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7 to implement maximum likelihood estimation sets initial values for the parameters ρ, β based on the CochraneOrcutt estimates produced by the code described previously. ) We then set some options for use in the optimization routine, and make a call to the fmins function using the data vector y and matrix X. 4f \n\n’,llike); fprintf(1,’number of iterations taken = %4d \n\n’,niter); CHAPTER 2. REGRESSION USING MATLAB 38 The resulting parameter estimates for ρ, β are returned from the fmins function and used to compute an estimate of σε2 .

4 Using the ols() function for Monte Carlo nobs = 100; nvar = 5; ntrials = 100; b = ones(nvar,1); % true betas = 1 CHAPTER 2. 4f \n’,bstd(1,i)); end; % provide a histogram for each bhat hist(bout); ylabel(’frequency of \beta outcomes’); xlabel(’Estimated \beta values’); legend(’\beta_1’,’\beta_2’,’\beta_3’,’\beta_4’,’\beta_5’); We recover the estimates βˆ from the ‘results’ structure each time through the loop, transpose and place them in the ‘ith’ row of the matrix ‘bsave’. After the loop completes, we compute the mean and standard deviations of the estimates and print these out for each of the 5 coefficients.

REGRESSION USING MATLAB 15 increasingly ill-conditioned least-squares problem. The γ parameter serves to control a near linear relationship between the intercept column and the last (n − 2) columns of the data matrix. As the parameter γ is increased, the last (n − 2) columns of the matrix X become more collinear with the intercept column producing a near linear combination between the intercept term and the last (n − 2) columns. This type of collinear relationship reflects a situation where each independent variable becomes more nearly constant, exhibiting a near linear relationship with the constant term vector.

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