1. What is Standard Error in Regression?

The standard error (SE) in linear regression measures the accuracy of predictions by quantifying the typical distance that the observed values fall from the regression line. It's essentially the standard deviation of the sampling distribution of a statistic.

2. How Does the Calculator Work?

The calculator uses the standard error formula:

Where:

• \( SSE \) — Sum of squared errors (residual sum of squares)
• \( n \) — Number of observations/samples
• \( k \) — Number of predictor variables
• \( X_{var} \) — Variance of the independent variable X

Explanation: The denominator (n - k - 1) represents the degrees of freedom, while X_var accounts for the spread in the predictor variable.

3. Importance of Standard Error

Details: Standard error is crucial for constructing confidence intervals and hypothesis tests about the regression coefficients. A smaller SE indicates more precise estimates.

4. Using the Calculator

Tips: Enter all required values (SSE, n, k, X_var). Ensure n > k + 1 and all values are positive. The calculator will compute the standard error of the regression model.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between standard error and R-squared?
A: R-squared measures the proportion of variance explained by the model, while SE measures the typical size of the residuals.

Q2: How does sample size affect standard error?
A: As sample size (n) increases, standard error typically decreases (all else being equal).

Q3: What's a good standard error value?
A: There's no universal "good" value - it depends on the scale of your dependent variable and research context.

Q4: Can standard error be zero?
A: In practice, almost never. A zero SE would imply perfect prediction with no variability.

Q5: How is standard error related to confidence intervals?
A: Confidence intervals for coefficients are typically calculated as estimate ± (critical value × SE).