Lines of best fit
- A line of best fit shows the trend on a scatter diagram. Draw it with roughly equal numbers of points on each side.
- A line of best fit drawn by eye should pass through the mean point (x̄, ȳ), found from the means of the two variables.
- Only draw a line of best fit when there is correlation.
The equation of the line
- A line of best fit has the equation y = a + bx. b is the gradient and a is the y-intercept.
- Gradient = change in y ÷ change in x. From (2, 10) to (6, 22), the gradient is 12 ÷ 4 = 3.
- Interpret the gradient in context: "for each extra hour of revision, the test score increases by about 3 marks."
- Interpret the intercept only if x = 0 makes sense: "a student who does no revision would score about 12."
Making predictions
- Substitute a value of x into the equation: if y = 12 + 3x and x = 4, then y = 24.
- Interpolation is predicting within the range of the data. It is fairly reliable.
- Extrapolation is predicting outside the range of the data. It is unreliable, because the pattern may not continue.
- Predictions are more reliable when the correlation is strong.
Key terms
- Line of best fit
- A straight line showing the trend on a scatter diagram.
- Mean point
- The point (x̄, ȳ) that a line of best fit should pass through.
- Gradient
- The change in y for each increase of 1 in x.
- Intercept
- Where the line crosses the y-axis.
- Interpolation
- Predicting within the range of the data.
- Extrapolation
- Predicting outside the range of the data.
Practise Lines of best fit, interpolation and extrapolation: 10 questions