Introduction

Establishing and understanding the relationship between quantities are principal goals in the physical sciences. As examples, we might be keen to know how the:

• size of a crystal depends on the growth time of the crystal;

• output intensity of a light emitting diode varies with the emission wavelength;

• amount of light absorbed by a chemical species depends on the species concentration;

• electrical power supplied by a solar cell varies with optical power incident on the cell;

• viscosity of an engine oil depends upon the temperature of the oil;

• rate of flow of a fluid through a hollow tube depends on the internal diameter of the tube.

Once an experiment is complete and the data presented in the form of an x–y graph, an examination of the data assists in answering important qualitative questions such as: Is there evidence of a clear trend in the data? If so, is that trend linear, and do any of the data conflict with the general trend? A qualitative analysis often suggests which quantitative methods of analysis to apply.

There are many situations in the physical sciences in which prior knowledge or experience suggests a relationship between measured quantities. Perhaps we are already aware of an equation which predicts how one quantity depends on another. Our goal in this situation might be to discover how well the equation can be made to ‘fit’ the data.