In your role as an economic analyst you have been asked the following question:
• How much does education affect wage rates?
The Excel data file (wage) contains 100 observations for each of the following variables:
|
Variable
|
Label
|
|
wage
|
Earnings per hour
|
|
ln_wage
|
The log of earnings per hour
|
|
educ
|
Years of education
|
|
educ2
|
Years of education squared
|
Instructions:
Conduct a simple linear regression analysis to examine the relationship between ‘education' (the independent variable) and ‘wage' (the dependent variable). Using the Excel data file, prepare a 2000 word report using the following structure:
• Purpose
• Background
• Method
• Results
• Discussion
• Recommendations
In preparing your report you must address the following questions:
(a) Obtain summary statistics and histograms for the variables WAGE and EDUC. Discuss the data characteristics.
(b) Estimate the linear regression WAGE = β1 + β2EDUC + ε and interpret the slope.
(c) Calculate the residuals and plot them against EDUC. Are any patterns evident and, if so, what does this mean?
(d) Estimate the quadratic regression WAGE = α1 + α2EDUC2 + ε and interpret the results. Estimate the marginal effect of another year of education on wage for a person with 12 years of education, and for a person with 14 years of education. Compare these values to the estimated marginal effect of education from the linear regression in part (b).
(e) Construct a histogram of ln(WAGE). Compare the shape of this histogram to that for WAGE from part (a). Which appears to be more symmetric and bell-shaped?
(f) Estimate the log-linear regression ln(WAGE) = γ1 + γ2EDUC + ε and interpret the slope. Estimate the marginal effect of another year of education on wage for a person with 12 years of education, and for a person with 14 years of education. Compare these values to the estimated marginal effects of education from the linear regression in part (b) and quadratic in part (d).
Your report must be submitted as a single file (maximum of 2000 words) with an appendix that contains the details of your statistical analyses.