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?

Collective bargaining provides for a representative of employees to negotiate with a representative of management over labor issues including wages.true or false?

True or false: a fitted model with more predictors will necessarily have a lower training set error than a model with fewer predictors.

The gilbert instrument corporation is considering replacing the wood steamer it currently uses to shape guitar sides. the steamer has 6 years of remaining life. if kept,the steamer will have depreciaiton expenses of $650 for five years and $325 for the sixthyear. its current book value is $3,575, and it can be sold on an internet auction site for$4,150 at this time. if the old steamer is not replaced, it can be sold for $800 at the endof its useful life. gilbert is considering purchasing the side steamer 3000, a higher-end steamer, whichcosts $12,000 and has an estimated useful life of 6 years with an estimated salvage value of$1,500. this steamer falls into the macrs 5-year class, so the applicable depreciationrates are 20.00%, 32.00%, 19.20%, 11.52%, 11.52%, and 5.76%. the new steamer is fasterand allows for an output expansion, so sales would rise by $2,000 per year; the newmachine's much greater efficiency would reduce operating expenses by $1,900 per year.to support the greater sales, the new machine would require that inventories increase by$2,900, but accounts payable would simultaneously increase by $700. gilbert's marginalfederal-plus-state tax rate is 40%, and its wacc is 15%.a. should it replace the old steamer? b. npv of replace = $2,083.51