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Standard Error of a Regression Coefficient (Simple Linear Regression) Calculator

Calculates the standard error of the regression slope coefficient (b) in simple linear regression.

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Standard Error of the Estimate

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Overview

The standard error of a regression coefficient () quantifies the precision of the estimated slope (b) in a simple linear regression model. A smaller indicates a more precise estimate of the true population slope. It is crucial for constructing confidence intervals for the slope and for performing hypothesis tests to determine if the predictor variable (X) has a statistically significant linear relationship with the outcome variable (Y).

Symbols

Variables

= Standard Error of the Estimate, ( - )^2 = Sum of Squared Deviations of X, = Standard Error of Regression Coefficient

Standard Error of the Estimate
Variable
Sum of Squared Deviations of X
Variable
Standard Error of Regression Coefficient
Variable

Apply it well

When To Use

When to use: Apply this formula when you need to assess the reliability or precision of the estimated regression slope (b) in a simple linear regression. It is essential for calculating confidence intervals for the slope and for conducting t-tests to determine the statistical significance of the predictor variable.

Why it matters: Understanding SE_b is fundamental in psychological research for evaluating the robustness of findings from regression analyses. It allows researchers to determine if an observed relationship between variables is likely due to chance or represents a true effect, thereby informing theoretical development and practical interventions based on predictive models.

Avoid these traps

Common Mistakes

  • Confusing with the standard deviation of the slope itself.
  • Incorrectly calculating the sum of squared deviations for X.
  • Applying this formula to multiple regression models.

One free problem

Practice Problem

In a simple linear regression, the standard error of the estimate () is 5.2, and the sum of squared deviations of the predictor variable (X) is 120. Calculate the standard error of the regression coefficient ().

Standard Error of the Estimate5.2
Sum of Squared Deviations of X120

Solve for:

Hint: Remember to take the square root of the sum of squared deviations.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Discovering Statistics Using IBM SPSS Statistics by Andy Field
  2. Statistics for Psychology by Arthur Aron, Elaine N. Aron, and Elliot Coups
  3. Wikipedia: Simple linear regression
  4. Andy Field, Discovering Statistics Using IBM SPSS Statistics
  5. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning with Applications in R.
  6. Howell, D. C. (2012). Statistical Methods for Psychology.
  7. Cohen et al. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences
  8. Field Discovering Statistics Using IBM SPSS Statistics