How to extrapolate the plot of continuous data points so as to extend the region of plot

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I have a set of continuous data points. I plot for the data and I see that I want to extrapolate the data to a certain 'x' value. I want the respective 'y' value and plot to be extrapolated. The file of data is attached below. The plot is to be extended till x=10.

Risposte (1)

John D'Errico
John D'Errico il 30 Mag 2020
In the space of one hundred and seventy six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over a mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oölitic Silurian Period, just a million years ago next November, the Lower Mississippi was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-pole. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo [Illinois] and New Orleans will have joined their streets together and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.
Mark Twain in Life on the Mississippi (1884)
The point is, long term extrapolation is a risky business. And with no intelligent model for the process, you can get any result you want to see.
Having said that, let me look at your data. I'll stretch the axis limits down to x==10 so we can get some perspective.
plot(x,y,'.')
axis([10 46 .45 .75])
So your data extends from roughly 28 to 46. You now want to extrapolate your data all the way down to x==10. Your data is pretty noisy. It has a strange behavior at the bottom end, so it is difficult to even have a clue where it might end up when you extrapolate all that distance down.
(ROFLMAO)
I'm sorry. While I'm trying to stifle the laughter, I can't. You seriously want to predict that far down, with that data? Let me check the date. Was this posted on April 1st? (no.) SERIOUSLY? I thought only politicians were allowed to do something like that? That is because they make up their own laws and their own rules, so they can claim anything they want.
Please reread that quote from Mark Twain.
I'm being as honest and direct with you as I can. Any extrapolation based on that data, down that far, will have a result that is literally a random number.
Note that most of that curve is pretty well-behaved. A straight line might not be unreasonable. But then at the bottom, i.e., at the point where any extrapolation must extend the curve from, the curve clearly starts to bend. How much of a toe is there? Does the curve even start to come back up? Does the curve just flatten out, and that is the beginning of a toe? Is that "toe" just something to be ignored, and the curve probably extends linearly below that point?
Any hope of extrapolation by any more than a very small amount is optimistic in the extreme. But the good news is, it fully qualifies you for any political office you want.

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