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This thesis is limited to a Monte Carlo study on the performance of the Lagrange multiplier test in terms of its power and robustness to collinearity when the independent variables are distributed both multivariate and lognormal with a given covariance matrix. Power is defined as the probability of rejecting the null hypothesis under the assumption that the alternative hypothesis is true. This probability is estimated for several sets of parameters and sample sizes using the Lagrange multiplier test. The results of the analysis indicate that very significant variations in the power of the test occur in the case of highly correlated multivariate normal independent variables. Mainly this variation occurs when the correlation between the independent variables is over 0.60 and when several seeds are used. It's hypothesized that the dispersion of the power of the test is a consequence of the violation of the assumption of independent variables, that is, the inverse of the cross products matrix must exist. The results based on multivariate and lognormal deviates indicate that the power of the test is significantly higher in the lognormal case, but the same dispersion on the power of test seen in the multivariate case still exists.