Regression Calculator
Perform simple linear regression to find slope, y-intercept, and equation (y = mx + b). Predict Y values, analyze residuals, and get R², F-statistic, and sum of squares.
Slope (m)
—
Y-Intercept (b) —
Equation —
R² (Fit Quality) —
Extended More scenarios, charts & detailed breakdown ▾
Slope (m)
—
Y-Intercept (b) —
Equation (y = mx + b) —
R² —
Professional Full parameters & maximum detail ▾
Regression Coefficients
Slope —
Intercept —
R² —
Standard Error of Estimate —
Significance Tests
F-Statistic —
t-Statistic (slope) —
Sum of Squares
SST (Total) —
SSR (Regression) —
SSE (Error) —
Autocorrelation
Durbin-Watson (approx) —
How to Use This Calculator
- Enter X values as comma-separated numbers (e.g., 1,2,3,4,5).
- Enter matching Y values in the same order.
- Click Calculate to get slope, intercept, equation, and R².
- Use the Predict tab to forecast Y for a new X value with a confidence interval.
- The Professional tab adds F-statistic, t-statistic, SST/SSR/SSE decomposition, and Durbin-Watson.
Formula
Slope (m) = Σ[(x−x̄)(y−ȳ)] / Σ(x−x̄)² | Intercept (b) = ȳ − m·x̄
Example
X: 1,2,3,4,5 | Y: 2,4,5,4,5 → y = 0.6x + 2.2, R² ≈ 0.81.
Frequently Asked Questions
- Linear regression finds the line y = mx + b that best fits your data by minimizing the sum of squared residuals (errors). The slope m tells how much Y changes per unit of X, and b is the Y value when X=0.
- R² (coefficient of determination) measures how well the regression line fits the data. R²=1 means a perfect fit; R²=0 means the line explains none of the variation. R²=0.8 means 80% of Y variation is explained by X.
- Correlation measures the strength of a relationship. Regression finds the actual equation of the line so you can make predictions. You can have strong correlation without a meaningful regression line.
- A residual is the difference between an actual Y value and the predicted Y from the regression line: residual = actual − predicted. Small residuals mean a better fit.
- The Durbin-Watson statistic tests for autocorrelation in residuals. Values near 2 suggest no autocorrelation; values near 0 indicate positive autocorrelation; values near 4 indicate negative autocorrelation.