Like I said, you don’t have a good model for predicting the future. If you did people wouldn’t need to go through the exercise.
You are applying a tool to data in an attempt to understand things and that’s applaudable, but fitting data has limits. You can’t interpolate a data set and expect to extrapolate from that fit. It almost never works, unless you have a good model to fit with already.
I say again, and only because you insist on making the point more evident with every one of your posts, you don’t even understand the excel tool you are using. And you clearly don’t understand least square fitting and what the R residual is.
Where do you think excel is getting the coefficients for those poly curves? Here’s a test ms PhD:
y = observables
x = variables
A = matrix of coefficients that get you from x to what you see in y
Tell us how you solve for A. That’s what excel has to do to give you your curves. Hint: it’s called least square fitting and it involves solving for the pseudo inverse of A.
Secondly, what is the error between the data set and the least square fit curve excel just solve. Hint: it’s related to R. Bigger hint: it is R. So little R means decent fit. Bigger R means fit is getting worse.
Finally, in one post you said once you see the curve break you would then derive the exponential equation. Really? Please explain how you are going to ‘derive’ that. Change the function in excel to include the exponential? That is not deriving, by the way.
I don’t try to tell you how a virus or cell multiplies. Please don’t try to tell me how you fit data to models. You are out of your lane. But don’t feel bad. Many so called experts in various science fields have grown up using tools they don’t understand in inappropriate applications and claiming they can predict behaviors that they really can’t. Climate scientists are one example where they have grossly misrepresented science and data by doing exactly that.
I encourage you, as a person who should be interested in understanding the data they are studying, to listen to experts in other fields who might be able to enlighten you to different methods or ways to look at things. I majored, both undergrad and postgrad in engineering, but I studied with some brilliant mathematicians and probably learned more from them about how to analyze problems than any other discipline I have run across. Mathematics is universal. It doesn’t lie. But statistics and assumptions are easily manipulated to get almost any answer you want. Ask a pollster.
(Mildly). I be thinking a piecewise fit might be a good idea.
Exponential, then fit to parabolic.
That being said — since the disease is NOT randomly distributed across the country, it might be a thought to do the piecewise fit separately for each of (say) a dozen blue city hotspots and go from there; realizing that day 0 for one city might lag day 0 from another.
And mindful that social distancing being unevenly practiced — hardly at all at first, and clamping down as people get alarmed — might affect the classic Gaussian-over-time parabolic shape.
Once again, I have no idea what you are going on about. Is the spread of Covid-19 described by an exponential growth function? Yes. Does my graph show that? Yes. Do my data points fit a theoretical curve determined mathematically? Yes.
Beyond that, there is no need or use for high level calculus. Calculus just does not describe biological processes until you get down to the atomic/molecular level. And even then, most of our calculations don’t rely on calculus.
The beauty of the built in Excel functions is that I don’t have to make macros to do exactly the same thing. Which I have done, back in the distant past before I really understood Excel.
I really have no idea what your profession is, but it is painfully clear that it has nothing to do with the life sciences.
You claim I should listen to experts in other fields? My experience is working in multidisciplinary teams with epidemiologists, statisticians, physicians, veterinarians, masters of public health, microbiologists, etc. etc. I highly value the input of other experts WHEN IT IS RELEVANT. You have yet to contribute anything relevant.