Multivariate Logarithmic and Exponential Regression Models

This study analyzes a multivariate exponential regression function. Two basic types of error assumptions are examined: multiplicative (logarithmic model) and additive (exponential model). The usual method of taking natural logarithms of the regression relationship and then using linear least-squares estimators for the parameter estimates assumes that the error is multiplicative. Analysis shows that only the estimate of the parameter in the coefficient term and its distribution are affected by whether the hypothetical regression function is equal to the expected value (the mean) of the dependent variable Y, or to the median. The other parameter estimates, their distribution, and the prediction interval of Y are not affected. The study also examines the exponential, or additive, model in which the error is assumed to be normally distributed and added to the function. This leads to the more difficult problem of least-squares estimation of a nonlinear form. Such a solution is not exact and may not be unique. Methods of comparing the two models are given. The bulk of the Memorandum describes, lists, and gives instructions for use of the Multivariate Logarithmic and Exponential Computer Program.