How to implement a parfor in place of a for loop?

I understand the idea behind what is and isn't allowed in a parfor loop, but I do not understand the practical application. I have the following segment of code. It works great, but it only uses 1 core and takes hours to complete. It should be trivial to parallelize but I don't see how to do it.

By the way, the preallocations are merely for the purpose of presenting it to you in a way that it will work.

 numfiles = 3249;
 LABTnum  = 61;
 for i=1:LABTnum
     adjusted_La{i} = rand(10,numfiles);
     adjusted_Sm{i} = rand(10,numfiles);
     adjusted_Yb{i} = rand(10,numfiles);
 end
 chem_LaSm = repmat(rand(10,1),1,numfiles);

 pcoefs = repmat([0.2 1.0 3.0],numfiles,1)';
 h  = 2;
 Mi = repmat(pcoefs(:,1),1,h+1);
 polys = zeros(h+1,numfiles);
 M = bsxfun(@power,Mi,0:h);

 for i=1:LABTnum
    bestCm_LaSm{i} = zeros(numfiles,numfiles);
    curSm_LaSm = adjusted_Sm{i}; % for La/Sm

     for k=1:numfiles
        curLa = repmat(adjusted_La{i}(:,k),1,numfiles);
        LaSm  = curLa./curSm_LaSm;
        difs  = [mean((LaSm*0.2-chem_LaSm).^2)' mean((LaSm-chem_LaSm).^2)' mean((LaSm*3-chem_LaSm).^2)']';

        for j=1:numfiles;
            polys(:,j) = M\difs(:,j);
        end
        bestCm_LaSm{i}(:,k) = -0.5*polys(2,:)./polys(3,:);
     end
 end

I do not understand how to modify a code like this in a way that is acceptable for parfor. Any help is appreciated.

EDIT:

I've found that I may rewrite the active part of the code as:

 for i=1:LABTnum
    bestCm_LaSm{i} = zeros(numfiles,numfiles);
    curSm_LaSm = adjusted_Sm{i}; % for La/Sm
     parfor k=1:numfiles
        polys{k} = zeros(h+1,numfiles);
        curLa = repmat(adjusted_La{i}(:,k),1,numfiles);
        LaSm  = curLa./curSm_LaSm;
        difs  = [mean((LaSm*0.2-chem_LaSm).^2)' mean((LaSm-chem_LaSm).^2)' mean((LaSm*3-chem_LaSm).^2)']';
        for j=1:numfiles;
            polys{k}(:,j) = M\difs(:,j);
        end
     end
     for k=1:numfiles
     bestCm_LaSm{i}(:,k) = -0.5*polys{k}(2,:)./polys{k}(3,:);
     end
 end

Is there a better way?