STEM Calculators

Standard Deviation of Random Errors

Statistics • Simple Linear Regression

Written by STEM Calculators Team Published Updated
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Standard Deviation of Random Errors

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Accepted separators: comma, tab, semicolon, or spaces. Empty lines are ignored.
The file should contain two columns: x and y (a header row is ok).
Use “Auto-detect” unless your file is unusual.
A vertical slice where the error spread is visualized using \(s_e\).
Choose a second x-value to compare the spread.
Vertical segments visualize \(e_i = y_i - \hat{y}_i\).
Used for the residual distribution graph.
\(s_e\): —
Regression assumptions checklist
\(E(\varepsilon)=0\) for each \(x\) Errors independent Errors normal (for each \(x\)) Constant variance
Scatter plot, regression line, and error spread
Click a point to inspect its residual.
Residual distribution (histogram + normal overlay)
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Calculation steps

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Frequently Asked Questions

What is the standard deviation of random errors in simple linear regression?

It measures the typical vertical distance between observed y values and the fitted regression line. It is often called the residual standard error or standard deviation of errors.

How is the standard deviation of errors computed from regression data?

It is computed from the residuals using the sum of squared errors (SSE) and the degrees of freedom n - 2. A common formula is se = sqrt(SSE / (n - 2)).

Why does the calculator show residual segments and a residual histogram?

Residual segments help you see each error ei = yi - yhat_i on the scatter plot, while the histogram shows the overall distribution of residuals. Together they help assess spread and potential normality of errors.

What do the xA and xB error-spread slices represent?

They mark vertical slices at two chosen x-values to visualize the typical error spread in y-units using se. Comparing slices helps you think about whether variability looks roughly constant across x.

When should you be cautious interpreting the standard deviation of errors?

Be cautious when regression assumptions are violated, such as non-constant variance, strongly non-normal residuals, or dependence among errors. Outliers and influential points can also inflate the error standard deviation.

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