4. MRA - Inference Flashcards
What is the normality assumption? (MLR.6)
The population error u is independent of the explanatory variables x1, x2, . . . , xk and is normally distributed with zero mean and variance
What are the classical linear model assumptions?
MLR.1-6. The Gauss-Markov assumptions plus the assumption of a normally distributed error term
What are the OLS assumptions known as under the classical linear model assumptions?
The minimum variance unbiased estimators
What is the minimum variance unbiased estimators?
Where the OLS has the smallest variance among unbiased estimators; we no longer have to restrict our comparison to estimators that are linear in y
What is the central limit theorem?
It states that the average from a random sample for any population with finite variance when standardised has an asymptototic standard normal distribution
Is the normality assumption required for OLS to be BLUE?
NO
What is the error distribution like?
The error distribution should be close to normal
What is the error term?
The sum of many different unobserved factors. The sums of independent factors are normally distributed.
What can the assumption of normality be replaced by?
A large sample size
How large do your degrees of freedom need to be to use a normal distribution?
> 120
What does standardising mean?
Take the mean out and divide by the standard deviation
What does k+1 show in the model?
The number of parameters (k) + the constant (1)
How do you run a t-test?
- Find your value (B^j/se)
- Use the degrees of freedom and level of significance to find the critical value
- If your value is beyond the critical value, we can be confident that the parameter is far enough from 0 to not be 0. If this test is run at 95% confidence, we can be 95% sure that the parameter isn’t 0
How do the results of the p-value differ to the critical value?
The P-value gives more information, instead of just having the fixed critical value, it tells you the moment when you become indifferent between rejecting H0 and accepting H0. It is the minimal significance level you can go to
What does a two-sided alternative test tell us and what are it’s limits?
A two-sided alternative test simply tests whether there is a relationship or not, however it does not tell us if this relationship is positive or negative
What does the t-test measure?
How many estimated standard deviations the estimated coefficient is from 0
What does a small p-value suggest?
Evidence against the null hypothesis because one would reject the null hypothesis even at small significance levels
How should you interpret the 95% confidence interval that stata generates?
- The bounds of the interval are random
- In repeated samples, the population coefficient will be included 95% of the time
What does a wide confidence interval suggest?
The effect is imprecisely estimated
How do we determine whether a result is statistically significant using the confidence interval?
The result is not statistically significant if 0 lies in the confidence interval
What is joint significance?
When you want to test whether a group of variables has an any impact on y
When do we reject the null hypothesis in favour of the alternative hypothesis in regards toa. T-test?
If the estimated coefficient B^j is larger than the critical value
Why, in a t-test, is a result statistically significant if 0 lies outside the interval?
Because in a t-test you are testing whether or not a variable is sufficiently different to zero to be significant
What is the basic premise of a joint significance/ f-test?
- Look at the SSR for the unrestricted model
- Compare it to the SSR of the restricted model
- Decide whether the difference big enough to make it worth having the 3 extra variables
What does it mean if your f-statistic is significant?
It means that your variables are jointly significant
If our f-test is significant, what does this likely mean?
The variables tested are jointly significant, the likely reason is multicollinearity between them which lowers the precision of our estimates which reduces our confidence to reject
What can an f-test help us think about regarding our model?
Helps diagnose our model, suggests that maybe our model isn’t very well specified given our high levels of multicollinearity and therefore you don’t see any individual significance in these variables so maybe you want to change your model and put some of these similar variables together
