[2008] Topic 8: The Two-Variable Model: Hypothesis Testing 相关习题

aianjie

 

AIM 1: List the assumptions of the classical linear regression model.

1、Which of the following is least likely an assumption of linear regression?

A) The residuals are normally distributed

B) There is a linear relation between the dependent and independent variables.

C) The independent variable is correlated with the residuals.

D) The variance of the residuals is constant.

aianjie

 

The correct answer is C

The assumption is that the independent variable is uncorrelated with the residuals.

aianjie

 

2、Which of the following is least likely an assumption of linear regression? The:

A) expected value of the residuals is zero.

B) variance of the residuals is constant.

C) residuals are mean reverting; that is, they tend towards zero over time.

D) residuals are independently distributed.

aianjie

 

The correct answer is C

The assumptions regarding the residuals are that the residuals have a constant variance, have a mean of zero, and are independently distributed.

aianjie

 

3、Which of the following is least likely an assumption of linear regression analysis?

A) The error term is normally distributed.

B) The Y values are all less than 3 standard deviations from the regression line.

C) The X values are uncorrelated with the error terms.

D) The expected value of the residuals is zero.

aianjie

 

The correct answer is B

In a normal distribution, approximately 99%, but not necessarily all, of the observations are within 3 standard deviations of the regression line.

aianjie

 

4、Which of the following statements about linear regression analysis is most accurate?

A) The coefficient of determination is defined as the strength of the linear relationship between two variables.

B) A perfectly negative correlation can be depicted by a correlation coefficient of +1.

C) An assumption of linear regression is that the residuals are independently distributed.

D) When there is a strong relationship between two variables we can conclude that a change in one will cause a change in the other.

aianjie

 

The correct answer is C

A perfectly negative correlation can be depicted by a correlation coefficient of -1. Even when there is a strong relationship between two variables, we cannot conclude that a causal relationship exists. The coefficient of determination is defined as the percentage of total variation in the dependent variable explained by the independent variable.

aianjie

 

5、The assumptions underlying linear regression include all of the following EXCEPT the:

A) disturbance term is normally distributed with an expected value of 0.

B) independent variable is linearly related to the residuals (or disturbance term).

C) disturbance term is homoskedastic and is independently distributed.

D) dependent variable and independent variable are linearly related. 

aianjie

 

The correct answer is B

The independent variable is uncorrelated with the residuals (or disturbance term).

The other statements are true. The disturbance term is homoskedastic because it has a constant variance. It is independently distributed because the residual for one observation is not correlated with that of another observation. Note: The opposite of homoskedastic is heteroskedastic. For the examination, memorize the assumptions underlying linear regression!