Consider the one-variable regression model Yi = βo + β1X1i+ Ui, and suppose that it satisfies the classical regression assumptions. Suppose that Yi is measured with error, so that the data are Yi = Yi + wi, where wi, is the measurement error which is i.i.d. and independent of Xi and Ui. Consider the population regression Yi = βo + β1X1i+ Vi, where Vi is the regression error using the measurement error in dependent variable, Yi.
a. Show that Vi = Ui + wi.
b. Show that the regression Yi = βo + β1X1i+ Vi satisfies the assumptions of the classical regression.
c. Are the OLS estimators consistent?
d. Can confidence intervals be constructed in the usual way?
e. Evaluate these statements: "Measurement error in the X's is a serious problem. Measurement error in Y is not."