The marginal effect is obtained by differentiating the conditional expected value of the dependent variable with respect to the explanatory variables: [partial derivative]E|y|[x.

The difference in the conditional expected value of y between men and women with respect to age is fully captured by the difference in the y intercept for men and women, estimated by the parameter [[beta].

we can write the conditional expected value of y to be a general function of the linear index function

1] on the conditional expected value of y or on the conditional probability that y takes on a particular discrete value, when an interaction term is added to the model?

For any model, it is impossible to predict the conditional expected value of the dependent variable without the constant term.

1] on the conditional expected value of y, when an interaction term is added to the model?

We further extend the existing literature by considering the purposeful acquisition of costly information that can be used to increase the precision of the conditional expected value estimate.

Asset Value, Observed Value, and the Conditional Expected Value

If future signals are highly informative, then the conditional expected value will closely track the FL value, and the revealed variance will be nearly equal to the FI variance.

Given the dynamics for the FI value and the observed value, Liptser and Shiryayev (1978) provide differential equations for the conditional expected value and the residual variance (see Appendix).

The conditional expected value is the arithmetic weighted average of the time zero conditional expected value, Z(0) + [[micro].

More weight is put on the time zero conditional expected value when more accumulating noise makes the current observed value less precise.