mxeff

Sure. ^_^

I am just curious. So may I ask what your math education is?

For reference, what is math education?

This case here.

In the case I am discussing, the data is generated using the exponential function exp(x).

I am well aware what a graph is and that it shows the actually values, but to obtain some actually values to perform manually some calculations we need to extract some explicit values from the image. This is however not arbitrarily precise and therefore will add some noise to the extracted values.

My data is simply y = exp(x).

Your data, no because I have no access to the actually values. But just a plot of a line that seems very straight (but does not necessarily need to be), and measuring it manually will introduce some noise.

In my data, that I generated, yes there I know for a fact that it is from an exponential.

But if the data originates from an exponential, any selection of two points will yield a different slope, because the data point lie not exactly on a straight line.

You suggested to model it linearly, that is what we are discussing here.

But this takes only into consideration the two selected point used to calculate the the slope and intercept. All other point will not exactly lie on linear function. And as you can choose any combination of two point you will get again infinitely many different parametrization a of the linear model.

But isn't the same true also for a linear model, which of the infinite possible linear functions could fit this curve?

Because I don't know how to.