Calculation of Beta Indicators by using matrices in Matlab to increase productivity on an agricultural farm.

Abstract

Today is essential to optimize resources and maximize yields. This study focuses on the calculation of Beta (β) indicators using matrix algebra in Matlab, as a tool to scientifically evaluate the relationship between soil variables and crop productivity. The β-coefficients allow us to identify which soil factors (pH, organic matter, nutrients) have the greatest impact on yield, thus avoiding the empirical use of inputs. Data were collected from 5 soil samples in coffee farms in Honduras, measuring: pH, organic matter (OM%), cation exchange capacity (CEC), nitrogen (N), phosphorus (P), potassium (K) and yield (kg/ha). These data were organized into an X matrix (predictor variables) and a Y vector (performance). Using Matlab, the multivariate regression formula was applied: β = (XTX)−1XTY to calculate the standardized coefficients. The model demonstrated 95% accuracy in predicting yields. The results confirm that: Organic matter is the most important factor in increasing productivity in tropical soils.The method reduces costs by avoiding superfluous applications (e.g., liming when pH is not limiting). The matrix calculation of β-indicators in Matlab: It provides a scientific approach to prioritizing agricultural inputs. Increases yields (up to 20% in pilot cases) by correcting only critical variables.