Lack of Synergy Regression Models

Abstract

Consider a model y _i  = β₀ + β₁ x _i1 + β₂ x _i2 + e _i , i = 1,…, n, with two explanatory variables. The synergy phenomenon deals with the case when . It is shown here that in the model with the regression vectors x ₁ = (x ₁₁,…, x _n1)′ and x ₂ = (x ₁₂,…, x _n2)′ such a phenomenon does not appear for all possible observation vectors y = (y ₁,…, y _n )′, if and only if or 1.

Keywords:

• Coefficient of determination
• Correlation coefficient
• Exhancement
• Multiple regression
• Synergy

Mathematics Subject Classification:

• Primary 62J05
• Secondary 62H20