ENROLMENT FOR THIS COURSE IS OPENING SOON

Collecting data is something everyone making measurements is familiar with. But knowing how to extract useful information from that data can be challenging.

A mathematical model describes the relationship between an independent variable (or variables), commonly called control or stimulus variables, and a dependent variable, commonly called a response variable. You may be used to drawing a straight line through data, or ‘adding a line of best fit’, and obtaining an equation for that line. In the world of modelling, this is known as a straight-line regression model and is the focus of this course.

There are many lines that could be drawn, arbitrarily, through a measured dataset. In school science we tended to do it ‘by eye’ with a pencil and ruler — we probably never quite drew the best possible line but managed something that looked plausible. Later, we learned to ‘add a trendline’ in spreadsheet software, and trusted that the software had drawn the appropriate line.

This course gives an introduction to how the ‘line of best fit’ is obtained. The line of best fit is a mathematical model that best describes how the dependent variable, Y, changes linearly with the input variable, X. It is obtained using an approach called ‘linear least-squares’, which selects a model so as to minimise the differences between the datapoints predicted by the model and the measured datapoints.

In the world of modelling, this is known as a ‘straight-line regression model’. In this course, we will explain how to build a straight-line regression model for a measured dataset and how to ‘solve’ that model to obtain estimates of unknown parameters, as well as to make predictions. Knowing whether or not you can trust the model you have built is also an important consideration, so this course also addresses how to validate a developed model.

This course is most relevant for metrologists, scientists, and engineers, as well as technical leaders and quality managers, who encounter measurement data in their day-to-day work and need to understand the measurement systems or experiments that generated the data or to make predictions, inferences or decisions based on the data.

No prior experience in mathematical modelling is required for this course, but a working knowledge of the following concepts is assumed:

• Standard uncertainties
• Variance and standard deviation
• Expectation
• Normal distribution
• Covariance
• What vectors and matrices are (there is a recap of how to do the fundamental matrix operations used in the course, but a general idea of what they are is assumed)

We also strongly recommend completing these e-learning courses from NPL as prerequisites for enrolment in this course:

• Introduction to Measurement and Metrology (essential)
• Introduction to Measurement Uncertainty (essential)
• Understanding Uncertainty Budgets (essential)
• Understanding and Evaluating Measurement Uncertainty (recommended)