An economist is interested in the following regression model that shows how the age of workers affects their earnings (wage is measured here by hourly pay), where e is the regression error: WAGE = a+b,AGE + b,AGE +e (1) a) What types of variable are WAGE and AGE, i.e. are they qualitative or quantitative; nominal, ordinal, interval or ratio? [10%] b) Discuss why the quadratic term is useful in this regression. If the values of the regression coefficients are & =0.5080 and b, =-0.0045 , interpret these values and [15%] use them to determine the age at which wages are maximised. c) Describe what dummy variables are and discuss why they are useful. [15%] d) How can the economist use a dummy variable to see whether wages are different for men and women? To do this, define an appropriate dummy variable, show how it can be introduced into regression model (1) and interpret what a positive or negative coefficient on the dummy variable would mean for the wages WAGE = a+b,AGE + b, AGE +e (1) a) What types of variable are WAGE and AGE, i.e. are they qualitative or quantitative; nominal, ordinal, interval or ratio? [10%] b) Discuss why the quadratic term is useful in this regression. If the values of the regression coefficients are =0.5080 and b, =-0.0045, interpret these values and [15%] use them to determine the age at which wages are maximised. c) Describe what dummy variables are and discuss why they are useful. [15%] d) How can the economist use a dummy variable to see whether wages are different for men and women? To do this, define an appropriate dummy variable, show how it can be introduced into regression model (1) and interpret what a positive or negative coefficient on the dummy variable would mean for the wages [15%] of men and women. e) The educational background of workers also has an influence on wages. Define a dummy variable that will help to identify whether a worker has a University degree, introduce it into the regression model created in part (d) above and discuss how the economist can interpret the coefficient in terms of the wages of those with and without degrees. [15%] f) Show how the economist can make use of an interaction variable to analyse whether the effect of having a degree on wages is different for male and female workers. To do this, define the interaction variable, introduce it into the regression that was created in part (e) above and discuss how the economist should interpret the coefficient. [15%] g) Suggest two other variables you could include in a wage regression that might help to explain the determinants of workers' wages? For each of your suggestions, show how the variable could be defined. [15%]