Researcher A regresses y on a constant and on x, obtaining OLS estimates a (intercept) and b (slope) and residual vector e. Researcher B, however, regresses y on a constant, on x, and on z, obtaining OLS estimates ,, and as the respective coefficient estimates, and as residuals. Explain in detail under what circumstances the following could be true. (a) b= (b) i=1ni2i=1nei2 (c) b is statistically significant at the 5% level yet is not. (d) is statistically significant at the 5% level yet b is not. Researcher A regresses y on a constant and on x, obtaining OLS estimates a (intercept) and b (slope) and residual vector e. Researcher B, however, regresses y on a constant, on x, and on z, obtaining OLS estimates ,, and as the respective coefficient estimates, and as residuals. Explain in detail under what circumstances the following could be true. (a) b= (b) i=1ni2i=1nei2 (c) b is statistically significant at the 5% level yet is not. (d) is statistically significant at the 5% level yet b is not