Download your Word document
Least-Squares Linear Regression Calculator result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Least-Squares Linear Regression Calculator — result sheet
Fit a straight line to paired observations and report the slope, intercept, prediction, correlation, and explained variation.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For paired data, b = Σ[(xᵢ−x̄)(yᵢ−ȳ)]/Σ[(xᵢ−x̄)²], a = ȳ−b x̄, ŷ = a+b x, and R² = 1−SSE/SST.
A least-squares line summarizes paired numeric observations with the straight line that minimizes the sum of squared vertical residuals. This page keeps the fitted coefficients separate from the prediction: the slope describes the modeled change in Y per unit X, the intercept is the line's value at X=0, and the target prediction is only an evaluation of that fitted line. Correlation and R² are reported as diagnostics, not as proof that one variable causes the other.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- X values — Enter 2 to 200 finite numbers separated by commas or spaces.
- Y values — Enter the same number of values as X, in matching order.
- Prediction x — The fitted line is evaluated at this x value.; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| X values | 1, 2, 3, 4, 5 |
| Y values | 2, 4, 5, 8, 10 |
| Prediction x | 6 |
The fitted line is ŷ = −0.2 + 2x; at x = 6 it predicts 11.8, with R² ≈ 0.9804.
Assumptions and limits
- X and Y are paired observations and must contain the same number of finite values.
- At least two pairs are required, and X must vary so the slope denominator is nonzero.
- The fit is ordinary least squares with one intercept and one predictor.
- R² describes the fraction of observed Y variation explained by the fitted line for this sample; it is not a causal measure.
- A prediction outside the observed X range is extrapolation and should be treated with additional caution.
- The calculator does not test residual normality, independence, equal variance, sampling design, or outliers.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.