1. Say that you want to estimate the "ceteris paribus" relationship between a dependent variable, y, and an independent variable, x1, in a regression framework with two control variables, x2 and X3. Let , be the estimate of the coefficient on x, in the simple regression of y on x1. Let , be the estimate of the coefficient on x, in the multiple regression of y on x1, X2, and X3. a. If x1 is highly correlated with X2 and x3 in the sample, and X2 and X3 have large partial effects on y, would you expect S, and , to be similar or very different? Explain. b. If x1 is almost uncorrelated with X2 and X3, but X2 and x3 are highly correlated, will B, and , tend to be similar or very different? Explain. c. If x1 is highly correlated with X2 and X3, and X2 and X3 have small partial effects on y, would you expect se(B, ) or se(B,) to be smaller? Explain. d. If x1 is almost uncorrelated with X2 and X3, X2 and x3 have large partial effects on y, and x2 and x3 are highly correlated, would you expect se(B,) or se(B1) to be smaller? Explain