this post was submitted on 31 May 2025
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Showerthoughts
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A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The most popular seem to be lighthearted clever little truths, hidden in daily life.
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- Both “200” and “160” are 2 minutes in microwave math
- When you’re a kid, you don’t realize you’re also watching your mom and dad grow up.
- More dreams have been destroyed by alarm clocks than anything else
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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?
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?
In the case I am discussing, the data is generated using the exponential function exp(x).
Which case is that? Have we moved goal posts or are you claiming this line:
Was generated using the function y=exp(x)?
This case here.
So your claim is that curve was generated using an exponential function?
I concede, that appears to be the case.
Now this one
What function generated this curve?
For reference, what is math education?
Its a thing you do to get into higher level classes. Then never think about again.
I am just curious. So may I ask what your math education is?
Uh, no. That's too personal. Either you take what im saying at face value or you dont. If there was a time I could sit down and pass a heat and mass transfer exam that is long passed.
Sure. ^_^
Lol