This paper uses the principal component analysis (PCA) to examine the possibility of using few explanatory variables (X’s) to explain the variation in Y. It applied PCA to assess the performance of students in Abia State Polytechnic, Aba, Nigeria. This was done by estimating the coefficients of eight explanatory variables in a regression analysis. The explanatory variables involved in this analysis show a multiple relationship between a dependent variable and independent variables. A correlation table was obtained from which the characteristic roots were extracted. Also, the orthonormal basis was used to establish the linear independence of the variables. The first principal component accounted for 51.6 percent of the total variation, while the second principal component accounted for 23.3 percent. The descriptive statistics and plots were considered. The principal components yielded good estimates, which leads to the structural co-efficient of the regression model.This led to the conclusion that PCA uses few explanatory variables to explain variations in a dependent variable and is therefore an efficient tool for performance assessment.
Keywords: Orthomormality, Eigenvalue,Diagonalizability, Vector, Standardised
Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 607 – 614