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 Source Ss df MS = 3,000 -187.25 0.0000 = 0.1579 Adj R-squared = 0.1571 = 38.312 Number of obs F (3, 2996) Model 824541.261 3 274847.087 ProbF Residual 4397544.45 2,996 1467.80522 R-squared Total 5222085.71 2,999 1741.27566 Root MSE wage Coef. Std. Err. (95% Conf., Interval] 0392763 5.463365 0042582 .0559749 11.18 0.000 4.730172 .3739337 12.65 0.000 age sa 0476256 age 3.99698 gender23,15548 1.409948 16.42 0.000 20.39092 25.92005 cons #8.388705 7.846589-1.07 0.285-23.77395 6.996542

Explanation / Answer

A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.

Spread of the residuals for plot1)residuals Vs linear prediction and 2)residuals vs age^2 is not so random so we can say that a non-linear model is more appropriate.While plot of esiduals vs age is random so linear model is appropriate.

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