Topic 7 of 7 · Form 4
Bivariate data, scatter diagrams and lines of best fit
Plotting paired data; positive, negative and no correlation; strong and weak correlation; outliers; correlation does not imply causation.
Notes for this topic 1 file, in order
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Scatter diagrams
Plotting paired data; positive, negative and no correlation; strong and weak correlation; outliers; correlation does not imply causation.
Line of best fit
- By eye, passing through the mean point (x̄, ȳ).
- Method of semi-averages: divide the ordered data into two halves, find the mean point of each half, and draw the line through both points.
Worked example: Data (1, 3), (2, 5), (3, 4), (4, 8), (5, 9), (6, 11). Find the line by semi-averages.
First half mean point (2, 4); second half (5, 28/3 ≈ 9.33)
Gradient = (9.33 − 4) ÷ 3 = 1.78; y = 1.78x + 0.44 (approximately)
Using the line
Interpolation (within the data range) is reasonably reliable; extrapolation (outside) may be unreliable. Interpret the gradient and intercept in context.
Spearman's rank correlation (where required)
rs = 1 − 6Σd² ÷ (n(n² − 1)) for ranked data.
Check yourself
- What does a negative correlation mean?
- Through which point should a line of best fit pass?
- Why is extrapolation risky?
Show answers
- As one variable increases, the other tends to decrease.
- The mean point (x̄, ȳ).
- The relationship may not continue beyond the range of the data.
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