Standard Error of Regression Calculator

Calculator

Choose a mode, provide inputs, then press Calculate.

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Calculation Mode

Paired data computes slope/intercept plus SER.

Paired Data Input

CSV columns: x,y (header optional).

Upload CSV (x,y)

Non-numeric rows are skipped.

X values

Separate by space, comma, or newline.

Y values

Must match X count.

SSE (Sum of Squared Errors)

SSE = Σ(y − ŷ)²

Sample size (n)

Total observations used in the model.

Predictors (k)

Predictors exclude the intercept.

Example Data Table

Try these paired values to see the full table output.

Row	X	Y
1	1	2
2	2	3
3	3	5
4	4	4
5	5	6

Manual entry example: X = 1 2 3 4 5, Y = 2 3 5 4 6

Formula Used

Standard Error of Regression (SER)

SER = √( SSE / df )

Where SSE is the sum of squared residuals, and df is degrees of freedom.

Degrees of Freedom

df = n − (k + 1)

n is observations, k is predictors. For simple linear regression, k=1 so df = n−2.

Simple Linear Regression (paired data mode)

b1 = Sxy / Sxx, b0 = ŷ − b1 x̄, ŷ = b0 + b1x

Residual: e = y − ŷ, and SSE = Σ e².

How to Use This Calculator

Choose From paired data to compute everything from X and Y.
Select manual lists or upload a CSV with columns x and y.
Press Calculate to see results above the form.
Use the download buttons to export CSV or PDF outputs.
Choose From SSE when you already know SSE, n, and k.

FAQs

1) What does the standard error of regression mean?

It summarizes typical prediction error around the fitted line, measured in Y units. Smaller values suggest tighter clustering of points around the model's predictions.

2) What is SSE and how is it computed?

SSE is the sum of squared residuals: Σ(y − ŷ)². Residuals are observed values minus predicted values from your regression equation.

3) Why do degrees of freedom matter?

Degrees of freedom adjust for the number of estimated parameters. Using df = n − (k+1) prevents underestimating uncertainty, especially in small samples.

4) Does this handle multiple regression from raw data?

The paired-data mode fits a simple linear model with one predictor. For multiple regression, use the SSE mode by entering your model's SSE, n, and k.

5) What file format should the CSV use?

Use a two-column CSV with x and y values. A header row is optional. Non-numeric rows are ignored to keep calculations clean.

6) What if my X values are all the same?

A slope cannot be estimated when X has no variation. In that case, the calculator will show an error and you should provide varied X values.

7) Is SER the same as RMSE?

They match when RMSE is computed using df rather than n. Some tools divide by n, so check the definition used in your reporting context.

Example Data Table

Formula Used

How to Use This Calculator

FAQs

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