Which of the following is NOT an assumption for linear regression?

Which of the following is NOT an assumption for linear regression?

• A. Independence of errors
• B. Normal distribution of errors
• C. Constant variance of variables
• D. No multicollinearity

Answer: (C)

In the context of linear regression, the assumption referred to in the correct answer regarding "constant variance of variables" is somewhat misleading. In linear regression, it is actually the errors (or residuals) that are assumed to have constant variance, a condition known as homoscedasticity. This means that the variability of the errors should be consistent across all levels of the independent variable(s). The assumption of constant variance applies to the errors rather than the variables themselves. If this assumption is violated (known as heteroscedasticity), it can lead to inefficiencies in the estimates and affect the validity of hypothesis tests. The other options are indeed fundamental assumptions of linear regression. For instance, the independence of errors ensures that the errors from one observation are not correlated with those from another, which is crucial for valid statistical inference. Similarly, the normal distribution of errors is important for conducting hypothesis tests and creating confidence intervals. No multicollinearity refers to the absence of highly correlated independent variables, which is necessary to isolate the effect of each variable. Hence, identifying constant variance of variables as a non-assumption aligns it with the key principles of linear regression.

In the context of linear regression, the assumption referred to in the correct answer regarding "constant variance of variables" is somewhat misleading. In linear regression, it is actually the errors (or residuals) that are assumed to have constant variance, a condition known as homoscedasticity. This means that the variability of the errors should be consistent across all levels of the independent variable(s).

The assumption of constant variance applies to the errors rather than the variables themselves. If this assumption is violated (known as heteroscedasticity), it can lead to inefficiencies in the estimates and affect the validity of hypothesis tests.

The other options are indeed fundamental assumptions of linear regression. For instance, the independence of errors ensures that the errors from one observation are not correlated with those from another, which is crucial for valid statistical inference. Similarly, the normal distribution of errors is important for conducting hypothesis tests and creating confidence intervals. No multicollinearity refers to the absence of highly correlated independent variables, which is necessary to isolate the effect of each variable. Hence, identifying constant variance of variables as a non-assumption aligns it with the key principles of linear regression.