Fichas
Inference
Fichas del conjunto (30)
- 1What is required in order to hypothesis test?need the full sampling distribution of β ̂_j
- 2What additional assumption must be made? Why?The population error u is independent of the explanatory variables and is normally distributed with zero mean and variance u ~ N(0, σ^2)
Needed because Gauss-Markov are not sufficient to pin down the distribution of β ̂_j which depends on the distribution of the error term - 3What are all 6 assumptions collectively known as?Classical Linear Model
- 4Under CLM assumptions, what is the distribution used in hypothesis testing?Normal
β ̂_j ~ N(β_j, Var(β_j))
(β ̂_j - β_j)/sd(β ̂_j) ~ N(0, 1) - 5How is the test statistic calculated for the t test?On the formula sheet
- 6What are the degrees of freedom for the t test?n - k - 1
- 7What is the difference between the normal and t distributions?the t distribution is the same as the normal with just fatter tails = higher probability of extreme values
- 8Why do we use the t distribution rather than the normal distribution?answer on a physical flashcard
- 9When is the null hypothesis less likely to be true?when β ̂_j is far from 0
- 10What does the t test statistic measure?how many sd β ̂_j is away from 0
- 11What does a lower significance level indicate?the probability of reject H0 when it is true is lower, more robust analysis
- 12When is the null hypothesis rejected?t_(β ̂_j) > c
- 13What is the effect of a high significance level on the critical value?decreases the critical value making H0 easier to reject
- 14What is observed as degrees of freedom increase?the t test distribution approaches the standard normal
- 15Give an example of a one-sided hypothesisH0: β_j =< 0
H1: β_j > 0 - 16Give an example of a two-sided hypothesisH0: β_j = 0
H1: β_j ≠ 0 - 17Which type of does STATA always conduct?two sided with the hypothesises:
H0: β_j = 0
H1: β_j ≠ 0 - 18Which value of t generally indicates the null hypothesis can be rejected?t > 2
- 19What is the more general form for the null hypothesis?H0: β_j = α_j
where α_j is our hypothesised value for β_j - 20What is the p-value? Why is it used?probability that a t distributed random variable exceeds the calculated t statistic
gives a more informative summary of the strengths of the evidence against the null hypothesis - 21What is the effect of using a large sample?more likely the coefficient is highly significant but only has a small economiceffect on the dependent variable
- 22When and why is an F test used?Used for testing 2 or more parameters to work out if one variable is more important than another or which variables are important
- 23What is the basic premise of the F test?The original model is unrestricted
Restrictions are imposed on the model through hypothesises
The SSR for both models are compared
If there is a large increase after the restrictions, then the excluded variables are important - 24Give the form of the hypothesisesH0: β1 = β2, β1 - β2 = 0
H1: β1 ≠ β2, β1 - β2 ≠ 0
H0: β1 =0, β2 = 0
H0: β1 ≠ 0, β2 ≠ 0 - 25How do you calculate the test statistic for an F test?On the formula sheet
- 26How do you calculate degrees of freedom?(q, n - k -1)
- 27How do you find the critical value in an F test?F table
columns = the number of restrictions, q
rows = n - k -1 - 28How do you calculate the SSR for the restricted model?answer on physical flashcard
- 29How do you calculate the SSR for the unrestricted model?answer on physical flashcard
- 30What restriction does calculating the F statistic using R2 encounter?Not valid for all linear formats
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- Year 2 ECN21004 - Econometrics Fichas sobre Inference, creado por Imogen Donoghue el 11/01/2023.
- Creado por
- Imogen Donoghue
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