A Note on Enhancement-Synergism: Reverse inequality between the coefficient of determination and the sum of squared correlation coefficient

This paper focuses on the surprising reverse inequality (enhancement-synergism) between coefficient of determination and the sum of two squared simple correlation coefficients in a two variable regression model. This condition significantly reduces the model's effectiveness and can direct misleading results. It has been observed that enhancement-synergism is more likely than non enhancement-synergism which is presented by a unifying box (Box 3.A). If the joint contribution of two explanatory variables is incremental over simple correlation then we encounter the condition of enhancement-synergism and in normal case where coefficient of determination is less than the sum of squared correlation coefficients, then the joint correlation is incremental over incremental correlation, which is presented by two mathematical examples. When the partial r-square value is greater than its simple r-square value of a variable then the enhancement-synergism condition occurs. A concise and easily understandable graphical and mathematical example provided to show the direct dependency of enhancement-synergism on the extent of the problem of multicollinearity.