Consider a regression with two variables, $in$ which $x_{1i}is$ the variable $of$ interest and $x_{2i}$

$is$ the control variable. Conditional mean independence requires:

$a.E(u_i|x_{1i},x_{2i})=E(u_i|x_{2i})$

$b.E(u_i|x_{1i},x_{2i})=E(u_i|x_{1i})$

$c.E(u_i|x_{1i})=E(u_i|x_{2i})$

$d.E(u_i)=E(u_i|x_{2i})$

Imperfect multicollinearity:

$a.$ implies that $it$ will $be$ difficult $to$ estimate precisely one $or$ more $of$ the partial

effects using the data $at$ hand.

$b.$ violates one $of$ the four Least Squares assumptions $in$ the multiple regression

model.

$c.$ means that you cannot estimate the effect $ofat$ least one $of$ the $xsonY.$

$d.$ suggests that a standard spreadsheet program does not have enough power $to$

estimate the multiple regression model.