## Analysing Non-Linear Data - This page is in the process of development

Analysing a **linear **(straight-line) relationship is relatively straight-forward using the techniques of linear regression and calculations of slope and intercept (see analysing a straight line).

However, the **method required **to analyse a **non-linear **data relationship depends on the **particular form of that relationship**.

It is important to be aware of the most common methods available so that it is possible to assess the best choice of method for a given problem. In some cases it is necessary to use a combination of more than one method.

**Common methods used to analyse non-linear data:**

This section provides short video clips, tutorials and examples - browse the different methods to find the one that applies to your particular problem.

**1. Linearise the data using a theoretical relationship for the data**

- Background notes on using logarithms with data variables

- Log-lin plots for exponential data, e.g.
*N*_{t }=*N*_{0}e^{kt}

- Use of growth/decay factors, e.g. half-life, decimal reduction time, etc

- Log-log plots for power relationships, e.g.
*E*=*AT*^{x}

- Change of variable plots for a variety of functions, e.g.
*P*=*nRT / V*

**2. Perform a numerical analysis using a theoretical relationship for the data**

- Least squares regression using Solver in Excel

Solver is a powerful analysis tool, available within Excel, capable of performing many functions.

- Statistical analysis software

**3. Perform a linear analysis on a selected section of the data **

- Avoids curvature and non-linearity due to second order effects

**4. Case studies**

- Common examples, e.g. Arrhenius equation, Beerâ€™s law

- Complex analytical problems

**Uncertainties / errors in non-linear regression:**

This section develops the handling of experimental errors, which can become distorted in non-linear analysis.

- Calculation of uncertainties in linear and non-linear regression
- Weighted least squares regression using Solver in Excel

**QVA Tutorials (questions + video answers):**

These short quizzes (5 - 10 questions each, with video feedback) provide a quick way of checking and increasing your knowledge and real understanding of the different forms of analysis.

- Choosing the correct method of analysis (
**Example quiz**) - Interpreting the results of common methods
- More complicated problems