MAT013 Coursework

Deadline: 2015-05-07 (7th of May) at 0900

Instructions

The outputs of this coursework will be:

• A written report describing your code (SAS and R) to be handed in to Joanna Emery.
• An appendix containing a commented version of your code (SAS and R) to be handed in to Joanna Emery.
• A file containing the required SAS code. Name this file SAS-lastname-STUDENTNUMBER (eg. SAS-Knight-123456) and email it to Joanna Emery with MAT013 as the subject. Note that all operations needed to complete the coursework should be included in the SAS code.
• A file containing the required R code. Name this file R-lastname-STUDENTNUMBER (eg. R-Knight-123456) and email it to Joanna Emery with MAT013 as the subject. Note that all operations needed to complete the coursework should be included in the R code.

Coursework

1. Using both SAS and R (in other words attempt this question using SAS and then using R):

   Write code (in SAS: a macro, in R: a function) that will reproduce a mathematical procedure covered in MAT001 or MAT002. Clearly document this procedure in your report.

   [20]

2. A perfect number is a natural number that is equal to the sum of its divisors (excluding itself). For example \(1,2,4,7\) and \(14\) divide \(28\) and \(28=1+2+4+7+14\).

   Write code in SAS that allows one to write to a csv file a data set with all natural numbers less than a given parameter \(N\) as well as a boolean variable indicating if the number is perfect or not. For example, for \(N=6\) the csv file would contain the following:

    1, False
    2, False
    3, False
    4, False
    5, False
    6, True
   

   [25]

3. Using R:

   Consider the data files Admissions.csv and Discharges.csv which contain admission and discharge data for two categories of patients.

   • Obtain distributions of the overall inter arrival rates (reciprocal of the time between arrivals).
   • Obtain distributions of the overall service rate (reciprocal of the length of stay).
   • Visualise and discuss the differences of arrival and service rates between patient categories.

   [25]

4. Using SAS or R:

   Consider the data set personality_performance.csv which contains data for student personality and performance in two separate subjects.

   The personality traits are measured according to the following 6 dimensions:

   • Openness-A
   • Openness-B
   • Conscientiousness
   • Extraversion
   • Agreeableness
   • Neuroticism

   Answer the following questions:

   1. Obtain summary statistics for each personality trait. [5]
   2. Obtain a suitable visualisation for the personality traits. [5]
   3. Identify a measure that indicates performance in subject 1 relative to subject 2 (‘How much better/worse students did in subject 1 relative to subject 2’). [10]
   4. Explore and attempt to indicate parameters that influence:
      • Performance in subject 1
      • Performance in subject 2
      • Relative performance

   [10]