You have three variables Y, X1, X₂. First you regress (OLS) Y on X₁ and X₂ to get the regression coefficients corresponding to X₁ and X₂ as b₁ and by respectively. Then you also regress (OLS) Y on X₁ and X₁ + X₂ to get the regression coefficients corresponding to X₁ and X₁ + X₂ as c₁ and c₂ respectively. Which of the following statements is correct? A. There is no need to run the second regression; c₁ and c₂ can be derived from b₁ and b₂ directly B. It is incorrect to run the second regression; it will not give an unbiased esti- mator C. It is better to run the first regression; Sum of Square of Residuals in the first regressions will be smaller than that of the second regression D. It is incorrect to run the second regression, the error term will be correlated with independent variables 44. Suppose we run OLS regression: Y₁ = a + ßX₁ + €į, where notations have their usual meaning. After this we get an estimate of Y; = â + BX;. Now we regress (OLS) Y; on Y. Estimated coefficient of Y; is . Which of the following is correct? A. = â B. = 3 C. =0 D. =
