Regression Equation Calculator - Linear Regression Calculator & Statistics Calculator
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: October 19, 2025
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Enter x-coordinates separated by commas
Enter y-coordinates separated by commas
Strong positive correlation (r = 1.0000)
How to Use:
- • Select regression type: Linear or Quadratic
- • Enter x-values separated by commas (e.g., 1,2,3,4,5)
- • Enter y-values separated by commas (e.g., 2,4,6,8,10)
- • The calculator will compute the regression equation using least squares method
- • R² shows how well the model fits the data (closer to 1 is better)
Regression Equation Calculator Types & Statistical Analysis
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
Quick Example Result
For data points (1,2), (2,4), (3,6), (4,8), (5,10):
Equation
y = 2x + 0
Correlation
r = 1.000
R²
1.000
How Our Regression Equation Calculator Works
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.
The Least Squares Method
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
Statistical Foundation
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.
- Linear regression assumes a linear relationship between variables
- The least squares method minimizes sum of squared residuals
- Correlation coefficient ranges from -1 to +1
- R-squared represents proportion of variance explained
- Higher R² values indicate better model fit
- Regression equations enable prediction and forecasting
Sources & References
- Introduction to Statistical Learning - James, Witten, Hastie, TibshiraniComprehensive coverage of regression analysis and statistical learning
- Statistics for Business and Economics - Anderson, Sweeney, WilliamsPractical applications of regression analysis in business contexts
- Khan Academy - Linear Regression and CorrelationEducational resources for understanding regression concepts
Need help with other statistical calculations? Check out our mean median mode calculator and standard deviation calculator.
Get Custom Calculator for Your PlatformRegression Equation Calculator Examples
Given Data:
- X values: 1, 2, 3, 4, 5
- Y values: 2, 4, 6, 8, 10
- Sample size: n = 5
- Regression type: Linear
Calculation Steps:
- Calculate sums: Σx=15, Σy=30, Σxy=110, Σx²=55
- Apply slope formula: m = (5×110-15×30)/(5×55-15²)
- Calculate slope: m = (550-450)/(275-225) = 100/50 = 2
- Calculate intercept: b = (30-2×15)/5 = 0
Result: y = 2x + 0 (or simply y = 2x)
Perfect linear relationship with correlation r = 1.000 and R² = 1.000.
Scattered Data Example
Points: (1,2.1), (2,3.9), (3,6.2), (4,7.8), (5,10.1)
y = 2.02x + 0.06, r = 0.999
Negative Correlation Example
Points: (1,10), (2,8), (3,6), (4,4), (5,2)
y = -2x + 12, r = -1.000
Frequently Asked Questions
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