2. 􀂃 State the 5 assumptions of the simple regression model.?

Question

𐂃 What does the assumption E(u|x) = 0 imply about the correlation between x and u? 𐂃 Which of these assumptions are necessary to show that the least squares estimators are unbiased? 𐂃 Which of these assumptions are necessary to derive the variance of 1ˆβ ?

Answer 1

Classical assumptions for regression analysis include:

1) The sample must be representative of the population for the inference prediction.

2) The error is assumed to be a random variable with a mean of zero conditional on the explanatory variables.

3) The independent variables are error-free. If this is not so, modeling may be done using errors-in-variables model techniques.

4) The predictors must be linearly independent, i.e. it must not be possible to express any predictor as a linear combination of the others. (Multicollinearity)

5) The errors are uncorrelated, that is, the variance-covariance matrix of the errors is diagonal and each non-zero element is the variance of the error.

6) The variance of the error is constant across observations (homoscedasticity). If not, weighted least squares or other methods might be used.

These are sufficient (but not all necessary) conditions for the least-squares estimator to possess desirable properties, in particular, these assumptions imply that the parameter estimates will be unbiased, consistent, and efficient in the class of linear unbiased estimators. Many of these assumptions may be relaxed in more advanced treatments.

Additional assumptions for linear regression are:

a) The sample is selected at random from the population of interest

b) The dependent variable is continuous on the real line

c) The error terms follow identical and independent normal distributions

♦ Which of these assumptions are necessary to show that the least squares estimators are unbiased? - It would be this one:

4) The predictors must be linearly independent, i.e. it must not be possible to express any predictor as a linear combination of the others. (Multicollinearity).

The same assumption could be the answer to first question.

Regarding your last question about variance - i think answer is: it' assumption about type of error distribution (c).