Assignment - Regression Models using Cross Section Data

Use the data set in DATA_ASSIGNMENT contains information on the cost of Vice Chancellors' remuneration packages in Australia. The variable remuneration is the annual remuneration in 2013 in thousands of dollars, rank is the university's rank from the Times Higher Education World University Rankings 2013-2014, studnum is the total number of students enrolled at the university, gradstudy is the % graduates in full-time study and grademp is the % graduates in full-time employment. The Times Higher Education World University Rankings is described as being among the most influential international university rankings.

(i) Present the descriptive statistics of the variables remuneration, rank and studnum. Comment on the means and measures of dispersion of the variables.

(ii) Estimate the following simple regression model of remuneration on rank.

remuneration = β₀ + β₁rank + u

Write down the sample regression function and interpret the coefficient estimates.

(iii) Now estimate the following simple regression model with a log-log specification,

log(remuneration) = β₀ + β₁log(rank) + u

Report your regression results in a sample regression function. Interpret the estimated coefficient of log(rank). Is the sign of this estimate what you expect it to be?

(iv) A model that relates the remuneration to the university's ranking and number of students is:

remuneration = β₀ + β₁rank + β₂ studnum + u

Report your results in a sample regression function. What can you conclude regarding comparison of the goodness of fit of this regression model versus the regression model in part (ii)?

(v) Now re-estimate the equation in (iv) but using the log of each variable. That is, estimate the model,

log(remuneration) = β₀ + β₁log(rank) + β₂ log(studnum) + u

Report the results in a sample regression function. What is the estimated elasticity of remuneration with respect to studnum? Test whether it is statistically significant at 1% level.

(vi) Using the estimated model in (v), test whether rank has a negative effect on remuneration at 1% level of significance.

(vii) Add the variables grademp and gradstudy to the log-log equation in (v) and estimate the following model.

log(remuneration) = β₀ + β₁log(rank) + β₂ log(studnum) + β₃ grademp + β₄ gradstudy + u

Test whether either of these variables grademp and gradstudy are individually significant at 1% level? Test if they are jointly significant at 5% level?

(viii) Test the overall significance of the model you estimated in part (vii) at 1% level of significance.

(ix) Suppose you want to test whether the Vice Chancellors of the universities located in Victoria are paid higher compared to those in other states. Specify a regression model which will enable you to test such a hypothesis using the model in (v) as a base. Report your results in a sample regression function and perform the hypothesis test at 5% level of significance. What would you infer?

Attachment:- Assignment Files.rar