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Welcome to GCSE Edexcel Maths revision.

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Topic M 41: Scatter graphs and correlation.

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This video covers Foundation and Higher tiers.

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A scatter graph displays pairs of numerical measurements for the same items.

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Plot one variable on each axis and do not join points in time order.

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Positive correlation and an estimated best-fit line

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Positive correlation means larger x values tend to accompany larger y values; negative correlation means larger x values tend to accompany smaller y values.

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No correlation means no clear relationship in the scatter.

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Strength describes how closely points follow a pattern, not the steepness of a trend line.

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A shallow but tightly clustered trend can be strong correlation.

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Correlation does not establish causation.

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A third factor, coincidence or the way a sample was selected could explain an association.

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An outlier is far from the general pattern.

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Investigate recording errors or unusual circumstances rather than automatically deleting it.

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For an approximately linear relationship, draw a line of best fit through the middle of the scatter, with roughly balanced points above and below.

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It need not pass through the origin or through two selected data points.

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Choose two well-separated points on your best-fit line to estimate its gradient and equation.

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They need not be original plotted observations.

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Worked example: A best-fit line passes through open bracket 2, 5 close bracket and open bracket 8, 17 close bracket .

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Gradient equals the fraction with numerator open bracket 17 minus 5 close bracket and denominator open bracket 8 minus 2 close bracket ,

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end fraction equals 2,

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so its equation is y is approximately equal to 2 x plus 1.

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At x equals 5 it predicts y is approximately equal to 11.

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Interpolation predicts within the observed x range and is usually more reliable.

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Extrapolation predicts outside that range, where the relationship may not continue.

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Predictions are estimates; scatter shows individuals may differ from the line.

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Do not report unjustified precision from a loosely scattered graph.

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For a clear curved pattern, a straight line is an inappropriate model.

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Describe the relationship and use a suitable smooth curve if the task calls for one.

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If study time and test scores are correlated, that alone does not prove an extra hour causes a fixed score increase.

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Prior knowledge, teaching and motivation may also matter.

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A large outlier can affect a fitted line strongly, especially with a small sample.

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Explain how the line's reliability might change if the observation is erroneous or exceptional.

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State the sample range, units and evidence behind a prediction.

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For example, predicting at 6 hours from observations between 1 and 8 hours is interpolation; predicting at 15 hours is extrapolation.

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That completes Scatter graphs and correlation.

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Revisit the notes and test yourself on the revision website.