Slope of a Multiple Linear Regression Line?

Question

The slope of a simple regression line (y=a+bx+e) is easy: it's 'b.' But I'm not clear on how to determine the slope of a multiple regression line (y+a+b1x1+b2x2+...+bKxK+e).

Please help!

Thanks.

Answer 1

There is no generalized way to define "slope" for an entire multiple regression line. Since the relationship among variables is multi-dimensional, the concept of "slope" isn't really meaningful.

However, it is possible to think of the "partial slope" of one variable. The partial slope is just the value of the regression coefficient of just one of the variables (the "beta" or "b" in your model above). It's just like in a regular line equation. It's a "partial" slope because it tells you how the dependent variable responds to a change in the one explanatory variable while holding all other variables constant.

Answer 2

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Answer 3

I can not presently remember so I suggest you obtain a book on statistics from your library or ask someone in your mathematics department.