A Multivariate Linear Regression on the Effect of Foreign Trade on Foreign Exchange Rates of Naira Using Bootstrap Approach

Abstract

This paper fits a multivariate linear Regression model for the relationship between four response variables; foreign trades (cost of oil imported, cost of non-oil imported, cost of oil exported and cost of non-oil exported) and two predictor variables; foreign exchange rate of US Dollar and Pounds Sterling  between 1960--2010. The null hypothesis that no linear relationship exists between foreign trades and foreign exchange rate were proposed. The model indicates an adequate relationship between the foreign trade and exchange rate. We observed from model 1 to model 4 of the multivariate linear regression that the multivariate bootstrap method when compared with the analytic method yielded a reduced standard error. This shows that multivariate bootstrap is good methods in controlling variation among observations. We further observed that the exchange rate of US Dollar and Pounds Sterling contributed 68% effect on the Nigerian foreign trades while 32% may be attributed to other unexplained factors. This indicates that multivariate bootstrap method offer considerable potentials in the estimation of multivariate linear regression parameters. Thus, the results reveal that bootstrap resampling allows empirical assessment of the analytical model and it is a good approximation to the analytical model.