4. MRA - Inference

Question 1

What is the normality assumption? (MLR.6)

Answer 1

The population error u is independent of the explanatory variables x1, x2, . . . , xk and is normally distributed with zero mean and variance

Question 2

What are the classical linear model assumptions?

Answer 2

MLR.1-6. The Gauss-Markov assumptions plus the assumption of a normally distributed error term

Question 3

What are the OLS assumptions known as under the classical linear model assumptions?

Answer 3

The minimum variance unbiased estimators

Question 4

What is the minimum variance unbiased estimators?

Answer 4

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

Question 5

What is the central limit theorem?

Answer 5

It states that the average from a random sample for any population with finite variance when standardised has an asymptototic standard normal distribution

Question 6

Is the normality assumption required for OLS to be BLUE?

Answer 6

NO

Question 7

What is the error distribution like?

Answer 7

The error distribution should be close to normal

Question 8

What is the error term?

Answer 8

The sum of many different unobserved factors. The sums of independent factors are normally distributed.

Question 9

What can the assumption of normality be replaced by?

Answer 9

A large sample size

Question 10

How large do your degrees of freedom need to be to use a normal distribution?

Answer 10

> 120

Question 11

What does standardising mean?

Answer 11

Take the mean out and divide by the standard deviation

Question 12

What does k+1 show in the model?

Answer 12

The number of parameters (k) + the constant (1)

Question 13

How do you run a t-test?

Answer 13

1. Find your value (B^j/se)
2. Use the degrees of freedom and level of significance to find the critical value
3. 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

Question 14

How do the results of the p-value differ to the critical value?

Answer 14

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

Question 15

What does a two-sided alternative test tell us and what are it’s limits?

Answer 15

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

Question 16

What does the t-test measure?

Answer 16

How many estimated standard deviations the estimated coefficient is from 0

Question 17

What does a small p-value suggest?

Answer 17

Evidence against the null hypothesis because one would reject the null hypothesis even at small significance levels

Question 18

How should you interpret the 95% confidence interval that stata generates?

Answer 18

• The bounds of the interval are random
• In repeated samples, the population coefficient will be included 95% of the time

Question 19

What does a wide confidence interval suggest?

Answer 19

The effect is imprecisely estimated

Question 20

How do we determine whether a result is statistically significant using the confidence interval?

Answer 20

The result is not statistically significant if 0 lies in the confidence interval

Question 21

What is joint significance?

Answer 21

When you want to test whether a group of variables has an any impact on y

Question 22

When do we reject the null hypothesis in favour of the alternative hypothesis in regards toa. T-test?

Answer 22

If the estimated coefficient B^j is larger than the critical value

Question 24

Why, in a t-test, is a result statistically significant if 0 lies outside the interval?

Answer 24

Because in a t-test you are testing whether or not a variable is sufficiently different to zero to be significant

Question 25

What is the basic premise of a joint significance/ f-test?

Answer 25

1. Look at the SSR for the unrestricted model
   
   2. Compare it to the SSR of the restricted model
   3. Decide whether the difference big enough to make it worth having the 3 extra variables

Question 26

What does it mean if your f-statistic is significant?

Answer 26

It means that your variables are jointly significant

Question 27

If our f-test is significant, what does this likely mean?

Answer 27

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

Question 28

What can an f-test help us think about regarding our model?

Answer 28

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