compute_ordinary_least_squares

Summary: Computes the Ordinary Least Squares (OLS) regression coefficients for a simple linear regression model. The function finds the best-fitting line y = b1 + b2 * x that minimizes the sum of squared residuals.

pure
double[2]
compute_ordinary_least_squares
(
double[] array_x_IN
,
double[] array_y_IN
)

Parameters

array_x_IN double[]

Input array representing the independent variable (X).

array_y_IN double[]

Input array representing the dependent variable (Y).

Return Value

Type: double[2]

result: A double array of size 2 containing: - b1: The intercept of the regression line. - b2: The slope (coefficient for x).

Notes: - The function enforces that both input arrays must have the same length. - The OLS formula for slope (b2) is: b2 = Σ (x_i - mean_x) * (y_i - mean_y) / Σ (x_i - mean_x)^2 - The intercept (b1) is computed as: b1 = mean_y - b2 * mean_x - Assumes that array_x_IN has variance; if all x values are equal, the denominator will be zero, leading to an undefined slope. - The function is designed for simple linear regression with one independent variable. - If residual analysis is required, consider calculating R² or Mean Squared Error (MSE). - OLS assumes linearity, homoscedasticity, and uncorrelated residuals.