BSc Mathematics / Course details

In this course statistical methods and concepts are put in the context of their practical, computational application with an emphasis on model selection, hypothesis testing and diagnostics. Students study a series of small projects in class and in example classes.

Unit is only available to students on the BSc/MMath Mathematics and Statistics or BSc Actuarial Science and Mathematics programmes.

This course unit aims to introduce some important statistical concepts and methodology and to provide the students with experience in the use of the statistical system R in applying them to data.  Skills in report writing are to be developed.

On completion of this unit students will be able to:

• estimate the sample correlation coefficient from a sample of bivariate data and make inferences about the true population value,
• formulate a simple linear regression model and use least squares to estimate the parameters,
• to carry out appropriate goodness-of-fit tests to assess distributional assumptions about sample data,
• to make inferences about the characteristics of an underlying bivariate distribution when the data is categorical,
• use the statistical software R to explore and interpret data using graphical presentations, data summaries,  model fitting,  confidence intervals and test statistics,
• to be able to use R to conduct simple Monte Carlo experiments to estimate parameter values and the sampling distribution of their estimators,
• to present informatively and discursively the results of computations arising from data analysis.

Exploratory data analysis (3 lectures) Data collection and presentation, Organisation of data analysis in R.

Correlation (3 lectures)  Sample correlation coefficient: numerical properties and interpretation, Estimation of population correlation and test for zero correlation, Rank correlation.

Linear regression (5 lectures) Simple linear regression, Multiple regression, Inference and diagnostics, Transformations of predictor and response variables.

Discrete data analysis (3 lectures) Discrete data; univariate probability models, Chi-squared goodness-of-fit test for univariate data;  bivariate discrete data and probability models, testing independence, testing the homogeneity hypothesis.

Monte Carlo Integration (1 lecture)

Assessing Goodness-of-Fit (7 lectures) The cumulative distribution function (cdf); distribution quantiles; sample order statistics and their properties; the probability integral transformation; the empirical cdf; empirical quantile function; quantile-quantile plots, simulating the sampling distribution of a statistic; Kolmogorov-Smirnov goodness-of-fit test.

100% coursework based on three take-home projects worth 30%, 30% and then 40%.

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturers, for example during the lecturers’ office hours.

The independent study hours will normally comprise the following. During each week of the taught part of the semester:

• You will normally have approximately 60-75 minutes of video content. Normally you would spend approximately 2-2.5 hrs per week studying this content independently
• You will normally have exercise or problem sheets, on which you might spend approximately 1.5hrs per week
• There may be other tasks assigned to you on Blackboard, for example short quizzes or short-answer formative exercises
• In some weeks you may be preparing coursework or revising for mid-semester tests

Together with the timetabled classes, you should be spending approximately 6 hours per week on this course unit.

The remaining independent study time comprises revision for and taking the end-of-semester assessment.

The above times are indicative only and may vary depending on the week and the course unit. More information can be found on the course unit’s Blackboard page.