The true relationship between y and three explanatory variables x can be written as follows:

y bob1xı + b2x23x3 u

however, you do not have access to the variables x1 and x2 in your data, so you estimate:

y = b3x3 + n

the relationship between the omitted variables and x3 can be expressed as follows:

601x3 + e3 x1 x2 = wo +w1x3 + €2

a) derive the expression for bo* and b3*
b) suppose that b1< 0 and b2> 0. now suppose that x3 is positively correlated with both x1 and x2. is b3 upward or downward biased. explain
c) suppose that y is income, xı is iq, x2 is work ethic, and x3 is years of education. argue that the estimate b3* is upward or downward biased using the expression you derived in part a)
d) what are two reasons why iq and work ethic might be omitted from the regression?