An international management consulting firm, is interested in evaluating their management salary structure. TPF&C uses their Compensation Management Service, a multiple regression model that is used to measure both the internal and external consistency of a company's pay policies to determine whether they reflect the management's intent. The natural log of annual compensation is used as the response variable,y. A number of explanatory variables are considered, as listed below:

• x₁: Years of experience
• x₂: Years of education
• x₃: Gender (1 for man, 0 for woman)
• x₄: Number of employees supervised
• x₅: Corporate assets (millions of dollars)

A random sample of 100 executives is used to fit a model.

Output for the model using all the first-order term of all five variables, plus the interaction term betweenx₃andx₄ and the square x₁ is given below.

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 9.862e+00 9.703e-02 101.640 < 2e-16 *** x1 4.364e-02 3.761e-03 11.605 < 2e-16 *** x2 3.094e-02 2.950e-03 10.488 < 2e-16 *** x3 1.166e-01 3.696e-02 3.156 0.00217 ** x4 3.259e-04 7.850e-05 4.152 7.35e-05 *** x5 2.391e-03 4.439e-04 5.386 5.49e-07 *** I(x1^2) -6.348e-04 1.383e-04 -4.589 1.41e-05 *** x3:x4 3.020e-04 9.238e-05 3.269 0.00152 **

Residual standard error: 0.06596 on 92 degrees of freedom Multiple R-squared: 0.9401, Adjusted R-squared: 0.9355 F-statistic: 206.3 on 7 and 92 DF, p-value: < 2.2e-16

Predict the natural log of the annual compensation for a man executive with 12 years of experience, 16 years of education and 400 employees supervised in a firm with $160 million in assets