Linear Regression Calculator
Fit a least-squares line y = mx + b to paired data and report slope, intercept and R².
Inputs
Slope (m)
1.990000
Intercept (b)
0.050000
R²
0.997305
Correlation (r)
0.998652
Step by step
Values used
X values (comma separated) = 1, 2, 3, 4, 5; Y values (comma separated) = 2.1, 3.9, 6.2, 7.8, 10.1
Slope
m = Σ(xᵢ−x̄)(yᵢ−ȳ) / Σ(xᵢ−x̄)²
Intercept
b = ȳ − m×x̄
Slope (m)
= 1.990000
Intercept (b)
= 0.050000
R²
= 0.997305
Correlation (r)
= 0.998652
How it works
Simple linear regression finds the best-fit line y = mx + b that minimises the sum of squared residuals. The slope m is the change in y per unit change in x, and R² indicates what fraction of y's variance is explained by x.
Formulas
Slope
m = Σ(xᵢ−x̄)(yᵢ−ȳ) / Σ(xᵢ−x̄)²
- xᵢ,yᵢ
- Data pairs
- x̄,ȳ
- Means
Intercept
b = ȳ − m×x̄
- ȳ
- Mean of Y
- x̄
- Mean of X
- m
- Slope
Frequently Asked Questions
What does R² = 1 mean?
It means all data points lie exactly on the line — x perfectly predicts y with no residual error.
Can the slope be negative?
Yes. A negative slope means y decreases as x increases, indicating a negative linear relationship.