Question

Which of the following statements is true about Assumption 5?

a. Distributional assumptions are required for calculating the coefficients in a model
b. Q-Q plots are not useful for testing this assumption
c. Normally distributed errors are required for a linear regression model
d. There are only three ways to test for normally distributed errors

Answer 1

Assumption 5 states that normally distributed errors are required for a linear regression model. Various methods can be used to test this assumption such as Q-Q plots, Shapiro-Wilk test, and Anderson-Darling test.

Step-by-step explanation:

Assumption 5, in the context of linear regression models, states that normally distributed errors are required for a linear regression model. This means that the errors or residuals (the differences between the actual observed values and the predicted values) should follow a normal distribution. The normal distribution assumption allows for the calculation of confidence intervals, hypothesis tests, and p-values based on the assumptions of normality.

This assumption is important because violating it can lead to biased estimates and incorrect inference. If the errors are not normally distributed, the conclusions drawn from the regression analysis may not be valid.

To test for the assumption of normally distributed errors, various methods can be used such as Q-Q plots, Shapiro-Wilk test, and Anderson-Darling test. Q-Q plots are actually useful for testing this assumption, contrary to statement b. The other statements a, c, and d are not true about Assumption 5.