I have the following set of data:
Plotting this on Excel gave me a nice, smooth curve:
With the Polynomial Regression function, I get a 5th order polynomial that fits very well:
The issue arises when I transfer both the data values and the best fit curve to Desmos. The two don't seem to have any correlation at all!
I've checked the equations and the data innumerable times, and there doesn't seem to be any typos. Any ideas for why this discrepancy arises? I've done the regression, the data plotting, and the typo-check numerous times (even on multiple laptops), but have had no luck so far.
Any help will be greatly appreciated, thanks in advance.
If you want to try with exact values of the coefficients for the model $$y=\sum_{i=0}^5 a_i x^i$$ $$a_0=-\frac{1367716921770523}{33264123750}$$ $$a_1=\frac{318769904368}{12096045}$$ $$a_2=-\frac{898557942649}{133056495}$$ $$a_3=\frac{115064631832}{133056495}$$ $$a_4=-\frac{490812512}{8870433}$$ $$a_5=\frac{3423040}{2419209}$$
As Joffan commented, the problem is more than likely due to the precision of the coefficients generated by Excel.
Edit
Concerning the problem of the overfit (as commented by Joffan), let us have a look at the sum of squares of residuals $S_n$ as a function of $n$, the degree of the polynomial. We have $$\left( \begin{array}{cc} n & S_n \\ 1 & 0.176991 \\ 2 & 0.050324 \\ 3 & 0.017965 \\ 4 & 0.003115 \\ 5 & 0.002169 \\ 6 & 0.000903 \\ 7 & 0.000707 \\ 8 & 0.000661 \end{array} \right)$$
As you can see, for $n > 4$, the improvement is just very marginal. If I may suggest, plot $S_n$ as a function of $n$ and this will become quite clear.