What does the standard error measure in your regression output?

1 SE Basics

The standard error of a coefficient in regression quantifies how much the estimated values vary around the true population parameter. It is derived from the standard deviation of the sample and the sample size. Essentially, it tells you how concentrated or spread out the estimates are around the actual parameter. A smaller standard error suggests that the sample estimate is likely to be closer to the true population value, providing a more precise estimate.

2 SE Calculation

To calculate the standard error of a regression coefficient, you typically use the formula SE = s / sqrt(n) , where s is the standard deviation of the sample and n is the sample size. This calculation gives you an idea of the uncertainty around the coefficient estimate. The standard error is automatically computed in most statistical software when performing regression analysis, so you don't have to calculate it manually.

3 SE Interpretation

Interpreting the standard error in your regression output involves comparing it to the coefficient itself. A rule of thumb is that if the coefficient is at least twice as large as the SE, the variable is likely to be a significant predictor in your model. However, this should be confirmed with a formal hypothesis test, such as the t-test, which uses the SE to determine if the coefficient is statistically significantly different from zero.

4 SE and Confidence

The standard error is also used to construct confidence intervals for your regression coefficients. A 95% confidence interval, for example, is typically calculated as the coefficient estimate plus and minus two times the standard error. This interval provides a range within which you can be 95% confident that the true population parameter lies, assuming a normal distribution.

5 SE and Sample Size

The relationship between standard error and sample size is inversely proportional; as your sample size increases, the standard error decreases. This occurs because larger samples tend to provide more accurate estimates of the population parameter. Therefore, if you have a large sample size, your regression coefficients will typically have smaller standard errors, leading to more precise estimates.

6 SE in Practice

In practical terms, when you analyze regression results, pay close attention to the standard error to assess the reliability of your coefficient estimates. Alongside p-values and confidence intervals, the SE provides a comprehensive picture of the strength and precision of your model's predictors. It informs decisions on model adequacy and whether additional data or model refinement is necessary for more accurate predictions.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?