Lines of Best Fit

Purpose of a Line of Best Fit

A line of best fit is drawn on a scatter graph to show the general trend or pattern in the data points. It summarises the correlation between two variables by providing a visual representation of how one variable tends to change as the other changes.

This line helps to predict or estimate values that are not explicitly plotted on the graph. For example, if you have data on hours studied and exam scores, the line of best fit can help estimate the expected exam score for a given number of study hours.

It is important to understand that the line of best fit does not have to pass through every point; instead, it balances the points above and below it to best represent the overall trend.

Drawing Lines of Best Fit

When drawing a line of best fit, you use visual estimation to draw a straight line that best represents the data trend. The key points to remember are:

• The line should have roughly equal numbers of points above and below it.
• It should follow the direction of the data points, showing the overall trend clearly.
• The line does not need to pass through any of the points, but it should be as close as possible to most points.

This method is often called "eyeballing" the line. It is a skill that improves with practice and helps summarise large sets of data simply.

For instance, if a scatter graph shows points rising from left to right, the line of best fit should slope upwards, balancing points above and below.

Interpreting Lines of Best Fit

The line of best fit helps interpret the correlation between two variables:

• Positive correlation: The line slopes upwards, indicating that as one variable increases, the other tends to increase.
• Negative correlation: The line slopes downwards, showing that as one variable increases, the other tends to decrease.
• No correlation: The line is roughly horizontal or no clear trend is visible.

The strength of the correlation is shown by how closely the points cluster around the line:

• Strong correlation: Points lie close to the line.
• Weak correlation: Points are more spread out from the line.

You can use the line of best fit to estimate values between known data points (interpolation) or beyond the range of data (extrapolation). Interpolation is generally more reliable because it involves estimating within the range of observed data, while extrapolation assumes the trend continues beyond the data and should be done cautiously.

For example, if the line of best fit shows the relationship between temperature and ice cream sales, you can estimate sales at a temperature not recorded in the data.

Learning Example

A scatter graph shows the number of hours students studied and their test scores. The points generally rise from left to right but are not perfectly aligned.

To draw the line of best fit:

• Draw a straight line that balances the points above and below.
• The line slopes upwards, indicating a positive correlation.
• The line does not have to pass through any points exactly.

Using this line, you can estimate the test score for a student who studied, say, 4 hours, even if no point is plotted for exactly 4 hours.