Question

How should I write a regression that models the wage as a function of: 1. S...

How should I write a regression that models the wage as a function of:
1. S - schooling
2. EXP - years of experience where the marginal effect of experience may have diminishing returns on the wage.
3. MALE - gender
4. Race - 3 categories: ETHWHITE, ETHBLAC, ETHHISP.
5. Region - 4 categories: REGNE, REGNC, REGS, REGW

A. WAGE = b1 + b2S +b3EXP + b4EXP2 +b5ETHBLAC + b6ETHHISP + b7ETHWHITE + b8REGNE + b9REGW + b10REGNC +b11REGS

B. WAGE = b1 + b2S +b3EXP + b4EXP2 +b5ETHBLAC + b6ETHHISP + b7REGS + b8REGNE + b9REGW

C. WAGE = b1 + b2S +b3EXP + b4EXP2 +b5ETHBLAC + b6ETHHISP + b7REGS + b8REGNE + b9REGW + b10REGS

D. WAGE = b1 + b2S +b3EXP +b5ETHBLAC + b6ETHHISP + b7REGS + b8REGNE + b9REGW

I believe that the answer is B, but would like some clarification as to why

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Answer #1

S is a continuous variable, it'll have one slope coefficient B2.

As experience has diminishing effect, it will be best represented with a polynomial of power 2 (EXP2).

The categorical variables will have coefficients each which take values 0 or 1.

All of these are satisfied in option B. Therefore, B is the correct option.

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