Q1. One of the underlying assumptions of a multiple regression is that the variance of the residuals is constant for various levels of the independent variables. This quality is referred to as:

A)   a linear relationship.

B)   a normal distribution.

C)   homoskedasticity.

Q2. Which of the following statements least accurately describes one of the fundamental multiple regression assumptions?

A)   The error term is normally distributed.

B)   The variance of the error terms is not constant (i.e., the errors are heteroskedastic).

Q3. Assume that in a particular multiple regression model, it is determined that the error terms are uncorrelated with each other. Which of the following statements is most accurate?

A)   Unconditional heteroskedasticity present in this model should not pose a problem, but can be corrected by using robust standard errors.

B)   This model is in accordance with the basic assumptions of multiple regression analysis because the errors are not serially correlated.

C)   Serial correlation may be present in this multiple regression model, and can be confirmed only through a Durbin-Watson test.

答案和详解如下：

Q1. One of the underlying assumptions of a multiple regression is that the variance of the residuals is constant for various levels of the independent variables. This quality is referred to as:

A)   a linear relationship.

B)   a normal distribution.

C)   homoskedasticity.

Correct answer is C)         

Homoskedasticity refers to the basic assumption of a multiple regression model that the variance of the error terms is constant.

Q2. Which of the following statements least accurately describes one of the fundamental multiple regression assumptions?

A)   The error term is normally distributed.

B)   The variance of the error terms is not constant (i.e., the errors are heteroskedastic).

C)   The independent variables are not random.

Correct answer is B)

The variance of the error term IS assumed to be constant, resulting in errors that are homoskedastic.

Q3. Assume that in a particular multiple regression model, it is determined that the error terms are uncorrelated with each other. Which of the following statements is most accurate?

A)   Unconditional heteroskedasticity present in this model should not pose a problem, but can be corrected by using robust standard errors.

B)   This model is in accordance with the basic assumptions of multiple regression analysis because the errors are not serially correlated.

C)   Serial correlation may be present in this multiple regression model, and can be confirmed only through a Durbin-Watson test.

Correct answer is B)

One of the basic assumptions of multiple regression analysis is that the error terms are not correlated with each other. In other words, the error terms are not serially correlated. Multicollinearity and heteroskedasticity are problems in multiple regression that are not related to the correlation of the error terms.

thanks