Calculate Residual Standard Error

Residual Standard Error Equation:

\[ RSE = \sqrt{\frac{RSS}{n - k - 1}} \]

Residual Sum of Squares (RSS):

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Sample Size (n):

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Number of Predictors (k):

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Residual Standard Error (RSE):

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1. What is Residual Standard Error?

The Residual Standard Error (RSE) is a measure of the standard deviation of the residuals (prediction errors) in regression analysis. It provides an estimate of the standard deviation of the unexplained variance in the dependent variable.

2. How Does the Calculator Work?

The calculator uses the RSE equation:

\[ RSE = \sqrt{\frac{RSS}{n - k - 1}} \]

Where:

\( RSS \) — Residual sum of squares (sum of squared differences between observed and predicted values)
\( n \) — Sample size (number of observations)
\( k \) — Number of predictors in the model

Explanation: The denominator (n - k - 1) represents the degrees of freedom in the model. The RSE is essentially the square root of the mean squared error, adjusted for degrees of freedom.

3. Importance of RSE

Details: RSE provides an absolute measure of the typical size of the residuals. A lower RSE indicates a better fit of the model to the data. It's particularly useful for comparing models with different numbers of predictors.

4. Using the Calculator

Tips: Enter the residual sum of squares (RSS), sample size (n), and number of predictors (k). Ensure n > k+1 for valid calculation. All values must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between RSE and RMSE?
A: RMSE (Root Mean Square Error) uses n in the denominator, while RSE adjusts for degrees of freedom (n - k - 1). RSE is preferred when comparing models with different numbers of predictors.

Q2: What is a good RSE value?
A: There's no universal "good" value - it depends on your data scale. Compare RSE values relative to the dependent variable's mean or standard deviation.

Q3: Can RSE be negative?
A: No, RSE is always non-negative since it's derived from squared residuals.

Q4: How is RSE related to R-squared?
A: While R-squared measures proportion of variance explained, RSE measures the absolute magnitude of unexplained variance. They complement each other in model evaluation.

Q5: When would RSE not be appropriate?
A: RSE assumes normally distributed residuals. For non-normal error distributions, other measures like mean absolute error might be more appropriate.