Q11. Which of the following is least likely an assumption of a simple regression?

A)   The variance of the error term is one.

B)   The expected value of the error term is zero.

C)   The error term is normally distributed.

Q12. 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)   An assumption of linear regression is that the residuals are independently distributed.

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

Q13. Which of the following is least likely an assumption of linear regression analysis?

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

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

C)   The error term is normally distributed.

答案和详解如下：

Q11. Which of the following is least likely an assumption of a simple regression?

A)   The variance of the error term is one.

B)   The expected value of the error term is zero.

C)   The error term is normally distributed.

Correct answer is A)

There is no requirement that the variance of the error term should be equal to one.

Q12. 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)   An assumption of linear regression is that the residuals are independently distributed.

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

Correct answer is B)

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.

Q13. Which of the following is least likely an assumption of linear regression analysis?

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

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

C)   The error term is normally distributed.

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.