Am I interpreting that properly?

[nosit]

Hello,

In linear regressions or derivatives, if Beta (slope) or a result of a derivative is, for example, 5 then I say that the function is increasing at a rate of 5 units of Y per unit of X.

I say that because the slope of a linear regression is ΔY/ΔX and in the derivative there is limit of h approaching 0 and the difference quotient, which also comes from ΔY/ΔX idea. In both cases, we are interested in the slope.

Basically, when I interpret an linear regression or a derivative I replace this 5 in ΔY/ΔX, so 5 represents ΔY and ΔX in this case would be the denominator 1.

Is my interpretation correct or you make it in a different way?

 

[JeffM]

The result of a linear regression is usually a linear approximation with the same slope at every point. The slope is global.

A derivative can be considered a slope at a point, but there is no implication that the slope is the same at other points. In fact, it is usually the case that the slope is different at different points. The slope is local.