Suppose data=(ui,vi) , i= 1,...n . and we want to estimate theta=corr(ui,vi) . My question is , does it matter if the u and v pair are obtained from some population or calculated for example from the following models;

ui=yhat1 ;    yhat1=a0+a1X1;

vi=yhat2;    yhat2= b0+b1X1+b2X2;

i.e. fitted values from two regression models with the same response but different predictors.In fact I would like to know , do I need to estimate the model and the use the result for bootstrapping, or I can just use output of the models and sample them for bootstrapping.In other words, should the bootstrapping procedure contains the estimation of the models or not?

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