Topic 5: Inference Flashcards
What is the formula for a confidence interval using the standard normal approximation?
beta^j +/- (c * se[beta^j])
What is c in the formula for the confidence interval?
It is the percentile from the t_(n-k-1) distribution
For the null hypothesis betaj = aj what is the rejection rule at 5% significance?
Reject if aj is not in the 95% confidence interval.
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?
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.
What is the null hypothesis for a joint significance test of variables in a model?
The null hypothesis is the desired variables all = 0
What is the alternative hypothesis for a joint significance test of variables in a model?
The alternative hypothesis is any of the variables does not = 0
What is the formula for the F statistic for a joint test?
[(SSRr - SSRur)/q] / [SSRur/(n-k-1)]
How do you use the F statistic to run a joint hypothesis test?
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.
How can you hypothesis test a linear combination of two variables?
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.
Multicollinearity causes OLS estimators to have what kind of standard errors?
Large.
What is the rejection rule for p-values?
Small p values reject the null hypothesis, large p values fail to reject.
How to use percentage versus percentage point?
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.
Is the p value the probability of the null hypothesis being true?
No, rather, how likely would it be to get a parameter like we did IF the parameter were really 0.
What is the formula for the t-stat?
(beta^j - betaj) / se(beta^j)
Stata: How do you generate a histogram of residuals of a regression?
Run the regression, predict newvar, resid, then histogram newvar, normal
Stata: how to check the correlation between variables?
cor xi x2 x3….etc
Stata: How to find the f statistic for the overall significance of a regression in a screenshot of the stata results of a regression?
The f stat for the overall regression is found next to F( x, y) =
What is MLR assumption 6, Normality?
The population error is independent of the explanatory variables and is normally distributed with zero mean,
Under MLR assumptions 1-6, what can we say about the variance of OLS estimators?
They have the smallest variance among unbiased estimators.
How do you find the max of a quadratic function?
the optimal value, x* = |(beta^1)/(2beta^2)|
What does the sampling distribution of the OLS estimators rely on?
The underlying distribution of the errors.
Normality vs homoskedasticity?
Normality is stronger than SLR5, because u is independent of x.
Classical Linear Model assumption?
All MLR1-5 plus normality of the error term.
CLM versus G-M assumptions?
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)
What is a t statistic?
Used to test hypotheses of interest, based on a significance level and rejection rule.
Do we use hypothesis testing on estimates?
No, we are testing population parameters (like if an unknown pop. parameter is 0)
If our hypothesis is something other than 0, how do we form the t stat?
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)
What is the p value?
It is the probability of observing a t stat as extreme or more than you actually observed.
What does it mean to say something is statistically significant?
Rejecting the null hypothesis that a parameter is equal to zero against a specified alternative at a chosen significance level.
What is economic significance?
the practical significance of an estimate, measured by sign and magnitude, as opposed to statistical significance.
How to calculate q, the numerator degrees of freedom?
Variables for pooled/restricted model minus variables of both unrestricted models (less the dummy), that is q independent variables are dropped
How to calculate dof?
the number of observations - number of estimated parameters
What is the relationship between the f-stat and t stat?
the F stat is the t-stat squared
What is the overall significance of the regression?
it is the f stat reported for a regression, and is a test of joint exclusion of all independent variables.
Chow test vs f test?
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)
