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Free regression equation calculator & linear regression calculator. Calculate regression equations, correlation coefficients, R-squared values & line of best fit. Our calculator uses least squares method to provide accurate regression analysis for statistics, data science, and research applications.
Last updated: February 2, 2026
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Enter x-coordinates separated by commas
Enter y-coordinates separated by commas
Strong positive correlation (r = 1.0000)
Linear equation
y = mx + b
Find the best-fitting straight line through data points
Quadratic equation
y = ax² + bx + c
Model curved relationships with parabolic functions
Correlation range
-1 ≤ r ≤ +1
Measure the strength and direction of linear relationships
Goodness of fit
0 ≤ R² ≤ 1
Measure how well the model explains data variance
Minimization method
Σ(y - ŷ)²
Minimize sum of squared residuals for best fit
Statistical analysis
Data Science
Essential tool for statistical analysis and research
For data points (1,2), (2,4), (3,6), (4,8), (5,10):
Equation
y = 2x + 0
Correlation
r = 1.000
R²
1.000
Our regression equation calculator uses the least squares method to find the best-fitting line or curve through your data points. The calculation applies statistical principles and mathematical optimization to minimize the sum of squared differences between observed and predicted values.
Slope: m = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²)Intercept: b = (Σy - mΣx) / nCorrelation: r = Σ(x-μₓ)(y-μᵧ) / √[Σ(x-μₓ)²Σ(y-μᵧ)²]The least squares method minimizes the sum of squared residuals (differences between actual and predicted values). This provides the optimal linear relationship that best represents your data.
Shows the least squares line minimizing the sum of squared residuals
Regression analysis is based on statistical theory and mathematical optimization. The least squares method provides unbiased estimates of regression parameters when certain assumptions are met. The correlation coefficient measures linear relationship strength, while R-squared quantifies how well the model explains data variance.
Need help with other statistical calculations? Check out our mean median mode calculator and standard deviation calculator.
Get Custom Calculator for Your PlatformResult: y = 2x + 0 (or simply y = 2x)
Perfect linear relationship with correlation r = 1.000 and R² = 1.000.
Points: (1,2.1), (2,3.9), (3,6.2), (4,7.8), (5,10.1)
y = 2.02x + 0.06, r = 0.999
Points: (1,10), (2,8), (3,6), (4,4), (5,2)
y = -2x + 12, r = -1.000
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