In nonlinear models,the expected change in the dependent variable for a change in one of the explanatory variables is given by
A)△Y = f(X1 + X1,X2,...Xk).
B)△Y = f(X1 + △X1,X2 + △X2,... ,Xk+ △Xk)- f(X1,X2,...Xk).
C)△Y = f(X1 + △X1,X2,... ,Xk)- f(X1,X2,...Xk).
D)△Y = f(X1 + X1,X2,... ,Xk)- f(X1,X2,...Xk).

Question

Quizplus · Accepted Answer

In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by the partial derivative of the function with respect to that explanatory variable, multiplied by the change in that variable. This corresponds to choice C, which shows the change in the dependent variable when only one explanatory variable (X1) is changed by a small amount (ΔX1). The other choices either combine multiple explanatory variables in the change or do not show the change as a partial derivative multiplied by the change in the explanatory variable.

In Nonlinear Models,the Expected Change in the Dependent Variable for a Change