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MAE256 Assignment Details

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Question:

(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.

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

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

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:

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, 

(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.

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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