FctExampleCode

Example MATLAB Code

This code is to be used with the Function discussion.

FunctionExample.m

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% This code loads data from a spreadsheet and uses OLSest to run a % regresion

[data,titles]=xlsread('OLSexample.xls');

n = size(data,1); depvar = data(:,1); expvar = [ones(n,1) data(:,2:end)];

[bhat,bhatse,resids,obs,resss,rsq] = OLSest(depvar,expvar,0); disp(bhat);

temp = 2;<\source>

OLSest.m

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function [b,bse,res,n,rss,r2] = OLSest(y,x,output); % This function performs an OLS estimation % input: y, vector with dependent variable % x, matrix with explanatory variable % function will automatically add a constant if the first col % is not a vector of ones % output, 1 = printed output % output: b, estimated parameters % bse, standard errors for bhat % res, estimated residuals % n, number of observations used % rss, residual sum of squares % r2, Rsquared

% select those rows that have observations for all variables ninit = length(y); testnan = [isnan(y) isnan(x)]; testnan = (sum(testnan,2)==0); y = y(testnan); x = x(testnan,:); % test whether first column is vector of ones temp = (x(x(:,1)==1)); if length(temp) ~= length(x)

 x = [ones(length(x),1) x];  % add constant of not included in x

end

[n,k] = size(x);  % sample size - n, number of explan vars (incl constant) - k xxi = inv(x'*x);  % Note that this is the inefficient way of calculating

                       % the inverse of x'*x, but as xxi is required later for 
                       % the calculation of bse, we are not really loosing
                       % anything

b = xxi*x'*y; res = y - x*b; rss = res'*res; ssq = rss/(n-k); s = sqrt(ssq); bse = ssq*xxi; bse = sqrt(diag(bse)); tstat = b./bse; pval = 2*(1-tcdf(abs(tstat),n-k)); ym = y - mean(y); r2 = 1 - (res'*res)/(ym'*ym); adjr2 = 1 - (n-1)*(1-r2)/(n-k); fstat = ((((ym'*ym))-(res'*res))/(k-1))/((res'*res)/(n-k)); pvalf = 1- fcdf(fstat,k-1,n-k); dw = corrcoef([res(1:end-1) res(2:end)]); dw = 2*(1-dw(2,1));

if output fprintf('===========================================================\n'); fprintf('===== Regression Output ==================================\n'); fprintf('Obs used = %4.0f, missing obs = %4.0f \n',n,(ninit-n)); fprintf('Rsquared = %5.4f \n',r2); fprintf('adj_Rsq = %5.4f \n',adjr2); fprintf('===== Estimated Model Parameters ==========================\n'); fprintf('= Par se(Par) t(Par) pval ==================\n'); format short; disp([b bse tstat pval]); fprintf('===== Model Statistics ====================================\n'); fprintf(' Fstat = %5.4f (%5.4f)\n',[fstat;pvalf]); fprintf(' standard error = %5.4f\n',sqrt(ssq)); fprintf(' RSS = %5.4f\n',rss); fprintf(' Durbin-Watson = %5.4f\n',dw); fprintf('===========================================================\n'); end temp = 2;<\source>