Assumptions behind the classical linear model and the use of quarterly dummy variables

Question 1

What is the first assumption behind the CLRM and what does it mean?

Answer 1

The error term ε is a random variable with a mean or expected value of zero
Beta0 and beta1 are constraints so for a given value of X the expected value of
Y= E (Y) = Beta0 + Beta1X

Question 2

What is the second assumption behind the CLRM and what does it mean?

Answer 2

Error term ε is a normally distributed random variable

Because Y is a linear function of ε, Y is also a normally distributed random variable

Question 3

What is the third assumption behind the CLRM and what does it mean?

Answer 3

The values of ε are independent

The value of ε for a paticular value of X is not related to the value of ε for any other value of X

Thus the value of Y for a paticular value of X is not related to the value of Y for an other value of X

Question 4

What is the fourth assumption behind the CLRM and what does it mean?

Answer 4

The variance of ε denoted by σ² is the same for all values of X

The variance of Y about the regression line = σ² and is the same for all values of X

Question 5

What do quaterly dummy variables do?

Answer 5

1. capture seasonality in the data
2. pick out and control for seasonal variation in the data

idea is to include a set of dummy variables per quarter which then NETS out average change in variable resulting from any seasonal fluctuations