lecture 3

Question 1

what is the genera; form a regression equation

Answer 1

y = a + bX + u

Question 2

what dpoes X represent in an regression equation

Answer 2

X is the independent or explanatory variable

Question 3

what dpoes y represent in an regression equation

Answer 3

Y is the dependent or explained variable

Question 4

what does u represent in a regression equ

Answer 4

u is a random error or disturbance

Question 5

what does ‘a and b)’ represent in a regression equation?

Answer 5

α and β are parameters which characterise the relationship between
Y and X. The parameters are not observable directly.

Question 6

what are the 2 interpretations of the regression model

Answer 6

1. X values are chose by the investigators e.g. process of experimentation
2. X and Y are jointly distributed random variables with cov(x,y)=/= 0

Question 7

whats is the method of least squares?

Answer 7

calculating an estiamte of an unknown value using observable data

method is to choose estimates of the parameters
which minimises the residual sum of squares.

min(𝑅𝑆𝑆)=∑(𝑌_𝑖−𝛼hat−𝛽hat𝑋)^2

this is OLS

Question 8

what is the estimate for Bhat?

Answer 8

‘sum of all’(X-Xbar)(Y-Ybar)/’sum of all(x-xbar)

covarience of X and Y over varience of X

Question 9

what is the estimate for a hat?

Answer 9

Ybar - bhat*Xbar

Question 10

what is the 2 stage procedure to calculate OLS

Answer 10

1.Calculate the slope coefficient as the ratio of the sample
covariance of X and Y to the sample variance of X

2. Calculate the intercept using the property that the regression
   line passes through the sample means of the data.

Question 11

what are ‘ a and b’?

Answer 11

population parameters

Question 12

what are ‘ahat and bhat’?

Answer 12

population parameters based on

sample data.

Question 13

what are estimators

Answer 13

random variables because they are
constructed from the random variables Y and (possibly) X.

The population parameters are not random variables. They
are unknown/unobservable parameters which we must estimate
using the data available.

Question 14

what is maximum likelehood?

Answer 14

alternative way to generate estimates of unknown parameters

The errors are assumed to be independent, identically distributed
(iid),normal random variables

take logs of the likelihood function

The method of maximum likelihood involves choosing
estimates of the population parameters which maximise the
log-likelihood function.

Question 15

compare Maximum likelihood and OLS

Answer 15

1st 2 FOC are identical to OLS equations

This is different from the formula normally used for the variance
of a least squares regression because it does not adjust for the
loss of degrees of freedom when estimating the other regression
parameters.

The maximum likelihood estimator of the error variance will be
biased in small samples. However, the bias will tend to zero as the
sample size becomes large