Regression and Principal Component Analyses: a Comparison Using Few Regressors

Abstract

This paper uses the regression analysis and principal component analysis (PCA) to examine the possibility of using few explanatory variables to explain the variation in the dependent variable. It applied regression analysis and principal component analysis (PCA) to assess the yield of turmeric, from National Root Crop Research Institute Umudike in Abia State, Nigeria. This was done by estimating the coefficients of the explanatory variables in the analysis. The explanatory variables involved in this analysis show a multiple relationship between them and the dependent variable. A correlation table was obtained from which the characteristic roots were extracted. Also, the orthonormal basis was used to establish the linearly independent relationships of the variables. The regression analysis shows in details the constant and the coefficients of the three explanatory variables. On the other hand the principal component analysis estimates the first principal component second principal component and both components accounted for 71.4 percent of the total variation. The regression analysis and principal component analysis (PCA) yielded good estimates, which leads to the structural coefficient of the regression model. The study shows that regression analysis and principal component analysis (PCA) use few explanatory variables to explain variations in a dependent variable and are therefore efficient tools for assessing turmeric yield depending on the set objective. But that PCA is more efficient since it uses fewer variables to achieve the same result.