4. [15 Marks] Data are collected on 3000 workers, their wages, ages and genders.

Question

4. [15 Marks] Data are collected on 3000 workers, their wages, ages and genders. The unit of wage is measured in thousands of pounds and the workers ages are measured in years. The gender equals 1 if the worker is male. Wages are regressed on age, age square (denoted as age.sq in the regression) and gender. The results can be seen listed in the table below. . reg wage age_sq age gender Number of obs F (3, 2996) 3 3,000 187.25 0.0000 0.1579 Adj R-squared 0.1571 38.312 Source sS df MS Model 824541.261 3 274847.087 Prob>F Residual 4397544.452,996 1467.80522 R-squared Total 5222085.71 2,999 1741.27566 Root MSE wage Coef. Std. Err. (95% conf. Interval] age sq0476256 .0042582 -11.18 0.000-.0559749 .0392763 .99698 5.463365 gender 23.15548 1.409948 16.42 0.00020.39092 25.92005 cons -8.388705 7.8465891.07 0.28523.77395 6.996542 age 4.730172 .3739337 12.65 0.000 (a) [5 Marks) At what age does the salary reach its peak?

Explanation / Answer

Here the quadratic regression line is

Wages = -8.3887 + 4.730172 * age - 0.0476256 * age2 + 23.155548 * Gender

so wages will be highest when

d(Wages)/ d(age) = 0

so differentiating the linear regression with respect to age.

4.730172 - 2 * 0.0476256 * age = 0

age (maximum) = 4.730172 /(2 * 0.0476256) = 49.66 years

so at the age of 49.66 years the wages shall be maximum.

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