$5.$ Predicted level value of the dependent variable using the smearing estimate

Suppose a data set of $177$ observations $($NN$=177)$ was analyzed using OLS to examine the factors influencing the salary of CEOs. The regression results are as follows, with standard errors in parentheses:

lsalary$=4\mathrm{.}7(0\mathrm{.}35)+0\mathrm{.}15(0\mathrm{.}06)$lsales$+0\mathrm{.}10(0\mathrm{.}04)$lmktval$+0\mathrm{.}010(0\mathrm{.}003)$ceotenlsalary$^=4\mathrm{.}7(0\mathrm{.}35)+0\mathrm{.}15(0\mathrm{.}06)$lsales$+0\mathrm{.}10(0\mathrm{.}04)$lmktval$+0\mathrm{.}010(0\mathrm{.}003)$ceoten

where

lsalarylsalary$=$ log of salary, measured in thousands of dollarslsaleslsales$=$ log of sales, with sales measured in millions of dollarslmktvallmktval$=$ log of market value of firm, with market value measured in millions of dollarsceotenceoten$=$ years as CEO at current firm

nn$=177$R$2$R$2=0\mathrm{.}331$$0$$0^=$ n$1$i$=1$nexp$($ui$)$n$1$i$=1$nexpui$^=1\mathrm{.}35$

The predicted log of salary for a CEO of a firm with $$4$ billion in sales $($or $$4,000$ million$)$ and a $$11$ billion market value $($or $$11,000$ million$),$ who has been the CEO for $11$ years, is $6\mathrm{.}2862.$

Suppose you would like the predicted salary, and not the predicted log salary, for a CEO of a firm with $$4$ billion in sales $($or $$4,000$ million$)$ and a $$11,000$ billion market value $($or $$11$ million$),$ who has been the CEO for $11$ years.

The predicted salary for a CEO in this scenario would be $$thousand$.$