8- Inference Flashcards
What are the 5 main steps to inference?
- Form a hypothesis about a parameter βj in the population
- Collect suitable data
- Perform a regression to obtain ^βj
- Perform a statistical test: if our hypothesis about βj is true, what are the odds of finding ^βj from the sample
- Reject the hypothesis if odds are sufficiently small
What is the 6th MLR assumption of normality?
The population error u is independent of the explanatory variables and normally distributed with mean 0 and variance σ^2
What are the 6 MLR assumptions collectively referred as?
The classical linear (CLM) assumptions
How do you standardise a variable to get it to be normally distributed?
Subtract the mean and divide by the standard deviation:
^βj-βj/sd(^βj)
What does the t-stat tell us?
How far away the estimator ^βj is away from the hypothesised value
Why and how do we use the t distribution in statistical inference?
We can’t use the normal distribution, because it depends on standard deviation which is unknown. We use ^σ instead which gives the standard error: t*=^βj-βj/se(^βj)
What are the 3 steps for a two-sided hypothesis test?
- Calculate t* = ^βj-a/se(^βj)
- Pick a significance level α (usually 5%)
- Reject H0 if |t| > c fail to reject H0 if |t| ≤ c
What is the critical value (c)?
It is the t value that ensures that the probability we reject H0 when it is true is α
What is a Type 1 error?
Rejecting H0 even though H0 is true
What is a Type 2 error?
Failing to reject H0 even though H1 is true
What is the definition of the p-value associated with a two-sided t-test?
The p-value tells us how likely it would be under the null hypothesis to randomly obtain a t-stat that is more extreme than the one we estimated (t)
Pr(T>t)
What is the interpretation of a confidence interval?
If we took many random samples and calculated a confidence interval each time, βj would lie in that confidence interval 95% of the time
When do you apply an F-test?
When you’re testing multiple restrictions e.g H0: β1 = 2, β2 = 3
What is the restricted model?
The regression with the restrictions from H0 imposed
