Line of Best Fit
Revise Line of Best Fit for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. A line of best fit summarises the trend in a scatter diagram and can be used to make predictions.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.
Topic overview
A line of best fit is a straight line drawn through the points on a scatter diagram to show the trend of the data.
It should follow the general direction of the points, with roughly equal numbers above and below it. It does not need to pass through any particular point, but it should pass through the mean point \((\bar{x}, \bar{y})\), the point given by the mean of each variable.
The line is used to estimate a value of one variable given the other. Its equation can be found in the form \(y = mx + c\), where the gradient \(m\) shows how much \(y\) changes for each unit increase in \(x\), and the intercept \(c\) is the value of \(y\) when \(x\) is zero.
Revision notes
Drawing the line
Follow the general direction of the points, with roughly equal numbers above and below.
It should pass through the mean point \((\bar{x}, \bar{y})\). It need not pass through any of the plotted points, and it must be a single straight line, not a curve joining points.
Finding the equation
Write it as \(y = mx + c\). The gradient \(m\) is found from two points on the line: \(m = \frac{\text{change in } y}{\text{change in } x}\).
The intercept \(c\) is where the line crosses the vertical axis. Use points on the LINE, not data points, when calculating the gradient.
Interpreting the equation
The gradient shows how much \(y\) changes for each unit increase in \(x\).
The intercept is the value of \(y\) when \(x\) is zero, though this may have no sensible meaning if zero lies far outside the data range.
Key points
- A line of best fit shows the trend.
- Roughly equal points lie above and below it.
- It passes through the mean point.
- It is a single straight line.
- The equation is \(y = mx + c\).
- Use points on the line to find the gradient.
Worked examples
Example 1
A line of best fit passes through \((2, 10)\) and \((6, 22)\). Work out its gradient. [2 marks]
Working
Example 2
Explain what the mean point is and why the line of best fit passes through it. [2 marks]
Working
Example 3
A line of best fit has gradient 4. Interpret this in context for hours worked against pay in pounds. [2 marks]
Working
Common mistakes
Joining the points instead of drawing a line.
It is a single straight line showing the trend.
Using data points to find the gradient.
Use two points that lie on the drawn line.
Forcing the line through the origin.
It passes through the mean point, not necessarily the origin.
Not interpreting the gradient in context.
Say what it means for the actual variables.
Exam tips
- Draw a single straight line, not a curve.
- Use points on the line for the gradient.
- Check the line passes through the mean point.
- Interpret the gradient in context when asked.
Key terms
- Line of best fit
- A straight line showing the trend of scatter data.
- Mean point
- The point \((\bar{x}, \bar{y})\) through which the line passes.
- Gradient
- The change in y for each unit increase in x.
- Intercept
- The value of y where the line crosses the vertical axis.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.