1. Simple Linear Regression Model

Question 1

What can stats methods be used for?

Answer 1

• testing economic theories
• estimating the magnitude of relationships
• forecasting
• policy evaluation

Question 2

7 steps for econometric

Answer 2

1. Formulate the question
2. Develop economic model
3. Specify the model
4. Set out hypotheses
5. Estimate the economic model
6. Conduct hypothesis test
7. Interpret results and draw conclusions

Question 3

Types of data

Answer 3

• cross sectional data
• time series data
• pooled cross sectional data
• panel (longitudinal) data

Question 4

What does the simple linear regression model look like?

Answer 4

y= B0+ B1x+ u

Question 5

What does u represent?

Answer 5

Factors other than x which aftect y

Question 6

Assumptions about u in simple linear regression model

Answer 6

1. On average the disturbance term is zero. E(u)=0. For any single observation it will be positive or negative
2. The disturbances are unrelated to the explanatory variable E(u|x)=E(u)

Question 7

Why is the zero conditional mean assumption important?

Answer 7

If E(u|x) =0 then E(y|x)=B0+ B1x

Question 8

What is the conditional mean assumption?

Answer 8

That E(u|x)=0

Question 9

Population regression function

Answer 9

A linear function of x where a one unit increase in x changes y by P. For any value of x, the distribution of y is centred about E(y|x)

Question 10

What does PRF tell us?

Answer 10

How the expected value of y changes with x

Question 11

What doesn’t the PRF tell us?

Answer 11

y=B0 + B1x for every observation. y is not always equal to E(y|x)

Question 12

OLS

Answer 12

Ordinary Least Squares

Question 13

OLS advantages

Answer 13

Works well

Simple

Question 14

What does OLS do?

Answer 14

Finds values of B0 and B1 that minimise the sun of the squared vertical distances between the points and the line

Question 15

What is another name for the OLS regression line?

Answer 15

SRF

Question 16

How does the SRF relate to the PRF?

Answer 16

The SRF is an estimate of the PRF

Question 17

Properties of OLS estimators

Answer 17

• unbiased

* efficient

Question 18

What are the two parts of the estimator of B1?

Answer 18

• a non random (deterministic) part that captures the true underlying relationship
• a random (stochastic) part responsible for variations around the population parameter

Question 19

What is the sampling distribution of the estimator of B1?

Answer 19

If the estimator of B1 is unbiased then it is normally distributed around B1 as the expected value

Question 20

Assumptions for unbiasedness of OLS parameters

Answer 20

1. Linear in parameters
2. Random sampling
3. Sample variation in explanatory variable
4. Zero conditional mean

Question 21

What happens to the estimate of B1 if there is a positive covariance of x and u?

Answer 21

The expected value of the estimate of B1 is greater than B1 so the estimate is biased upwards

Question 22

How realistic is the assumption of linear in parameters?

Answer 22

• It is a good first approximation.

- Non linear relationships are quite common but they can be accommodated for

Question 23

How realistic is the assumption of random sampling?

Answer 23

• It isn’t always valid
• important to understand how data was generated
• we will assume random sampling

Question 24

How realistic is the assumption of sample variation in explanatory variable?

Answer 24

• Almost always valid

- It is possible x won’t vary much, this will affect the accuracy of our estimates

Question 25

How realistic is the zero conditional mean assumption?

Answer 25

-It often isn’t valid usually because factors affecting y and correlated with x have been omitted from the model

Question 26

What does OLS estimators being efficient mean?

Answer 26

They are the best linear unbiased estimators, they have the smallest dispersion and the minimum variance

Question 27

Homoskedasticity

Answer 27

The assumption that the error U has the same variance given any value of the explanatory variable Var(u|x)= ó^2

Question 28

Heteroskedastic

Answer 28

When the var(u|x) varies as x varies so it isn’t equal to a constant

Question 29

How realistic is the assumption of homoskedasticity?

Answer 29

Not very realistic. Typically the greater x, the greater the variance

Question 30

What factors determine our estimate of the variance of B1

Answer 30

• As n (sample size) increases, variance decreases
• if the variance of u increases then so will the variance of our estimate of B1
• more variation in x will decrease the variance

Question 31

What are the standard errors?

Answer 31

They are the standard deviation of our estimates of B0 and B1

Question 32

Properties of standard errors

Answer 32

• unbiased

* random variables that take a different value for each sample of data

Question 33

Standard error of the regression (root mean square)

Answer 33

The standard deviation of u. This is a measure of the accuracy of the measure as a whole

Question 34

How do OLS estimators minimise the standard error of the regression?

Answer 34

OLS estimators minimise the sum of the squared residuals. This makes up part of the standard error of the regression so if this is minimised so will the standard error of the regression