Bivariate Data 2: Lines of Best Fit and Prediction
Draw lines of best fit and make predictions from scatter graphs. MYP Year 5 Standard Maths — interpolation, extrapolation, and Criterion D skills.
Moving from Observation to Prediction
In Bivariate Data 1, you learned to plot scatter graphs and describe trends. This topic takes the next step: drawing a line of best fit (LOBF) and using it to make predictions from data.
Drawing a Line of Best Fit
A line of best fit is a straight line drawn through the scatter of points that best represents the overall trend. It does not need to pass through any specific point, but it should:
- Follow the general direction of the data
- Have roughly equal numbers of points on either side
- Pass through (or near) the mean point (x̄, ȳ) where this is given
Draw the line with a ruler. A freehand curve is not acceptable in assessed work.
Using the LOBF to Predict
Once drawn, you can read off estimated values for one variable given a value of the other. This involves drawing guidelines from the axis to the line and reading the corresponding value.
Interpolation vs Extrapolation
Interpolation means estimating a value within the range of the original data. This is generally reliable. Extrapolation means estimating beyond the data range — this is less reliable because the trend may not continue.
MYP questions often ask you to evaluate the reliability of a prediction. Always state whether you are interpolating or extrapolating and comment on what this means for reliability.
Common Mistakes
- Drawing the LOBF to start or end at a plotted point rather than extending across the graph
- Using extrapolated values without flagging the reduced reliability
- Misreading the value from the line due to poor scale reading
Criterion D Connection
Prediction tasks are a natural fit for Criterion D. You may be asked to make a prediction, evaluate its reliability, and suggest limitations of the model — all in the context of a real-world scenario.