4.8.3 Line of best Fit
A line of best fit (also called a trend line) is a straight line that best represents the relationship between two variables in a scatter plot. The line of best fit can be used to help visualize the trend or pattern in the data.
To draw a line of best fit, follow these steps:
Plot the data points on a scatter plot, with the \( x \)-axis representing one variable and the \( y \)-axis representing the other variable.
Determine the type of relationship between the variables.
If there is a clear linear relationship (positive or negative correlation) between the variables, a straight line can be used as the line of best fit.
Draw a straight line that passes through the middle of the data points, with roughly equal numbers of data points above and below the line.
Adjust the line until it represents the general trend of the data as closely as possible.
It’s important to note that a line of best fit is not always appropriate or necessary for a scatter plot.
For example, if there is no clear pattern or relationship between the variables, a line of best fit may not be useful. In such cases, it is better to rely on visual inspection of the scatter plot to draw conclusions about the data.
Worked example:
Aisha records the distance she runs and her average speed.
The results are shown in the diagram.
The table shows the results of four more runs.
On the scatter diagram, plot these points.
Plot the points \( (4.2, 13.4), (5.7, 11.8), (7.1, 9.8) \)and \( (8.8, 8.3)\).
Read the scales carefully.
What type of correlation is shown in the scatter diagram?
As the distance increases, the average speed decreases.
The graph shows negative correlation.
On the scatter diagram, draw a line of best fit.
A line of best fit is a straight line that best represents the relationship between two variables in a scatter plot.
Try to have approximately the same number of points both above and below the line.
Test yourself
Question 1:
The scatter diagram shows the number of people and the number of phones in each of \( 8 \) buildngs.
One of the buildings contains \( 42 \) people.
Write down the number of phones in this building.
[1]
What type of correlation is shown in the scatter diagram.
[1]
Question 2:
“We eat more ice cream as the temperature rises.”
What type of correlation is this?
[1]
Question 3:
The scatter graph shows some information about \( 10 \) cars, of the same type and make.
The graph shows the age years and the value \( $ \) of each car.
The table shows the age and the value of two other cars of the same type and make.
On the scatter graph, plot the information from the table.
[1]
Describe the relationship between the age and the value of the cars.
[1]
Question 4:
A delivery driver records for each delivery the distance he drives and the time taken.
The scatter graph shows this information.
For another delivery he drives \( 22 \) kilometers and take \( 50 \) minutes.
Show this information on the scatter graph.
[1]
What type of correlation does the scatter graph show?
[1]
The driver has to drive a distance of \( 10 \) km for his next delivery.
[2]
During one of the deliveries, the driver was delayed by road works.
Using the graph write down the time taken for this delivery.
[1]