Equation (Edexcel GCSE Statistics): Revision Notes
Equation
What is the equation of a line of best fit?
The equation of a line of best fit follows the standard linear form , where:
- a represents the gradient (slope) of the line
- b represents the y-intercept (where the line crosses the y-axis)
This equation allows you to predict values and understand the relationship between two variables shown in a scatter diagram. The line of best fit shows the general trend in your data, even when individual points don't lie exactly on the line.
The line of best fit is also called the trend line or regression line. It doesn't need to pass through every data point - instead, it shows the overall pattern with roughly equal numbers of points above and below the line.
Finding the gradient (a)
The gradient tells you the rate of change between your two variables. Here's how to calculate it:
Step-by-step method:
- Choose any two clear points on your line of best fit
- Draw a right-angled triangle between these points
- Measure the vertical distance (height/rise)
- Measure the horizontal distance (base/run)
- Calculate:
You can also use coordinates:
Understanding gradient direction:
- Positive correlation → positive gradient (line slopes upward from left to right)
- Negative correlation → negative gradient (line slopes downward from left to right)
Always check that your calculated gradient sign matches the type of correlation you can see in the scatter diagram!
Finding the y-intercept (b)
The y-intercept is much simpler to find - it's simply the value of y when x equals zero. Look at where your line of best fit crosses the y-axis and read off this value.
Alternative method when the line doesn't cross the y-axis on your graph:
- Take any point on your line
- Substitute into:
This calculation method is particularly useful when your graph doesn't show the y-axis or when the y-intercept falls outside your plotted range.
Worked example walkthrough
Worked Example: Finding the Line of Best Fit Equation
Let's examine a scatter diagram showing temperature (x-axis) and drink sales (y-axis):
Step 1: Finding the gradient
- Choose two points on the line: and
- Calculate the differences:
- Height (y-difference) =
- Base (x-difference) =
- Gradient =
Step 2: Finding the y-intercept
- Using the point and gradient :
Step 3: Complete equation
Step 4: Interpreting the gradient The gradient of means that for each increase in temperature, approximately more drinks are sold.
Common exam tips and traps
✅ Do:
- Use the coordinate method rather than counting squares (more accurate)
- Check your gradient sign matches the correlation type
- Show all working clearly
- Include units in your interpretation if asked
❌ Avoid:
- Mixing up which value is x and which is y
- Forgetting negative signs
- Using points that aren't clearly on the line
- Giving answers without context when interpreting gradients
⚠️ Watch out for:
- Questions asking what the gradient means in context - always relate it back to the real-world scenario
- Y-intercepts that might not be realistic (e.g., negative temperatures might not make sense)
- Lines that don't pass through the origin - the y-intercept won't be zero
Key takeaways
Key Points to Remember:
- The equation format is always where a is the gradient and b is the y-intercept
- Gradient = using any two points on the line of best fit
- Positive correlation = positive gradient, negative correlation = negative gradient
- The y-intercept is where the line crosses the y-axis (when )
- Always interpret gradients in the context of the question - explain what the rate of change means for the real situation