IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF COMPUTER SCIENCE AND MATHEMATICAL THEORY (IJCSMT )

E-ISSN 2545-5699
P-ISSN 2695-1924
VOL. 9 NO. 4 2023
DOI: https://doi.org/10.56201/ijcsmt.v9.no4.2023.pg69.79

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Investigation of the Effects of Box-Cox transformation and Interaction Term on the R2 And VIF: A Regression Approach

Onu, Obineke Henry, Ejukwa, Justin Odadami and Nwanneako, Sabinus Nnamdi

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Abstract

The study investigated the effects of Box-Cox Transformation and the introduction of interaction term on the coefficient of determination (?2) and the variance inflation factor (VIF) using regression approach. The regression equation used was built with employment and insecurity as the predictors while the small and medium scale enterprises (SMEs) was used as the response variable. There were three different analysis known as analysis 1, 2 and 3. Analysis 1 was the regression analysis without interaction and transformation (RAWoIT), 2 was the regression analysis with transformation and without interaction (RAWTWoI) while 3 was the regression analysis with transformation and interaction (RAWTI). The p-values, t-values, analysis of variances and Pareto charts among others were employed in this work. It was found that the Box- Cox transformation introduced in analysis 2 had no visible effects on the VIF and p-values of the employment and the constant term but decrease the ?2and adjusted ?2 by 4.34% and 4.91% respectively. In analysis 3, when interaction term and Box-Cox transformation was included in the model, it was observed that the VIF increased from 1.03 recorded for analyses 1 and 2 to 25.06, 613.64 and 595.50 for employment, insecurity and the interaction term, respectively. It was recommended that: to reduce VIF and or multicollinearity in a system, interaction term should not be included and that the Box-Cox transformation reduces the coefficient of determination.

keywords:

SMEs, Employment, Insecurity, Box-Cox transformation, Variance Inflation Factor and Coefficient of determination.

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References:

Atkinson, A. B. (2000). The Box-Cox transformation: review and extensions. Statistical
Science. ISSN 0883-4237 (In Press).

Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations (with discussion). Journal
of the Royal Statistical Society, Series B, 26, 211=252.
Henriques-Rodrigues, L. and Gomes, M. I. (2022). Box-Cox Transformations and Bias
Reduction in Extreme Value Theory. Computational and Mathematical Methods, 2022,
1-15.

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