Multivariate data often arise in empirical investigation. In Engineering studies, for example, multivariate data may be collected on the effect of different processing conditions on the characteristics of a machine output. Such data sets may present highly correlated variables. In this paper, we investigate the effect of correlation among dependent variables on their regression modeling. Four regression techniques are discussed and compared: ordinary least squares regression, generalized least squares regression, seemingly unrelated equations regression, and multivariate regression. Since regression models are most frequently used for prediction purposes, we compare modeling strategies using the prediction variance as a performance measure. The paper contains a case study from the food processing industry.
multivariate regression techniques; prediction variance; correlation
