Simple Linear Regression & Prediction Calculator
Fit y = a + bx to paired observations, inspect correlation and optionally calculate a point prediction with extrapolation clearly flagged.
Separate interpolation from extrapolation when using the fitted line
The optional prediction field substitutes an X value into the fitted least-squares equation. Lynara also reports the observed X range so it can mark a requested point outside that range as extrapolation rather than presenting every prediction as equally supported by the data.
A point prediction from the line is not a prediction interval and does not represent individual uncertainty. The slope, r and r² summarize a linear pattern in the entered pairs; they do not by themselves justify causal interpretation.
Privacy: calculator inputs are processed in your browser; Lynara does not need to upload these values to calculate the result.
Formula
slope b = cross-deviation sum ÷ SSx; intercept a = ȳ − b x̄; predicted ŷ = a + bx
Example
For X = 1, 2, 3 and Y = 2, 4, 6, the line is y = 2x; entering X = 4 predicts Y = 8 and is flagged as extrapolation.
Useful for
- Intro regression homework
- Line-of-best-fit calculations
- Prediction from a fitted line
- Paired-data summaries
Questions
How does the prediction work?
The entered X value is substituted into the fitted line. Lynara flags it when X lies outside the observed X range.
Can regression be calculated if every X value is identical?
No. With zero X variance, a unique slope cannot be estimated.