The standard error of regression uses degrees of freedom equal to n-2.

The standard error of regression uses degrees of freedom equal to n-2.

• A. It uses n-1 degrees of freedom
• B. It uses n degrees of freedom
• C. It uses n-2 degrees of freedom
• D. It is not related to degrees of freedom

Answer: (C)

In simple linear regression, you estimate two parameters from the data—the intercept and the slope. Each estimated parameter uses up a degree of freedom, so the residual degrees of freedom become n minus 2. The standard error of regression, which is the typical size of the residuals, is computed as the square root of the mean squared error, SSE divided by its degrees of freedom. Since that divisor is n-2, the standard error of regression uses n-2 degrees of freedom. This contrasts with n-1, which would apply if only one parameter (like a single mean) were estimated, and with n, which would imply no parameters were fitted. In broader terms, for a model with p estimated parameters, the residual degrees of freedom are n - p.

In simple linear regression, you estimate two parameters from the data—the intercept and the slope. Each estimated parameter uses up a degree of freedom, so the residual degrees of freedom become n minus 2. The standard error of regression, which is the typical size of the residuals, is computed as the square root of the mean squared error, SSE divided by its degrees of freedom. Since that divisor is n-2, the standard error of regression uses n-2 degrees of freedom. This contrasts with n-1, which would apply if only one parameter (like a single mean) were estimated, and with n, which would imply no parameters were fitted. In broader terms, for a model with p estimated parameters, the residual degrees of freedom are n - p.