Suppose that you are interested in estimating the ceteris paribus relationship between y and x₁. For this purpose, you can collect data on two control variables, x2 and x3. (For concreteness, you might think of y as final exam score, x₁ as class attendance, x2 as GPA up through the previous semester, and x3 as SAT or ACT score.) Let B₁ be the simple regression estimate from y on x₁ and let ẞ, be the multiple regression estimate from y on x1, x2, 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 B₁ and B₁ 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 B₁ and ẞ, 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[B₁] or se[B₁] 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[B₁] or se[B₁] to be smaller? Explain.