When there reasonable correlation between two variables on a scatter plot, it is possible to draw a *line of best fit*. This line represents the underlying relationship between the two quantities. When drawing a line of best fit the aim is to keep the distances of all the points from the line to a minimum. Sometimes it is helpful to try to keep the number of points above the line the same as the number of points below the line.

Lines of best fit can be used to make predictions. The accuracy and reliability of those predictions will depend on the strength of the correlation between the two variables.

Draw a line of best fit for the points in the following scatter graph:

(a)

Use the data to draw a scatter graph.

Note that there are 3 points above the line and 3 below. The total distances to the points above the line is similar to the total distance to the points below the line.

(b)

Use the line to predict the value of y when x = 12.

Using the dotted line, we have *y* = 6.4 when *x* = 12.

The following data was collected from an experiment. In the experiment, objects of different masses were placed on a horizontal surface and the force needed to make them start to move was recorded.

Mass(kg) | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 5.0 |
---|---|---|---|---|---|---|

Force(N) | 2.1 | 3.8 | 6.1 | 7.9 | 13.2 | 19.1 |

Use a scatter graph to estimate the force needed for a 2.5 kg mass.

The graph also shows that the estimated force for a 2.5 kg mass is 10 N.