Section 3

Question 1

What is X in the bivariate linear model?

Answer 1

Explanatory/exogenous variable/regressor

Question 2

What is Y in the model?

Answer 2

Dependent/endogenous variable/regressand

Question 3

Is a model still linear if it has the form:

a) X^2
b) X1X2
c) β^2?

Answer 3

Yes yes no

Question 4

What’s the best method to estimate the regression line?

Answer 4

Minimise sum of squared errors - this is called ordinary least square estimation (OLS)

Question 5

See 3.2.1 OLS method

Answer 5

Now

Question 6

How can we say the OLS is the best estimation?

Answer 6

If the classical linear regression assumptions apply

Question 7

What are the 5 classical linear regression assumptions?

Answer 7

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)

Question 8

What does homoskedastic mean?

Answer 8

The variance of the error is constant for all observations

Question 9

What does it mean for error terms to be not autocorrelated?

Answer 9

Means there is no correlation between them

Question 10

What does the Gauss-Markov Theorem state and why?(2 reasons)

Answer 10

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

Question 11

How can we tell β estimates are normally distributed?

Answer 11

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

Question 12

Notes

Answer 12

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!)

Question 13

What does the coefficient of determination measure?

Answer 13

Goodness of fit

Note: although OLS finds best fitting line, doesn’t mean the line is good necessarily

Question 14

What do TSS, ESS and RSS stand for?

Answer 14

TSS = total sum of squares
ESS = explained sum of squares
RSS = residual sum of squares

Question 15

What does a small RSS imply?

Answer 15

A good fit

Question 16

What does R^2 tell us?

Answer 16

It tells us how much of the total variation in the Y variable is explained by the regression model

Question 17

Learn 3.4.1 and 3.4.2 and 3.5

Answer 17

T test and test of significance and confidence bands

Question 18

What are the 5 columns of the Eviews output?

Answer 18

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)

Question 19

If doing a 2 sided 5% test, at what range of p value will you reject the null?

Answer 19

P-value<0.05

Question 20

Prove the OLS estimators for the simple regression model?

Answer 20

see notes

Question 21

Prove the OLS estimators for the simple regression model are unbiased

Answer 21

see notes

Question 22

Prove the OLS estimators variance for the simple regression model

Answer 22

see notes

Question 23

What is meant by a “linear estimator”?

Answer 23

An estimator is linear if it is a linear function of the sample observations

Question 24

What is meant by an “unbiased estimator”?

Answer 24

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)