Optimizing Recursive Residual Code in Matlab

I have coded an algorithm to compute recursive residuals in matlab in a for loop, that is, regressing the second variable on the first, third variable on the first and second, and so on, and calculating the residuals.

While the code works, it's much slower than what I would like (22 seconds second for 200000 observations and 2 variables). I am looking for suggestions to optimize this code, preferably by vectorizing it as much as possible. I am new to Matlab. Please help.

Here is the code that I have been testing:

 tic

 %Create Random Data
 mu = [10, 20];
 sigma = [1,1.5;1.5,3];
 mu2 = [-10,-20];
 RandomData1 = mvnrnd(mu, sigma, 100000);
 RandomData2 = mvnrnd(mu2, sigma, 100000);
 RandomData3 = [RandomData1;RandomData2];
 vargs = [2 0.25 0.5 4];

 %Set Variable Size
 beta = cell(0);
 U = cell(0);
 Y = cell(0);
 h = zeros(200000,2);
 residual = zeros(200000,2);
 beta{1} = RandomData3(1,1);

 for n=2:200000
   for i = 1
   residual(n,i) = RandomData3(n,1)-beta{1}/(n-1);
   beta{1} = beta{1} + RandomData3(n,1);
   h(n,i) = 1/(n-1);
   end

   for i=2:2
    if(i>=n); break; end

    % update variance estimate   
    if(n==i+1) % first time, compute cholesky decomp directly
       Xtmp = [ones(n-1,1) RandomData3(1:n-1,1:i-1)];
       U{i} = chol(Xtmp'*Xtmp);
       Y{i} = Xtmp'*RandomData3(1:n-1,i);
    end
    x = [1;RandomData3(n,1:i-1)'];
    z0 = (U{i}')\x;
    z = U{i}\z0;
    h(n,i) = x'*z;

    w = (U{i}')\Y{i};
    beta{i} = U{i}\w;
    residual(n,i) = RandomData3(n,i) - x'*beta{i};

    % update the cholesky decomp
    U{i} = cholupdate(U{i},x);
    Y{i} = Y{i} + x*RandomData3(n,i);

    end   
end

 %Calculate Recursive Residuals
 h = sqrt(h + 1);
 r = bsxfun(@rdivide, residual, h);

 toc