Prediction Interval
Calculate Prediction Interval instantly with the exact formula and a worked example.
Prediction Interval
Prediction ŷ at x₀
Residual standard error s
Sample size n
Prediction point x₀
Sample mean of x
Standard deviation of x
Confidence level%
Prediction interval half-width (±)
10.8833
Lower bound
39.1167
Upper bound
60.8833
CI half-width for the mean response
2.8458
Critical t
2.1009
Degrees of freedom
18
More about: Prediction Interval
What it calculates
The “Prediction Interval” calculator computes Prediction interval half-width (±) from 7 parameters: prediction ŷ at x₀, residual standard error s, sample size n, prediction point x₀, sample mean of x, standard deviation of x, confidence level (%).
A core calculation for studying, engineering tasks, and checking solutions.
Example calculation
With parameters Prediction ŷ at x₀ = 50, Residual standard error s = 5, Sample size n = 20, Prediction point x₀ = 12, Sample mean of x = 10, Standard deviation of x = 3, Confidence level = 95 % the result is 10.88.
How to use
- Enter prediction ŷ at x₀, residual standard error s, sample size n, prediction point x₀, sample mean of x, standard deviation of x and confidence level — each field above is adjustable with a slider.
- Prediction interval half-width (±) is calculated automatically as you type.
- Check the worked example below to see the formula applied to real numbers.
- Copy the result or bookmark this calculator.
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FAQ
How is Prediction Interval calculated?
The Prediction Interval calculator computes Prediction interval half-width (±) from prediction ŷ at x₀, residual standard error s, sample size n, prediction point x₀, sample mean of x, standard deviation of x, confidence level. Enter your values above and the exact formula is applied instantly; a worked example with real numbers is shown below.
Is the Prediction Interval calculator free?
Yes. It is completely free, needs no signup, runs entirely in your browser, and sends no data to any server.
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