Evaluating the effectiveness of principal component regression vs. multiple linear regression for black gram cultivation in Tamil Nadu

This study examines the comparison between Multiple Linear Regression and Principal Component Regression for black gram cultivation in Tamil Nadu. This research addresses the problem of accurately modeling and predicting the factors that influence the yield and productivity of black gram cultivation in Tamil Nadu. The challenge lies in identifying which statistical technique, Principal Component Regression (PCR) or Multiple Linear Regression (MLR), is more effective in capturing the complex relationships between various environmental, economic and agricultural variables that affect black gram production. Secondary data were collected from 1999 to 2022 (23 years). Considering yield as a dependent variable and the independent variables are Seed, Fertilizer, Manure, Human labour and Animal labour. According to Multiple Linear Regression, the regression coefficients of fertilizer and human labour significantly influence the yield. The coefficients of Fertilizer and Human labour are found to be 0.049 and 0.07 respectively. According to Principal Component Analysis, the 2 principal components are chosen because the eigenvalue is more than 1.0. These 2 components, PC1 and PC2, cover 36 % and 34 % respectively. The loadings revealed that fertilizer, manure and animal labour significantly contributed to PC1 and Seed and human labour contributed significantly in PC2. The Multiple Linear Regression and Principal Component regression are compared using R square, Adjusted R Square, Root Mean Square, Mean Absolute Error and Mean Absolute Percentage Error. The adjusted R square reveals that Principal Component Regression is better than Multiple Linear Regression. The lowest value of Root Mean Square Error, Mean Absolute Error and Mean Absolute Percentage Error shows the best model among the 2 models. The error is lower for Principal Component Regression compared to Regression. PC1 captures the relationship between fertilizer, manure and animal labor, representing an "input utilization efficiency" dimension. PC2 reflects the trade-off between human labor and seed usage, defining a spectrum between "labor-intensive" and "seed-reliant" farming strategies.