An economist decides to examine the standard of living of workers in a developing country. A survey was conducted and a representative sample of 2166 observations was obtained. He is particularly interested to determine the relationships among the following variables:
Wage - Weekly wage of worker (in dollar amount, $)
Female - 1 if worker is female. 0 if worker is male
Age - Age of worker (in years)
Education variables:
Lowedu - 1 if worker's highest qualification level is primary, 0 if otherwise
Interedu - 1 if worker's highest qualification level is secondary, 0 if otherwise
Highedu - 1 if worker's highest qualification level is tertiary, 0 if otherwise
Temp - 1 if worker holds a temporary work permit, 0 if otherwise
Training - 1 if worker has been through some form of training, 0 if otherwise
A partial view of the data is provided below. The full set of data is given in worksheet 'raw_data' of the data file. There are two parts to question 3, concerning simple regression and multiple regression.
A. Simple Regression:
(a) Obtain a scatter plot of Wage against Age. Is there a relationship between Wage and Age? If so, is the direction what you would expect?
(b) If you were to conduct a regression model, what will be your dependent variable and explanatory variable?
(c) Fit a regression model based on your answer in part (b). Be sure to show your Excel summary output and state the estimated equation.
(d) Interpret the estimated coefficients. Does the sign of each make sense?
(e) Using a 5% level of significance, perform a test to determine whether Age has a significant effect on Wage. Be sure to state your null and alternative hypotheses, and ALL other relevant information.
(f) Now create a new variable ln(Wage) where ln(Wage) is the natural log of Wage. Now graph a scatter plot of ln(Wage) against Age. Is there a relationship between In(Wage) and Age? Compare your answer with part (a) and identify the differences.
(g) Briefly explain how does using ln(Wage) change the relationship between Wage and Age, if any?
(h) Now fit a regression model based on ln(Wage) and Age. Be sure to show your Excel summary output and state the estimated equation.
(i) Interpret the estimated coefficients. Does the sign of each make sense?
(j) Compare your model in part (c) and part (h), which model performs better? What measures do you use to assess your model?
Note: In answering parts of the questions where statistical inference is required, you must include some or all of the following (as appropriate) for full credit:
1. the reason for using a particular formula or distribution
2. the null and alternative hypotheses
3. the critical value(s) used
4. the level of significance
5. the test statistics and its distribution employed in a test,
6. the decision rule, and
7. the conclusion.
Attachment:- RawData.rar