squared)

Answer 22

σ^2/(SST_j *(1-R_j^2))

Question 23

Formula for standard error of Bj, SLR?

Answer 23

√(SSR/(n-2))/√SSTx

Question 24

Formula for standard error of Bj, MLR?

Answer 24

√(SSR/df)/√(SST_j (1-R_j^2))

Question 25

Variance of regression?

Answer 25

SSR/(df)

Question 26

RMSE (standard error of regression)?

Answer 26

√(SSR/df)

Question 27

How to calculate residual?

Answer 27

yi - ^yi (actual y – predicted y)

Question 28

How to calculate SST?

Answer 28

∑(actual y – avg y)2

Question 29

How to calculate SSE?

Answer 29

∑(predict y – avg y)2

Question 30

How to calculate SSR?

Answer 30

∑ (actual y – predict y)2 or ∑u2

Question 31

How to calculate R squared?

Answer 31

SSE/SST or 1 – SSR/SST

Question 32

How to calculate correlation given covariance and variances?

Answer 32

(Cov(X,Y))/√(Var(X)Var(Y))

Question 33

Formula for F statistic (SS form?)

Answer 33

((SSRr-SSRur)/q/

SSRur/(n-k-1)

Question 34

Formula for F statistic (R squared form?)

Answer 34

((R^2r-R^2ur)/q/

1-R^2ur)/(n-k-1

Question 35

Change in y with respect to change in x when you have a quadratic? (B0+B1x1+B2x2^2+u)

Answer 35

change in y/change in x=

B1+2*B2x

Question 36

What are advantages of using LPM (OLS) for a binary DV?

Answer 36

easy estimation and interpretation of coeffs. That are reasonably good

Question 37

Disadvantages of using LPM (OLS) for a binary dv?

Answer 37

predicted probs. May be greater than 1 or less than zero (Marginal probability effects sometimes logically impossible)

Partial effects of explanatory variables are constant

LPM is heteroskedastic -have to use OLS with robust standard errors

Non-normality of errors (are binomial)

Question 38

True or false: Partial effects from logit models are nonlinear and depend on the level of x

Answer 38

True

Question 39

What values do researchers typically hold other covariates at when generating marginal effects?

Answer 39

holds all other covariates at their means (which might not make sense for dummy variables)

Question 40

What does MLE do?

Answer 40

use a likelihood function, which gives us the liklehood of the data given a set of proposed parameters

Computer keeps running iterations of the above until the improvements in the liklehood are small; process called “convergence”

Question 41

What distribution does logit model use for hypothesis testing? What kind of stat will you get?

Answer 41

Use normal distribution; report z-statistics

Question 42

How can you measure goodness of fit from logit model?

Answer 42

Percent correctly specified

Pseudo r-squared

Chi-square test (like f-test, tests null that all coeff. Are zero)