Present descriptive statistics of the variables remuneration

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Reference no: EM131971077

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?

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Reference no: EM131971077

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Reviews

len1971077

5/5/2018 1:21:31 AM

UNIT NAME Analytical method in economies and finance. Code MAE256. I have attached rubrics, instruction and data file. Word Limit: 1500 words excluding appendices, figures and tables. This is an INDIVIDUAL Assignment. We strongly discourage plagiarism, as it will be penalized as much as possible. However, it is not collusion if you discuss the questions with other students, but you need to submit your own original work. Note that we may request you come in and explain your assignment in person if we feel your assignment is too similar to another students’ work.

len1971077

5/5/2018 1:21:25 AM

This assignment in total has 30 marks that correspond to 20% of your final grade. Once completed, you will need to submit your ‘Microsoft Word’ document via CloudDeakin. You must submit a single file only that contains a cover page with your name and student ID. If you are submitting your assignment as a PDF document, please ensure that you are also submitting as a Word document to enable word counting. Please ensure the Word document is self-contained (i.e. all your tables and figures should be in the word document). You will not need to submit a hardcopy.

len1971077

5/5/2018 1:21:19 AM

Provides statistical output of descriptive statistics of the three variables, remuneration, rank and studnum. Also, provides excellent explanations of means and measures of dispersion of the variables. Provides the estimation of the sample regression function and writes the estimated model. Provides correct interpretation of the estimates of the regression parameters. Provides the sample regression function or the estimated log-log model. Correctly interprets the estimates of log(rank) and explains whether the sign of the estimated coefficient complies with expectations.

len1971077

5/5/2018 1:21:14 AM

Provides the sample regression function, i.e., the estimated model of remuneration on the two independent variables. Provides excellent interpretation of the goodness of fit of the models and compares with that in the other model as stated in the question. Provides the sample regression function, i.e., the estimated log-log model. Correctly interprets the elasticity of remuneration with respect to studnum and correctly tests the statistical significance of the elasticity at the stated level of significance.

len1971077

5/5/2018 1:21:08 AM

Provides correct and full details of the test of significance of rank on the dependent variable remuneration. Provides the sample regression function, i.e., the estimated model after including the additional independent variables, grademp and gradstudy. Provides full and correct details of the tests of single and joint significance of these two variables at the given levels of significance. Provides correct and full details of the overall test of significance at the specified level of significance. Provides the correctly specified sample regression function, i.e., the estimated model. Provides interpretation of the estimate of the relevant coefficient and details of the test of significance of the relevant variable at the specified level of significance. Provides clearly the inference drawn based on the test result.

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