Linear Regression Calculator: Line of Best Fit & r²

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Formula at a glance

Linear Regression Calculator: Slope — b = Σ(x − x̄)(y − ȳ) / Σ(x − x̄)². Example: Six points → Regression line: y = 0.771429x + 1.8 — How the Linear Regression Calculator works: Slope — b = Σ(x − x̄)(y − ȳ) / Σ(x − x̄)²

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📘 About the Linear Regression Calculator

Simple linear regression finds the straight line that best fits paired data, by making the sum of squared vertical distances (residuals) as small as possible. The slope tells you how much Y changes for each unit of X; r² tells you how much of the variation the line explains. It is used for trends, forecasts and calibration curves.

Paste X and Y in matching order. The calculator gives the regression equation, slope, intercept, r and r², the standard error of the estimate, a t-test of the slope, predicted values and residuals, and draws the data with the fitted line.

🧮 Formula

Slope

b = Σ(x − x̄)(y − ȳ) / Σ(x − x̄)²

Intercept

a = ȳ − b·x̄

Prediction

ŷ = a + b·x

✏️ Worked examples

Six points

You enter
X values	1, 2, 3, 4, 5, 6
Y values (same order)	2, 4, 5, 4, 5, 7
Predict y at x = (optional)	7

You get
Regression line	y = 0.771429x + 1.8
Slope b	0.7714285714
Intercept a	1.8
r · r²	0.87831 · 0.771429
Standard error of the estimate	0.87831
Is the slope significant?	t = 3.6742, p = 0.0213116
Predicted y at x = 7	7.2 (outside the data — extrapolation)

y = 0.771429x + 1.8.

Advertising vs sales

You enter
X values	10, 20, 30, 40, 50
Y values (same order)	25, 41, 58, 79, 95
Predict y at x = (optional)	60

You get
Regression line	y = 1.78x + 6.2
Slope b	1.78
Intercept a	6.2
r · r²	0.998929 · 0.997858
Standard error of the estimate	1.50555
Is the slope significant?	t = 37.387, p = 0.00004209
Predicted y at x = 60	113 (outside the data — extrapolation)

y = 1.78x + 6.2.

🧭 How to use this calculator

What you enter

X valuesSeparate numbers with commas, spaces or new lines.
Y values (same order)
Predict y at x = (optional)

What you get

Regression line
Slope b
Intercept a
r · r²
Standard error of the estimate
Is the slope significant?

❓ Frequently asked questions

What is the line of best fit?

The least-squares line: of all straight lines, it has the smallest total of squared vertical distances to the points.

What does r² mean?

The proportion of the variation in Y explained by the line. r² = 0.8 means 80% is explained by X and 20% is scatter.

Can I predict outside my data?

You can, but extrapolation is risky — the relationship may not hold beyond the range you measured.

📏 Linear Regression Calculator (Line of Best Fit)