Section 3 Flashcards
What is X in the bivariate linear model?
Explanatory/exogenous variable/regressor
What is Y in the model?
Dependent/endogenous variable/regressand
Is a model still linear if it has the form:
a) X^2
b) X1X2
c) β^2?
Yes yes no
What’s the best method to estimate the regression line?
Minimise sum of squared errors - this is called ordinary least square estimation (OLS)
See 3.2.1 OLS method
Now
How can we say the OLS is the best estimation?
If the classical linear regression assumptions apply
What are the 5 classical linear regression assumptions?
1) E(εi)=0 (errors have a 0 mean)
2) Var(εi)=σ^2 for all i (homoskedastic)
3) Cov(εi,εj)=E(εiεj) (errors are not autocorrelated)
4) E(Xiεj) = E(Xi)E(εj) = 0 (X and ε are independent)
5) εi ~ N(0,σ^2) (each error has the same normal distribution with same μ and σ^2)
What does homoskedastic mean?
The variance of the error is constant for all observations
What does it mean for error terms to be not autocorrelated?
Means there is no correlation between them
What does the Gauss-Markov Theorem state and why?(2 reasons)
It states OLS estimators are the best linear unbiased estimators
Why?
Unbiased; sampling distributions of estimators are centred around their true values
Efficient; smallest variance compared with all other linear estimators
How can we tell β estimates are normally distributed?
Since Y is a function of the linear errors tf is normally distributed and OLS estimators are linear function of Y, OLS estimators too must be normally distributed
Notes
Since the gauss Markov theorem tells us OLS is unbiased, the means of the sampling distributions of the estimators are just β1 and β2
(Learn equations to find the variance!)
What does the coefficient of determination measure?
Goodness of fit
Note: although OLS finds best fitting line, doesn’t mean the line is good necessarily
What do TSS, ESS and RSS stand for?
TSS = total sum of squares ESS = explained sum of squares RSS = residual sum of squares
What does a small RSS imply?
A good fit
What does R^2 tell us?
It tells us how much of the total variation in the Y variable is explained by the regression model
Learn 3.4.1 and 3.4.2 and 3.5
T test and test of significance and confidence bands
What are the 5 columns of the Eviews output?
1) variable (name of variable)
2) coefficient (OLS parameter estimates)
3) standard error (of the estimate)
4) t statistic (P(β)=0, equal to 2/3)
5) probability (p value measures probability under t distribution that lies above t statistic value)
If doing a 2 sided 5% test, at what range of p value will you reject the null?
P-value<0.05
Prove the OLS estimators for the simple regression model?
see notes
Prove the OLS estimators for the simple regression model are unbiased
see notes
Prove the OLS estimators variance for the simple regression model
see notes
What is meant by a “linear estimator”?
An estimator is linear if it is a linear function of the sample observations
What is meant by an “unbiased estimator”?
An estimator is unbiased if, on average, the estimate coincides with the true value. If an estimator x^ of x is unbiased then E(x^)=x (see 4b and 4c and 4d class 1)
