1. Assumptions of Multiple Regression Model and OLS
2. Goodness of fit:

1. R-squared
2. Adjusted R-squared
3. Information criteria: AIC, BIC

3. F test for regression significance
4. Student’s t test for significance of a parameter

Econometrics, Lecture 4, 2014-03-11

Econometrics, Lecture 4, 2014-03-11

Assumptions of Multiple Regression Model and

OLS

Consequences:
A – parameter estimates are wrong
B – standard errors of OLS estimator are wrong
C – probability distributions of test statistics are

different than specified

Econometrics, Lecture 4, 2014-03-11

Assumptions of Multiple Regression Model and

OLS

Assumption

What if false?

Consequenc

e

Model equation is true

- functional form of equation is correct

wrong functional form

A

- parameters are constant over

population

instability of parameters

A

- no important variable is missing

omitted variables

problem

A

- there are no unnecessary variables

insignificant variables

problem

B

rk(X) = K, K < n

perfect

multicolinearity

not possible to

estimate

param.

near multicolinearity

B

Econometrics, Lecture 4, 2014-03-11

Assumptions of Multiple Regression Model and

OLS

Assumption

What if false?

Consequenc

e

error term carries

systematic

information on

dependent variable

A

error term carries

information on

independent variables

A

heteroskedasticity –

variance of error term

is not constant

B, C

autocorrelation –

elements of error term

vector are correlated

B, C

 

0





E

 

0





T

X

E

 

I

Var

2







Possible combinations of F and Student’s t tests

results:

Test results

Conflict?

Reject H

0

in F test and reject H

0

for

all independent variables in
Student’s t test

No

Reject H

0

in F test and reject H

0

for

some independent variables in
Student’s t test

No

Reject H

0

in F test and do not

reject H

0

for any independent

variable in Student’s t test

Yes

Do not reject H

0

in F test and do not

reject H

0

for any independent

variable in Student’s t test

No

Do not reject H

0

in F test and reject

H

0

for at least one independent

variable in Student’s t test

Yes

Econometrics, Lecture 4, 2014-03-11