MAE 256 : Analytical Methods In Economics And Finance
Added on 2021-06-17
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MAE256 T1AssignmentStudent Name[Pick the date]
(i)The descriptive statistics (numerical summary) of the variables “ remuneration, rank and studnum” are highlighted below (Lehman and Romano, 2006):CommentRemuneration – From the descriptive statistics that capture the given sample data, it is evidentthat the average remuneration package for the Vice Chancellor is $801,270. The median value is1
slightly higher at $ 805,000 which implies that 50% of the Vice Chancellors in the given datawould have salary equal to or lower than $ 805,000. However, the mode value is still higher at $895,000. The non-coincidence of the central tendency measures is an indication that theprobability distribution in the given case would not be normal. Also, there would be presence ofnegative skew having a slight distortionary effect on the average value. The standard deviationfor the salaries is low to medium indicating that while disparities do exist they do not tend to betoo extreme. The IQR values highlights that 50% of the values i.e. from 25% to 75% would liewithin this compensation interval of about $230,000 (Fehr and Grossman, 2003).Rank – The average rank of the University in the given sample is 336.81. The median rank ishowever significantly greater at 376 which implies that 50% of the sample universities have arank lower than or equal to 376. The deviation between the median and mode values is indicativeof the presence of some universities which have a considerably low rank which is responsible fordistortion of the mean. The various measures of dispersion highlight that the dispersion in rankof the universities in the given sample is quite high considering that there are universities at boththe lower end as well as the higher end (Liberman, et. al., 2013). Studnum – The average students studying in a university are about 38,410. The average figure isclearly distorted owing to presence of universities with very high intake of students owing towhich the median value is comparatively much smaller at 29,214. Hence, the median is a betterindicator of the average number of students in a university rather than the mean. Further, themeasures of dispersion suggest that there is very high amount of dispersion that is seen in thegiven variable for the sample data provided (Harmon, 2011).(ii)Simple regression model 01remuneratioanr nk uRemuneration = dependent variable Rank = Independent variable 2
Remuneration($000's)=1032.54−(0.687∗Rank)+138.9987The intercept coefficient for the above repression is 1032.54 which tends to highlight the salary level of the Vice Chancellor when the rank is zero. Since the rank theoretically cannot be zero, the predicted value of Vice Chancellor’s remuneration cannot exceed the intercept value.Further, the slope coefficient for the above relation is negative which implies that as rankincreases by 1, there is a decrease in the remuneration of the Vice Chancellor by $687. Thuspoorer the rank of the University, the lower would be the expected remuneration of the ViceChancellor.(iii)Simple regression model by taking log-log specification 01loglogremuneratioanunr k3
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