Refer to the Wage data, which report information on annual wages for a sample of 100 workers. Also included are variables relating to industry, years of education, and gender for each worker. Determine the regression equation using annual wage as the dependent variable and years of education, gender, years of work experience, age in years, and whether or not the worker is a union member.

a. Write out the regression equation. Discuss each variable.

b. Determine and interpret the R2 value.

c. Develop a correlation matrix. Which independent variables have strong or weak correlations with the dependent variable? Do you see any problems with multicollinearity?

d. Conduct a global test of hypothesis on the set of independent variables. Interpret your findings. Is it reasonable to continue with the analysis or should you stop here?

e. Conduct a test of hypothesis on each of the independent variables.

Would you consider deleting any of these variables? If so, which ones?

f. Rerun the analysis deleting any of the independent variables that are not significant. Delete the variables one at a time.

g. Develop a histogram or a stem-and-leaf chart of the residuals from the final regression equation. Is it reasonable to conclude that the normality assumption has been met?

h. Plot the residuals against the fitted values from the final regression equation. Plot the residuals on the vertical axis and the fitted values on the horizontal axis.