1. What is Standard Error in Linear Regression?

The standard error (SE) in linear regression measures the accuracy of the coefficient estimates. It indicates how much the estimated coefficient might vary from the true population value.

2. How Does the Calculator Work?

The calculator uses the standard error formula:

Where:

• \( y \) — Actual dependent values
• \( y_{pred} \) — Predicted values from regression
• \( x \) — Independent variable values
• \( \bar{x} \) — Mean of independent variable
• \( n \) — Number of observations

Explanation: The numerator represents the standard deviation of residuals, while the denominator is the square root of the sum of squared deviations of the independent variable.

3. Importance of Standard Error

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

4. Using the Calculator

Tips: Enter comma-separated values for actual y, predicted y, and x values. All arrays must be of equal length with at least 3 values.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between standard error and R-squared?
A: R-squared measures goodness of fit (0-100%), while SE measures precision of coefficient estimates.

Q2: How does sample size affect standard error?
A: SE decreases as sample size increases, as the estimate becomes more precise.

Q3: What's a good standard error value?
A: There's no universal "good" value - it depends on the scale of your data. Compare SE to coefficient values.

Q4: Can standard error be zero?
A: Only if there's perfect fit (all points on regression line) and x values are not all identical.

Q5: How is standard error used in hypothesis testing?
A: The t-statistic is calculated as coefficient divided by its standard error.