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Simple Regression Prediction Interval

Calculate a prediction interval for one new response using regression summary quantities.

Statistics workspace● Runs in your browser
01 Your input
02 Your result
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FormulaSe Prediction = s*sqrt(1+1/n+(x-mean)**2/sxx); Lower = prediction-critical*s*sqrt(1+1/n+(x-mean)**2/sxx); Upper = prediction+critical*s*sqrt(1+1/n+(x-mean)**2/sxx)
Sources and model references

Made for real tasks

  • Calculate a prediction interval for one new response using regression summary quantities.
Explore step-by-step workflows →

Worked example

Inputs

Predicted response
20 number
Residual standard error
2 number
Training observations
30 count
New predictor value
6 number
Training predictor mean
5 number
Centered predictor sum of squares
100 number
Selected t critical value
2.048 number

Expected results

Se Prediction
2.042873793 number
Lower
15.81619447 number
Upper
24.18380553 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter predicted response, residual standard error, training observations, new predictor value, training predictor mean, centered predictor sum of squares, selected t critical value.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "prediction": 20,
  "s": 2,
  "n": 30,
  "x": 6,
  "mean": 5,
  "sxx": 100,
  "critical": 2.048
}

Accuracy and scope

Simple linear regression with intercept. User supplies the t quantile for n−2 degrees of freedom; not a mean-response confidence band.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.