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)
