Nope. There isn’t an infinite number of linear functions that will fit this curve. Based on the slope and y intercept there is only one linear function. There may be other approximations but only one line of best fit that will predict future outcomes.
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 if it is a linear function it doesnt matter if you only use two points. Unless the function is not linear. If the line isn’t completely smooth you could also use a polynomial function that would fit the curve. Unless it exhibits exponential behavior why would you ever model it as an exponential if linear or polynomial models the data more accurately?
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.
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.
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.
Nope. There isn’t an infinite number of linear functions that will fit this curve. Based on the slope and y intercept there is only one linear function. There may be other approximations but only one line of best fit that will predict future outcomes.
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 if it is a linear function it doesnt matter if you only use two points. Unless the function is not linear. If the line isn’t completely smooth you could also use a polynomial function that would fit the curve. Unless it exhibits exponential behavior why would you ever model it as an exponential if linear or polynomial models the data more accurately?
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.
Does the data originate from an exponential? Can you prove it?
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.
The actual values are exactly as shown on the graph. Do you know what graphs are?
In your data what is the exponential function?
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).
That’s the curve of the line?
Your data as in you generated it? Or that’s the function that fits the curve shown in the graph?