Why do I get disjoint data when I try extrapolate after using polynomial regression
SDG
I wanted to extrapolate some of the data I had, as shown in the plot below. The blue line is the original data and the red line is the extrapolation that I wanted.
To use regression analysis, I used the function polyfit:
sizespecial = size(i_C);
endgoal = sizespecial(2);
plothelp = 1:endgoal;
reg1 = polyfit(plothelp,i_C,2);
reg2 = polyfit(plothelp,i_D,2);
Where i_C and i_D are the vectors that represent the original data. I extended the data by using this code:
plothelp=1:endgoal+11;
for in = endgoal+1:endgoal+11
i_C(in) = (reg1(1)*(in^2))+(reg1(2)*in)+reg1(3);
i_D(in) = (reg2(1)*(in^2))+(reg2(2)*in)+reg2(3);
end
However, the graph I output now is:
I do not understand why the extra notch is introduced (circled in red). Do not hesitate to ask me to clarify any of the details on this questions and thank you for all your answers.
Dan
What I imagine is happening is that you are trying fit a second order polynomial over all your data. My guess is that this polynomial will look a lot like the curve I have drawn in in orange. If you follow Matt's advise from his comment and plot your regressed polynomial over the your original data as well (not just the extrapolated part) you should confirm this.
You might get better results by fitting a higher order polynomial. Your data have two points of inflection so a 3rd order polynomial will probably work quite well. One danger of extrapolating on higher order polynomial however is that they could have fairly dramatic inflections outside of the domain of your data and produce unexpected and wild results.
One way to mitigate against this is by rather performing a linear regression over the final x data points of your series. These are the points highlighted in yellow in the figure. You can tune x as a parameter such that it covers as much of the approximately linear final portion of your curve as makes sense. The red line I have drawn in will be the result of a linear regression performed on only those data (as opposed to the entire data set)
Another option might be to rather fit a spline curve and extrapolate on that. You can use the interp1 function specifying 'spline' or 'pchip' for that.
However which is the best choice will depend largely on the nature of the problem you are trying to solve.
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