12. Predicted level value of the dependent variable using the smearing estimate
Suppose a data set of 177 observations (N = 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:
lsalaryˆ=4.7(0.35)+0.15(0.06) lsales+0.10(0.04) lmktval+0.010(0.003) ceoten
where
lsalary = log of salary, measured in thousands of dollarslsales = log of sales, with sales measured in millions of dollarslmktval = log of market value of firm, with market value measured in millions of dollarsceoten = years as CEO at current firm
n = 177R2 = 0.331α0ˆ = n−1∑i=1nexp(uiˆ) = 1.35
The predicted log of salary for a CEO of a firm with $7 billion in sales (or $7,000 million) and a $12 billion market value (or $12,000 million), who has been the CEO for 10 years, is .
Suppose you would like the predicted salary, and not the predicted log salary, for a CEO of a firm with $7 billion in sales (or $7,000 million) and a $12,000 billion market value (or $12 million), who has been the CEO for 10 years.
The predicted salary for a CEO in this scenario would be thousand.