L5 Hypothesis testing and confidence intervals

Question 1

How do you in general calcualte the t-statistic

Answer 1

the result of the estimator subtracted by the hypothized value divided by the standard error of the estimator

Question 2

When should you reject the null hypothesis given a confidence level of 95%

Answer 2

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%.

Question 3

How large does n have to be to be considered large

Answer 3

50

Question 4

How do you write a regression report in a consise way

Answer 4

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

Question 5

are b0 and b1 OLS estimators

Answer 5

Yes

Question 6

what is the confidence interval for b1 at 95% confidence

Answer 6

b1+- 1.96*SER(b1)

Question 7

Are binary regressors called dummy variables

Answer 7

Yes

Question 8

What is the slope called in a binary regressor

Answer 8

population difference in group means. This is because it would not make sense to call something binary a slope.

Question 9

What is the intercept in a binary regression distribution

Answer 9

the mean of Y when X is 0

Question 10

What is Homoskedasticity

Answer 10

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

Question 11

if group variances are equal is the standard error homo or hetro -skedastic

Answer 11

homoskedastic

Question 12

if group variances are unequal in the standard error of a binary-regression is the standard error homo or hetero skedastic

Answer 12

heteroskedastic

Question 13

What is the difference between homoskedacity and E(u|X=x)=0

Answer 13

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.

Question 14

Is there special formulas for homoskedastic standard errors

Answer 14

Yes, they are called homoskedastic-only standard error formulas

Question 15

What is the standard error that works for both homo and hetero skedacity

Answer 15

robust standard errors

Question 16

What are the advatanges of a homoskedastic only standard error formula

Answer 16

It is simpler than the robust formulas although it cannot calculate the standard error in case of heteroskedacity

Question 17

Is homoskedacity only standard errors the default in most statistical softwares

Answer 17

Yes, if you want robust you must change the settings but that you cannot do in excel as it is the only option

Question 18

Should you always use robust formulas

Answer 18

Yes if you can although the formulas coencide when n is large

Question 19

OLS in unbiased but not consistent

Answer 19

False it is both unbiased and consistent

Question 20

What is the Gaus Markov theorem

Answer 20

That if OLS is homoskedastic the estimated slope has the smallest variance of all possible linear estimators

Question 21

When does the result of the OLS estimator have the smallest variance of all consistent functions for Y, all linear and non linear estimators

Answer 21

If we assume both homoskedacity and that the errors are normally distributed

Question 22

What are the drawbacks of the OLS estimator

Answer 22

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

Question 23

Estimated slopes in multiple regression are generally independently distributed

Answer 23

False, so nether are their test statistics

Question 24

What is a joint hypothesis test when talking about regression

Answer 24

A test that specifies a null value for multiple coefficients. Often the null is that the coeficient of them both is the same

Question 25

What is the q in joint hypothesis tests

Answer 25

The number of restrictions that are attempted to be disproved.

Question 26

In joint hypothesis testing can you test the two hypothesis after each other

Answer 26

No because that would make the significance level misleading. If you test at 5% significance and give it 2 chances to fail the confidence is altered. 5% significance is in reality 9.75%

Question 27

What mesure is used to test joint hypotesis tests

Answer 27

You use the F-statistic

Question 28

Can the F-statistic be negative

Answer 28

No it cannot

Question 29

When does an F-test tell us that the variables matter

Answer 29

When the F statistic is large, then we reject that the coefficients are 0

Question 30

What does the general test of linear restrictions test

Answer 30

If the value of some coefficients are 0

Question 31

What does the F statistic signify in excell

Answer 31

A small number means that it is likely that all coefficients of the variables that are tested are zero

Question 32

What is a prediction interval

Answer 32

The confidence interval for a specific instance

Question 33

Why are confidence intervals smaller than prediction intvals

Answer 33

Because the prediction interval also hinges on the uncertainty of the error of the confidence interval and thus relies on more random variables.