Understanding Least-Squares Error in Statistics
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems by minimizing the sum of the squares of the residuals made in the results of every single equation. By evaluating the discrepancy between observed values and those depicted by the linear or polynomial approximation, researchers can accurately measure statistical variation.
Formula Used
For a standard linear relationship, the Sum of Squared Errors ($SSE$) is calculated using the following mathematical formulation:
$$SSE = \sum_{i=1}^{n} (y_i - (\mathfrak{m}x_i + c))^2$$
Where $y_i$ represents actual observed dependent values, $x_i$ represents independent predictor variables, $\mathfrak{m}$ represents the calculated regression slope, and $c$ represents the y-intercept.
How to Use This Calculator
- Input your numeric series for independent variables into the X dataset box.
- Input corresponding dependent parameters into the Y dataset box, ensuring matching item counts.
- Choose your preferred mathematical model from the advanced configuration options.
- Click the submit action button to instantly compute comprehensive error metrics.