The answer is you cant know that’s why it would be crazy to model it that way. With the infinite possible exponential functions that could fit this curve.
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.
Great question! Why dont you try to answer it.
Because I don’t know how to.
The answer is you cant know that’s why it would be crazy to model it that way. With the infinite possible exponential functions that could fit this curve.
But isn’t the same true also for a linear model, which of the infinite possible linear functions could fit this curve?
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?