1. What is Standard Error in Linear Regression?

The standard error (SE) in linear regression measures the accuracy with which the regression coefficients are estimated. It represents the average distance that the observed values fall from the regression line.

2. How Does the Calculator Work?

The calculator uses the standard error formula:

Where:

• \( res \) — Residuals (difference between observed and predicted values)
• \( df \) — Degrees of freedom (n - p - 1, where n is sample size and p is number of predictors)
• \( dev \) — Deviations of predictor variable from its mean

Explanation: The formula accounts for both the model's error (residuals) and the variability in the predictor variable.

3. Importance of Standard Error

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

4. Using the Calculator

Tips: Enter residuals and deviations as comma-separated values. Ensure degrees of freedom is appropriate for your model (typically n - 2 for simple linear regression).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between standard error and R-squared?
A: R-squared measures proportion of variance explained, while SE measures precision of coefficient estimates.

Q2: How does sample size affect standard error?
A: SE decreases as sample size increases, as we have more information to estimate the coefficients.

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

Q4: Can standard error be zero?
A: Only in perfect fit situations (all points exactly on regression line), which is extremely rare with real data.

Q5: How is standard error related to p-values?
A: The t-statistic (coefficient/SE) is used to calculate p-values for hypothesis tests about coefficients.