# error message using polynom

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Locks on 25 Apr 2013
hi,
I have the following code:
data16=zeros(size(data12,1),16);
data16(:,1:12)=data12;
numberEl=length(data16(:,9));
numberID=[1:numberEl]';
data16(:,13)=numberID;
dates=730755;
for i= 1:length(dates)
date=dates(i);
%msgbox(num2str(date))
Ts = 0.22192
for indexT = 1:length(Ts)
T = Ts(indexT);
%msgbox(num2str(T))
number=dataT(:,13);
if length(dataT(:,1))==1
SlopeSkew(number)=0;
elseif length(dataT(:,1))==2
SlopeSkew(number)=0;
elseif length(dataT(:,1))==3
SlopeSkew(number)=0;
elseif length(dataT(:,1))==4
SlopeSkew(number)=0;
%nur zum probieren
else
% x is the Strike
x= dataT(:,2);
%is the implied volatility
y=dataT(:,10);
p = polyfit(x,y,2);
f = polyval(p,x);
plot(x,y,'o',x,f,'-')
xlabel('Strike Price K');
ylabel('Implied volatility \sigma');
a=p(3);
b=p(2);
c=p(1);
SlopeSkew(number)=b+2*c.*x;
Slope=SlopeSkew';
end
end
end
for whatever reson the polynom function gives me the following error message:
values, reduce the degree of the polynomial, or try centering
and scaling as described in HELP POLYFIT
I thought that I have fixed the problem, but unfortunately I havent reallly,
the data on which the code is run is the following:
1444. 1500 1 27.3125 0.22192 730755 0.068116 0.963071 60 0.183247087 0.342050308 247.5717725 60
1444. 1500 2 81.875 0.22192 730755 0.068116 1.038345044 61 0.183247281 -0.642946883 247.5718217 61
1444. 1505 1 24.625 0.22192 730755 0.068116 0.959871429 62 0.178451585 0.323180754 242.1932319 62
1444. 1505 2 85.75 0.22192 730755 0.068116 1.041806194 63 0.185184067 -0.654919572 244.2372928 63
1444. 1515 1 21.5 0.22192 730755 0.068116 0.953535644 64 0.177080297 0.294048585 232.5459004 64
1444. 1520 1 19.875 0.22192 730755 0.068116 0.950399013 65 0.175645711 0.278919192 226.8732368 65
1444. 1525 1 18.5 0.22192 730755 0.068116 0.947282951 66 0.174985304 0.264986129 221.2360078 66
1444. 1530 1 17.125 0.22192 730755 0.068116 0.944187255 67 0.174006888 0.25092381 215.1342839 67
1444. 1550 1 12.125 0.22192 730755 0.068116 0.932004194 68 0.169039366 0.196212196 187.2126905 68
1444. 1575 1 7.625 0.22192 730755 0.068116 0.917210476 69 0.164247859 0.138365666 149.5401411 69
Obviously the original dataset was much larger but I have reduced it to the part which is not working. The dataset consists of more than 3 point and therefore I do not see why polyfit is not working

Walter Roberson on 25 Apr 2013
The 4th line, (1505, 0.185184067) is a big difference in trend compared to the other lines. combine with the fact that it is the same x (1505) as the previous value (1505, 0.178451585), and you get a poorly determined polynomial.

Ahmed A. Selman on 25 Apr 2013
A polynomial P(x) is said to be (badly conditioned) when a small variances of x leads to large errors of P, causing unstable error estimation, i.e., error doesn't converge between x and x+dx for even small dx. This is also called (ill-conditioned polynomial) in parallel to (ill-conditioned matrix).
So, as the warning message suggests, try including other (and outer) values of x to walk around the anomaly, or use polyfit(x,y,1).
Keep in mind this is a warning, so it might still work fine within your data set, but even if it does, however, do not fully trust it for other values of data.