Line of Best Fit

 

What Is a Line of Best Fit?

When you draw a scatter graph and the points show a clear trend (either increasing or decreasing), you can draw a line of best fit.

It’s a straight line that:

• Follows the general pattern of the data
• Helps you estimate values (predict things!)
• Shows the strength and direction of the relationship

 

How Do I Draw a Line of Best Fit?

Step-by-step:

1. Use a ruler and draw a single straight line.
2. The line should go through the middle of the points — not necessarily through any of them.
3. Try to balance the points — roughly the same number above and below the line.
4. Ignore outliers (extreme points that don’t match the pattern).
5. Extend the line across the full data range.

 

Tip: Slide your ruler up and down until the line feels “right” — this is often done by eye.

 

How Do I Use a Line of Best Fit?

Once drawn, the line can be used to:

• Estimate a value (called interpolation)
  • e.g. “If x = 6, what’s the estimated y?”

• Predict a value outside the data range (called extrapolation)

Be careful — these estimates are less reliable.

 

Example

Olivia is researching mobile phone battery life and price. Her results:

 

Battery Life (hrs)	Price (£)
8	120
10	150
12	180
9	135
15	210
14	200
11	160

 

(a) Plot a scatter graph

• x-axis: Battery Life
• y-axis: Price

Plot the points as crosses. No lines joining them.

(b) Draw a line of best fit

• Place a ruler to follow the general trend
• Balance the number of points above and below
• Ignore any odd outliers

(c) Describe the type of correlation

The points rise from left to right

This is positive correlation:

As battery life increases, price increases.

(d) Estimate the price of a phone with 13 hours of battery life

• Use your line of best fit
• Go to x = 13, draw upwards to meet your line
• Read across to the y-axis

Estimate: About £190