An analyst considers a linear relationship Yi = 0 + 1Xi + ui , and assumes E[ui | X] = 0. Suppose that (Yi , Xi) have a joint distribution with the following properties: E[Y | X = 0] = 2, E[Y | X = 2] = 3. In other words, conditional on X = 0, the mean of Y is 1, and conditional on X = 2, the mean of Y is 3. i. Suppose the analyst has a sample of independent and identically distributed observations of the pair (Yi , Xi). The analyst regresses Yi on Xi and obtains the OLS slope coefficient, 1. (Yi is the regressand, and Xi is the regressor.) Using the information above, what do you think 1 should be close to if the sample size is very large?

Problem 2 An analyst considers a linear relationship Yi = Bo + BIXit Wi, and assumes Elui | X] = 0. Suppose that (Yi, Xi) have a joint distribution with the following properties: EY | X = 0] = 2, E[Y [ X = 2] = 3. In other words, conditional on X = 0, the mean of Y is 1, and conditional on X = 2, the mean of Y is 3. i. Suppose the analyst has a sample of independent and identically distributed observations of the pair (Yi, Xi). The analyst regresses Y; on Xi and obtains the OLS slope coefficient, B1. (Y; is the regressand, and Xi is the regressor.) Using the information above, what do you think B1 should be close to if the sample size is very large