Purpose: A line of best fit is a straight line drawn through the center of the data points to model the underlying trend and facilitate predictions.
Drawing Technique: The line should be drawn 'by eye' using a ruler, ensuring it follows the general direction of the points and has roughly an equal number of points above and below it.
Handling Outliers: When drawing the line, extreme values that do not fit the general pattern (outliers) should be ignored to prevent them from skewing the trend line.
Extent: The line should generally extend across the full range of the plotted data points but does not necessarily need to pass through the origin unless the context requires it.
Interpolation: This involves estimating a value within the range of the existing data points. It is generally considered reliable because it is supported by observed evidence on both sides of the prediction.
Extrapolation: This involves extending the line of best fit to predict values outside the range of the original data. This is risky and often unreliable, as the trend may not continue indefinitely.
| Feature | Interpolation | Extrapolation |
|---|---|---|
| Data Range | Inside existing bounds | Outside existing bounds |
| Reliability | High | Low/Uncertain |
| Method | Reading between points | Extending the trend line |
The Principle: A strong correlation between two variables does not prove that one variable causes the change in the other.
Third Variables: Often, two variables correlate because they are both influenced by a hidden third factor (a confounding variable).
Logical Fallacy: Assuming causation from correlation is a common error; for example, ice cream sales and shark attacks may correlate positively, but both are actually caused by warm weather, not by each other.
Precision in Plotting: Always use a sharp pencil and mark points with small, clear crosses; examiners look for accuracy within half a small square.
Line Placement: When drawing a line of best fit, use a transparent ruler so you can see the points underneath it to balance them correctly.
Interpreting the Context: When asked to 'describe the relationship,' always mention the type of correlation (e.g., 'positive') and explain it in the context of the variables (e.g., 'as age increases, height increases').
Sanity Checks: If a prediction via extrapolation seems physically impossible (e.g., a negative height), state that the model is not valid for those values.
