Suppose data are generated by where E$[$u $|$ educ$]=0.$

wagei $=\backslash$beta $0+\backslash$beta $1$educi $+$ ui$,$

$($i$)$ Provide an expression for E$[$wage $|$ educ$]$ that references $\backslash$beta $0$ and $\backslash$beta $1.$ Potential Solution: E$[$wage $|$ educ$]=\backslash$beta $0+\backslash$beta $1$educ.

$($ii$)$ Suppose an analyst has data from workers with $9$ years of education and with $11$ years of educa$-$

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tion. The analyst calculates the average wage for each group, finding E$[$wage $|$ educ $=9]=14$ and $$

E$[$wage $|$ educ $=11]=16.$ Using these estimates, provide an estimate of $\backslash$beta $1.$