Question

Consider the following regression model:

yᵢ = β₁ + β₂xᵢ₂ + ⋯ + βₖxᵢₖ + eᵢ

where E[eᵢ | xᵢ] = 0 and Var[eᵢ | xᵢ] depends on the value of xᵢ, i.e., Var[eᵢ | xᵢ] ≠ σ². Choose the correct statement.

a. To get around the problem, we often assume that eᵢ is normally distributed.

b. To fix the problem, we need to have an instrumental variable.

c. This problem implies that errors are correlated with one of (xᵢ₂, ⋯, xᵢₖ).

d. If we assume Var[eᵢ | xᵢ] = σ², the confidence interval is not valid.

e. None of the above is correct.

Answer 1

The correct statement is c. This problem implies that errors are correlated with one of (xᵢ₂, ⋯, xᵢₖ).

Step-by-step explanation:

The correct statement is c. This problem implies that errors are correlated with one of (xᵢ₂, ⋯, xᵢₖ). In the given regression model, the assumption is made that the error term, eᵢ, has an expected value of zero given the values of xᵢ. However, it is stated that the variance of eᵢ is dependent on the value of xᵢ, meaning that Var[eᵢ | xᵢ] ≠ σ². This implies that the errors are correlated with one or more of the independent variables xᵢ. Therefore, option c is the correct statement.