The calculation, without hidden assumptions
Simple linear regression fits the line ŷ = a + bx that minimizes the sum of squared vertical residuals. MAXScanner keeps the paired observations visible, shows Sxx and Sxy before calculating the slope, reports Pearson r and R² as companion diagnostics and provides a prediction at an editable X value without pretending that extrapolation is automatically reliable.
How to use this calculator
Paste matching X and Y lists in the same row order.
Enter an optional X value for a point prediction.
Review slope/intercept, r, R² and residual table; inspect whether a straight-line model is plausible before using the prediction.
Where people use it
- •Line-of-best-fit checks for paired measurements
- •Estimating a simple linear trend from spreadsheet columns
- •Teaching slope, intercept, residuals and R² with the arithmetic visible
Example: study hours → score
If the fitted line is ŷ = 50 + 4x, each additional hour corresponds to a four-point increase in the fitted response. R² describes how much sample variation is explained by this straight-line fit, not whether the relationship is causal.
What the result does not assume
- •A strong R² does not establish causation.
- •Least-squares results can be highly sensitive to outliers and influential points.
- •Predictions far outside the observed X range are extrapolations and can be unreliable even when the in-range fit looks strong.
Frequently asked questions
What does the regression slope mean?+
It is the fitted change in Y associated with a one-unit increase in X under the simple straight-line model.
What is R²?+
R² is the fraction of observed Y variation explained by the fitted line in simple regression with an intercept. It ranges from 0 to 1.
Is regression the same as correlation?+
No. Correlation is a symmetric standardized association measure. Regression chooses an outcome Y and predictor X and fits an equation for Y from X.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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Keep the result connected to the real job
MAXScanner keeps the formula and assumptions beside the result so you can verify the number before using it in a drawing, estimate, specification, worksheet or document. Where a supplier, manufacturer, drawing or applicable standard owns a requirement, that source remains authoritative.