Answer to Question #161946 in Statistics and Probability for Tazbiha

Question

Consider the following regression of wages (w) on the mean years of schooling of 

workers (s) and the female share in an occupation (p):

𝑙𝑜𝑔𝑤 = 0.924 + 0.150𝑠 − 0.003𝑝

 (0.154) (0.011) (0.0001)

a) Interpret the regression coefficients carefully.

b) How much variations in wages can be explained by the two regressors?

c) Would you reject the hypothesis that workers’ mean years of schooling has no 

influences on wages across professions?

Answer 1

The Given regression equation is

$𝑙𝑜𝑔𝑤 = 0.924 + 0.150𝑠 − 0.003𝑝$

(a) On comparing the given equation with the standard regression equation $Y=\beta_0+\beta_1x_1+\beta_2x_2$

Regression coeffiecient are as follows.

We get $\beta_1=0.15, \beta_{2}=-0.003$

(b) As the coffiecient $\beta_2$ is very small So The wage $w$ is not too much influenced and on changing other coeffecient. The wage w is increased rapidly.

(c) No. The mean year of schooling also affects the wage of the worker since It has a positive regression coefficient. On a small change in mean year of schooling can change the wages.