How to get rid of "negative data ignored" warning in a loglog plot

In fitting a least square line through a set of points on a loglog scale, MATLAB is returning the warning "Negative data ignored". For example,

N = [56 112 224 448 896 1792 3584 7168 14336];

T_max = [0.444793435182132 0.4395279003565365 0.43638330717684004 0.4344924804848505 ...

0.43374154539955007 0.43337438343040974 0.4331928605464643 ...

0.4331026128636092 0.4330576104805632];

T_min = [0.4172265675535062 0.42604231767208034 0.4304025036668112 ...

0.4317013137271798 0.4324741371494442 0.4328174950027687 ...

0.4329158371978752 0.4329426670435078 0.43298763322951783]

T_exact = 5*sqrt(3)*(0.1/2);

T_min_exact = abs(T_min - T_exact);

c2 = polyfit(N,T_min_exact,1);

y2 = polyval(c2,N);

loglog(N,T_min_exact, '*',N,y2,'R')

The above code produces the warning "Negative data ignored" and is producing the following plot:

How to overcome this problem and what am I doing wrong here?

Answer 1

[Image Analyst]

If you want to fit a line on the log-log plot, you'll have to take the log of x and log of y and fit that to a line. Then to display with loglog(), you'll have to "unlog" the line (exponentiate the fitted x and fitted y) to get it in the original space as the original data. You don't want to use loglog() on data that has already been logged!

Or better yet, use nlmfit(). I'm attaching several examples of nlmfit().

[Sulaymon Eshkabilov]

If this is the case, follow the suggested points by Image Analyst.

Good luck.

[Avishek Mukherjee]

I am not quite sure what you meant by "you'll have to "unlog" the line (exponentiate the fitted x and fitted y) to get it in the original space as the original data".

I tried the following code and got the graph

c1 = polyfit(log(N),log(T_max_exact),1);
y1 = polyval(c1,log(N));
loglog(N, T_max_exact, 'O')
hold on
plot(log(N),exp(y1),'G')

[Avishek Mukherjee]

I got the desired results. Thanks a lot!

I made an unintentional mistake of plugging in the log befor N.

Answer 2

[Sulaymon Eshkabilov]

You had better select higher order of polynomial to fit or choose a different fit model, e.g., log function

...
c2 = polyfit(N,T_min_exact,8);  % Order # 8. 
y2 = polyval(c2,N);
loglog(N,T_min_exact, '*',N,y2,'r-')

[Avishek Mukherjee]

I am trying a least square fit here with a straight line, so degree 8 will not work.

Sorry for the confusion. I should have mentioned that in my post. My apologies.