Question

Which of the following are the assumptions that underlie the classical linear regression model? Please select all that apply!

Multiple select question.
A. The regression model given by y = β0 + β1x1 + β2x2 +... + βkxk + ɛ is linear in the parameters β0, β1,..., βk.
B. There is an exact linear relationship among the predictor variables; or, in statistical terminology, there is no perfect multicollinearity.
C. Conditional on x1, x2,.., xk, the error term ɛ is uncorrelated across observations; or, in statistical terminology, there is no serial correlation.
D. The error term ɛ is correlated with any of the predictor variables x1, x2,..., xk

Answer 1

The correct assumptions that underlie the classical linear regression model are that the model is linear in parameters, there's no perfect multicollinearity among predictor variables, and the error terms are uncorrelated across observations.

Step-by-step explanation:

The assumptions that underlie the classical linear regression model include the following:

• A. The regression model y = β0 + β1x1 + β2x2 +... + βkxk + ε is linear in the parameters β0, β1,..., βk.
• B. There should be no exact linear relationship among the predictor variables; or, in other words, there should be no perfect multicollinearity.
• C. Conditional on x1, x2,.., xk, the error term ε is uncorrelated across observations; this means there is no serial correlation.
• The error term ε should not be correlated with any of the predictor variables x1, x2,..., βk. This statement is incorrect as an assumption of the classical linear regression model is that the error term should be uncorrelated with the predictor variables.

The correct assumptions for a classical linear regression model, based on your selections, are A, B, and C.