Principal Component Factor Analysis of Some Development Factors in Southern Nigeria and Its Extension to Regression Analysis

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Abstract
This study was conducted to evaluate some development factors in Southern Nigeria in order to ascertain common factors that explained the interrelationships among them and identify best cities for recommendation. A total sample of 250 cities from different states in three geopolitical zones in Southern Nigeria was used in this study and 11 development factors were considered. Kaiser-Meyer-Olkin (KMO) of (> 0.5) was computed to test the sampling adequacy; Bartlett’s Test of Sphericity (Significant at 0.001) was conducted to test whether the correlation between the variables are sufficiently large for factor analysis; correlation matrix was computed to confirm the inter-item correlation. In this analysis, principal component factor analysis was the factor extraction method. Varimax rotation technique was used for factor rotation. The result showed that three new factors with eigenvalues greater than 1 were successfully constructed. The three new factors accounted for 71.63% of total variance in the dataset and assigned as the common factors influencing sustainable development in Southern Nigeria. The communalities results ranging from 0.32-0.88 depicted that factor model was adequate. The results of factor analysis were extended to multiple regression analysis. The multiple regression model was fitted using development scores as dependent variable and rotated factors as independent variables. The coefficient of determination,, for the regression model was 99% and this shows that the model is adequate to evaluate the Southern Nigerian cities. The higher the estimated development scores, the better a city. Tolerance and VIF values showed that there was no multicollinearity in the regression model.