Relationships

It is important to be able to identify relationships in data. This allows trends to be recognised and may allow for predictions to be made. Relationships in data can be identified in several ways.

Scatter graphs

Scatter graphs show the relationship between two sets of data, eg number of tourists and number of tourist facilities or weight and height.

A scatter graph showing a positive correlation has points close together, increasing along both axes.

A line of best fit or trend line can be added to the scatter graph to show the relationship between the two variables. When drawing a line of best fit or trend line it is important to have as many points as possible going through the line.

A strong correlation is when the points on the scatter graph lie very close to the line of best fit. With a strong correlation, the two variables are related to one another - as one changes, so does the other.

A line of best fit is a line drawn through points in a way that goes through the majority of the points.

A weak correlation is when the points lie far away from the line of best fit. In this case, the two variables are not necessarily related to one another - a change in one does not mean a change in the other.

A positive correlation is when an increase in one factor is morrored by an increase in another (the line of best fit goes from the bottom left to the top right).

A negative correlation is when an increase in one factor is mirrored by a decrease in another (the line of best fit goes from the top left to the bottom right).

An interpolate trend is when a value is found within the data set, using the line of best fit. The value was not originally plotted, but can be read off the line of best fit.

Interpolation is drawing an imaginary line up to the line of best fit, then drawing another imaginary line along the other axis to find a value.

An extrapolate trend is when a value is found outside of the data set. Extrapolation may provide uncertain results as it is based on extending the line of best fit beyond a known set of data.

Extrapolation is extending the line of best fit beyond the observed data, and using that to find a value.