# Drawing the Line of Best Fit

## Key Concepts

• Experimental data points rarely fit perfectly on a straight line or a smooth curve due to experimental errors.

• A line of best fit, or a curve of best fit, is drawn through these points to allow us to make predictions.

• The line of best fit will be drawn so that it:

(i) passes through, or is as close to, as many points as possible

(ii) has as many points above the line as there are below it

• You can draw an approximate line of best fit through data points just by looking at it (the eyeball method).

• A line of best fit can also be calculated (you won't be expected to do this in High School, so we have included a tool for members that you can use to draw the line of best fit for your experimental data)

## Eyeball Method

Imagine an experiment in which you take different masses of magnesium, ignite each magnesium sample in a closed vessel containing excess oxygen, then weigh the product of each reaction (the magnesium oxide).

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Just by looking at the points on the scatter graph we can see that the general pattern of the points is a straight line. We are confident that we could draw a straight line through these points which could then be used to describe the relationship between the mass of magnesium oxide produced during combustion and the mass of magnesium used in the experiment, and, to predict results of similar experiments.

The line of best fit through a set of data points is a line which:

• passes through, or is as close to, as many points as possible (ignoring points which are clearly different to the general pattern of points)

• has as many points above the line as there are below it

The more data points you have, the more reliable the line of best fit becomes.
If you only have 2 points to plot on the graph, there is only 1 line that you can draw through the points so a Chemist would not think of this line as a line of best fit because it is the only possible line.
If you have 3 points that look like a straight line, then you can find a line of best fit since not all the points might lie exactly on the line.

## Line of Best Fit by Calculation

You only need to know the position of 2 points in order to draw a straight line.
You can use the tool below to calculate the position of the first and last points on the line of best for a set of data points, then you can draw a line through those two points which will be the line of best fit.

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