L5 Hypothesis testing and confidence intervals Flashcards
How do you in general calcualte the t-statistic
the result of the estimator subtracted by the hypothized value divided by the standard error of the estimator
When should you reject the null hypothesis given a confidence level of 95%
If the absolute of the t-statistic is greater than 1.96. Than the likelihood of getting such an extreme outcome assuming the null hypothesis is true is less than 5%.
How large does n have to be to be considered large
50
How do you write a regression report in a consise way
Estimation = intercept_in_numbers with standard error of intercept in parenthases under - coefficient_in_numbers with standard error in parenthases under *SRE, R² = regression, SER = standard error
are b0 and b1 OLS estimators
Yes
what is the confidence interval for b1 at 95% confidence
b1+- 1.96*SER(b1)
Are binary regressors called dummy variables
Yes
What is the slope called in a binary regressor
population difference in group means. This is because it would not make sense to call something binary a slope.
What is the intercept in a binary regression distribution
the mean of Y when X is 0
What is Homoskedasticity
It is when the variance of the standard error does not depend on the independent variable var(u|X=x) = const otherwise it is hetroskedastic
if group variances are equal is the standard error homo or hetro -skedastic
homoskedastic
if group variances are unequal in the standard error of a binary-regression is the standard error homo or hetero skedastic
heteroskedastic
What is the difference between homoskedacity and E(u|X=x)=0
E is concerned about if there is a normally distributed area where the expected error is 0, if the normally distributed areas variance stays constant than we have homoskedacity if does not we have heteroskedacity.
Is there special formulas for homoskedastic standard errors
Yes, they are called homoskedastic-only standard error formulas
What is the standard error that works for both homo and hetero skedacity
robust standard errors
What are the advatanges of a homoskedastic only standard error formula
It is simpler than the robust formulas although it cannot calculate the standard error in case of heteroskedacity
Is homoskedacity only standard errors the default in most statistical softwares
Yes, if you want robust you must change the settings but that you cannot do in excel as it is the only option
Should you always use robust formulas
Yes if you can although the formulas coencide when n is large
OLS in unbiased but not consistent
False it is both unbiased and consistent
What is the Gaus Markov theorem
That if OLS is homoskedastic the estimated slope has the smallest variance of all possible linear estimators
When does the result of the OLS estimator have the smallest variance of all consistent functions for Y, all linear and non linear estimators
If we assume both homoskedacity and that the errors are normally distributed
What are the drawbacks of the OLS estimator
the conditions for perfection are rare as relationships are often not linear and errors often not homoskedastic. It is also sensitive to outliers, never the less it is often the default in statistical software and if n is over 50 it is usually quite good
Estimated slopes in multiple regression are generally independently distributed
False, so nether are their test statistics
What is a joint hypothesis test when talking about regression
A test that specifies a null value for multiple coefficients. Often the null is that the coeficient of them both is the same
