Assume that you had found correlation of the residuals across observations.This may happen because the regressor is ordered by size.Your regression model could therefore be specified as follows:
Yi = β0 + β1Xi + ui
ui = ρui-1 + vi;

Question

Assume that you had found correlation of the residuals across observations.This may happen because the regressor is ordered by size.Your regression model could therefore be specified as follows:
Yi = β0 + β1Xi + ui
ui = ρui-1 + vi;  < 1.
Furthermore,assume that you had obtained consistent estimates for β0,β1,ρ.If asked to make a prediction for Y,given a value of X(= Xj)and  j-1,how would you proceed? Would you use the information on the lagged residual at all? Why or why not?

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The Answer of Assume that you had found correlation of the residuals across observations.This may happen because the regressor is ordered by size.Your regression model could therefore be specified as follows:
Yi = β0 + β1Xi + ui
ui = ρui-1 + vi;  < 1.
Furthermore,assume that you had obtained consistent estimates for β0,β1,ρ.If asked to make a prediction for Y,given a value of X(= Xj)and  j-1,how would you proceed? Would you use the information on the lagged residual at all? Why or why not?

Assume That You Had Found Correlation of the Residuals Across