Inference Flashcards
What is assumption MLR.6?
- Normality of errors
- it is assumed that the unobserved factors are normally distributed around the population regression function
What is the name given to MLR.1-MLR.6?
Classic Linear Model assumptions
What is theorem 4.1?
- Normal sampling distribution
- estimators are normally distributed around the true population parameters
- the standardised estimators follow a standard normal distribution
What does t-statistic measure?
How many standard deviations the estimated coefficient is away from 0
What is the general null and alternative hypothesis?
Ho: Bj=0 H1=Bj not equal to 0
What is a p-value?
The p-value is the smallest significance level at which a t-statistic is just rejected
I.e it is the SL where CV=TS
What does a small p-value mean?
- Evidence against Ho
- it means one would reject the hypothesis even at small significance levels
What does a large p-value mean?
- Evidence in favour of Ho
- Ho only rejected at larger significance levels
What is the interpretation of a 95% confidence interval?
- In repeated samples 95% of CI’s constructed using the same method will contain the population parameter
What is the relationship between confidence intervals and hypothesis tests?
If hypothesized value is not within the interval/CI we can reject the null in favour of the alternative hypothesis
Why is SSRr > SSRur?
- because in the restricted model there is at least one less explanatory variable than in the unrestricted model
- SSR measures sum of residuals
- residuals increase the less explanatory power the regression has
What is the meaning of consistency?
- as sample size gets larger, distribution of estimator gets narrower
- as n approaches infinity the distribution of the estimator approaches true value point
What is the weaker version of MLR.4-Zero Conditional Mean?
- Cov(Xj,u)=0
- all explanatory variables must be uncorrelated with error term
-for consistency of OLS only weaker version has to hold
