Consider the one-variable regression model Y = Bo + B.X; + u; and sup- pose that it satisfies the least squares assumpti

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Consider The One Variable Regression Model Y Bo B X U And Sup Pose That It Satisfies The Least Squares Assumpti 1 (215.21 KiB) Viewed 27 times

Consider the one-variable regression model Y = Bo + B.X; + u; and sup- pose that it satisfies the least squares assumptions in Key Concept 4.3. Suppose that Y; is measured with error, so the data are ; = Y; + wi, where w; is the measurement error, which is i.i.d. and independent of Y; and X;. Consider the population regression Ỹ; = Bo + B1X; + vi, where v; is the regression error, using the mismeasured dependent variable, Ỹ;. a. Show that v; = U; + Wi. b. Show that the regression Ỹ; = Bo + B1X; + v; satisfies the least squares assumptions in Key Concept 4.3. (Assume that w; is inde- pendent of Y, and X, for all values of i and j and has a finite fourth moment.) c. Are the OLS estimators consistent? d. Can confidence intervals be constructed in the usual way?