12.5.2 Interpreting Multiple Regression Analysis

[SPDA36]

Hello, I am seeking clarification for terms unique and marginal effects. I personally have never heard of the term unique effect in any of my statistics or econometric courses but its definition on page 260 is the definition I have heard for marginal effect and I'm not quite sure what to make of the definition on page 261.

Below is an excerpt from Cran R Project https://cran.r-project.org/web/packages/margins/vignettes/Introduction.html Marginal effects are partial derivatives of the regression equation with respect to each variable in the model for each unit in the data...In ordinary least squares regression with no interactions or higher-order term, the estimated slope coefficients are marginal effects.

The obvious is that if there is interactions or higher-order terms, then we take the partial derivative to get the marginal effect.

I'm not exactly sure this section of the books' definition of marginal effect on page 261 matches Cran's definition from above: in contrast, the marginal effect of x_j on y can be assessed using a correlation coefficient or simple linear regression model relating to x_j to y; this effect is the total derivative of y with respect to x_j