Perform simple linear regression using Ordinary Least Squares (OLS)
npm install @tpmjs/tools-linear-regression-olsPerform simple linear regression using Ordinary Least Squares (OLS) to find the best-fit line for your data.
``bash`
npm install @tpmjs/tools-linear-regression-ols
`typescript
import { linearRegressionOLSTool } from '@tpmjs/tools-linear-regression-ols';
// Use with AI SDK
const result = await linearRegressionOLSTool.execute({
x: [1, 2, 3, 4, 5],
y: [2, 4, 5, 4, 5],
});
console.log(result);
// {
// slope: 0.6,
// intercept: 2.2,
// rSquared: 0.581,
// residuals: [-0.8, 0.6, 0.4, -0.6, 0.4],
// predictions: [2.8, 3.4, 4.0, 4.6, 5.2],
// metadata: {
// n: 5,
// meanX: 3,
// meanY: 4,
// sst: 5,
// sse: 2.096
// }
// }
`
- x (number[], required): Independent variable values (predictor). Minimum 2 values.
- y (number[], required): Dependent variable values (response). Minimum 2 values. Must have same length as x.
`typescript`
{
slope: number; // Slope of the regression line (β₁)
intercept: number; // Y-intercept (β₀)
rSquared: number; // Coefficient of determination (0-1)
residuals: number[]; // Residuals (y - ŷ) for each point
predictions: number[]; // Predicted values (ŷ) for each x
metadata: {
n: number; // Number of observations
meanX: number; // Mean of x values
meanY: number; // Mean of y values
sst: number; // Total sum of squares
sse: number; // Sum of squared errors
}
}
The tool implements simple linear regression using the OLS method:
1. Model: ŷ = β₀ + β₁x
2. Slope: β₁ = Σ((x - x̄)(y - ȳ)) / Σ((x - x̄)²)
3. Intercept: β₀ = ȳ - β₁x̄
4. R-squared: R² = 1 - (SSE / SST)
Where:
- ŷ = predicted value
- x̄ = mean of x
- ȳ = mean of y
- SSE = sum of squared errors
- SST = total sum of squares
R² measures the proportion of variance in y explained by x:
- 1.0: Perfect fit (all points on the line)
- 0.8-0.99: Strong relationship
- 0.5-0.79: Moderate relationship
- 0.2-0.49: Weak relationship
- 0.0-0.19: Very weak relationship
`typescript
const result = await linearRegressionOLSTool.execute({
x: [1, 2, 3, 4, 5],
y: [2.1, 3.9, 6.2, 7.8, 10.1],
});
// Use slope and intercept to predict new values
const predictY = (x: number) => result.intercept + result.slope * x;
console.log(predictY(6)); // Predict y for x=6
// Output: ~12.0
``
- Modeling linear relationships between variables
- Making predictions based on historical data
- Understanding the strength of relationships (via R²)
- Identifying trends in data
- Simple forecasting
- Assumes a linear relationship
- Sensitive to outliers
- Doesn't handle multiple independent variables (use multiple regression)
- Assumes independence of observations
- Best with normally distributed residuals
MIT