Topic 5: Inference

Question 1

What is the formula for a confidence interval using the standard normal approximation?

Answer 1

beta^j +/- (c * se[beta^j])

Question 2

What is c in the formula for the confidence interval?

Answer 2

It is the percentile from the t_(n-k-1) distribution

Question 3

For the null hypothesis betaj = aj what is the rejection rule at 5% significance?

Answer 3

Reject if aj is not in the 95% confidence interval.

Question 4

What is the interpretation for a regression where removal of a variable leads to an increase in the coefficient on another variable, but the p value of that variable decreases to zero?

Answer 4

With a p value of 0, the coefficient of that variable is now statistically significant. This occurred because the two variables were correlated, so their effect was spread between the two variables.

Question 5

What is the null hypothesis for a joint significance test of variables in a model?

Answer 5

The null hypothesis is the desired variables all = 0

Question 6

What is the alternative hypothesis for a joint significance test of variables in a model?

Answer 6

The alternative hypothesis is any of the variables does not = 0

Question 7

What is the formula for the F statistic for a joint test?

Answer 7

[(SSRr - SSRur)/q] / [SSRur/(n-k-1)]

Question 8

How do you use the F statistic to run a joint hypothesis test?

Answer 8

Create your null and alternative hypotheses, run each regression for the restricted (fewer vars) and unrestricted model. Grab the SSR for each. The value q is the # of restrictions and (n-k-1) is the DOF for the unrestricted model.

Question 9

How can you hypothesis test a linear combination of two variables?

Answer 9

Create a new parameter that is the linear combination for which you need the standard error, solve it for one of the existing parameters and substitute it into the equation. Create a new variable that is the combination found from the rearranging. This will give us the coefficient and standard error for the desired new parameter, as well as a t-stat and p value.

Question 10

Multicollinearity causes OLS estimators to have what kind of standard errors?

Answer 10

Large.

Question 11

What is the rejection rule for p-values?

Answer 11

Small p values reject the null hypothesis, large p values fail to reject.

Question 12

How to use percentage versus percentage point?

Answer 12

When the units of the given variable are already in percent, the change is in percentage points. When the units are not already a percent, the change is in percent.

Question 13

Is the p value the probability of the null hypothesis being true?

Answer 13

No, rather, how likely would it be to get a parameter like we did IF the parameter were really 0.

Question 14

What is the formula for the t-stat?

Answer 14

(beta^j - betaj) / se(beta^j)

Question 15

Stata: How do you generate a histogram of residuals of a regression?

Answer 15

Run the regression, predict newvar, resid, then histogram newvar, normal

Question 16

Stata: how to check the correlation between variables?

Answer 16

cor xi x2 x3….etc

Question 17

Stata: How to find the f statistic for the overall significance of a regression in a screenshot of the stata results of a regression?

Answer 17

The f stat for the overall regression is found next to F( x, y) =

Question 18

What is MLR assumption 6, Normality?

Answer 18

The population error is independent of the explanatory variables and is normally distributed with zero mean,

Question 19

Under MLR assumptions 1-6, what can we say about the variance of OLS estimators?

Answer 19

They have the smallest variance among unbiased estimators.

Question 20

How do you find the max of a quadratic function?

Answer 20

the optimal value, x* = |(beta^1)/(2beta^2)|

Question 21

What does the sampling distribution of the OLS estimators rely on?

Answer 21

The underlying distribution of the errors.

Question 22

Normality vs homoskedasticity?

Answer 22

Normality is stronger than SLR5, because u is independent of x.

Question 23

Classical Linear Model assumption?

Answer 23

All MLR1-5 plus normality of the error term.

Question 24

CLM versus G-M assumptions?

Answer 24

Under the CLM assumptions OLS estimators have stronger efficiency than G-M assumptions and are the minimum variance unbiased estimators, but are no longer restricted to linear in the yi (BUE, not BLUE)

Question 25

What is a t statistic?

Answer 25

Used to test hypotheses of interest, based on a significance level and rejection rule.

Question 26

Do we use hypothesis testing on estimates?

Answer 26

No, we are testing population parameters (like if an unknown pop. parameter is 0)

Question 27

If our hypothesis is something other than 0, how do we form the t stat?

Answer 27

by using the formula: (beta^j - aj)/se(beta^j), where aj is the something other than 0 in the null hypothesis (Ho: betaj = aj)

Question 28

What is the p value?

Answer 28

It is the probability of observing a t stat as extreme or more than you actually observed.

Question 29

What does it mean to say something is statistically significant?

Answer 29

Rejecting the null hypothesis that a parameter is equal to zero against a specified alternative at a chosen significance level.

Question 30

What is economic significance?

Answer 30

the practical significance of an estimate, measured by sign and magnitude, as opposed to statistical significance.

Question 31

How to calculate q, the numerator degrees of freedom?

Answer 31

Variables for pooled/restricted model minus variables of both unrestricted models (less the dummy), that is q independent variables are dropped

Question 32

How to calculate dof?

Answer 32

the number of observations - number of estimated parameters

Question 33

What is the relationship between the f-stat and t stat?

Answer 33

the F stat is the t-stat squared

Question 34

What is the overall significance of the regression?

Answer 34

it is the f stat reported for a regression, and is a test of joint exclusion of all independent variables.

Question 35

Chow test vs f test?

Answer 35

The chow test is used when dummy variables are involved and the formulas are different. The SSRur for the f test is replaced with the SSR of both restricted models. The numerator dof is 1/k+1 in chow, and the denominator dof is 1/n-2(k+1)