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.

Thanks a lot. But how does this exclude, that it might be an exponential?

Could you please show us how to determine whether the shown function graph is linear or exponential or something else?

Have a nice day.

What do you mean by with “R^2 for 'advancement of AI”?

My initial argument was no statement about AI at all, but just an additional comment about the properties of the exponential function.

What do you mean? Exponential growth is best described by the exponential function.

I have at this point absolutely no idea anymore, what you want to tell me. Would you care to rephrase your statement, on which we are disagreeing, so we can back on track and have a constructive discussion.

Exponential growth is always exponential, not just if it suddenly starts to drastically increase in the arbitrarily choosen view scale.

A simple way, to check wether data is exponential, is to visualize it in loc-scale, and if it shows there a linear behavior, it has a exponential relation.

Exponential growth means, that the values change by a constant ratio, contrary to linear growth where the data changes by a constant rate.