Suppose the true regression model is given by (4-8). The result in (4-10) shows that if either
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Suppose the true regression model is given by (4-8). The result in (4-10) shows that if either P1.2 is nonzero or β2 is nonzero, then regression of y on X1 alone produces a biased and inconsistent estimator of β1. Suppose the objective is to forecast y, not to estimate the parameters. Consider regression of y on X1 alone to estimate β1 with b1 (which is biased). Is the forecast of y computed using X1b1 also biased? Assume that E[X2 | X1] is a linear function of X1. Discuss your findings generally. What are the implications for prediction when variables are omitted from a regression?
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If the regression model is y X 1 1 X 2 2 and y is regressed on X 1 alone then Eb 1 1 P 12 2 The prediction will be y X 1 b 1 The prediction error will ...View the full answer
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