This worksheet teaches students to describe the strength, direction and linearity of association shown in a scatterplot, find the line of best fit for bivariate data, and use it to make predictions. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A scatterplot displays the relationship (association) between two numerical variables, one on each axis.
- Association is described by direction (positive: both increase together; negative: one increases as the other decreases), strength (how closely the points follow a trend), and linearity (whether the trend is a straight line or curved).
- The line of best fit (least-squares regression line) summarises a linear trend, and can be used to interpolate (predict within the range of the data) — predicting far outside the data range (extrapolation) is much less reliable.
- The correlation coefficient r ranges from −1 to +1: values near ±1 indicate a strong linear association, values near 0 indicate a weak or no linear association. The sign of r matches the direction.
- A correlation coefficient near 0 does not necessarily mean "no relationship" — it only rules out a linear one; a strong non-linear (curved) relationship can still exist.
What your child will practise:
- Describing a scatterplot's association in terms of direction, strength and linearity.
- Calculating the correlation coefficient r for a bivariate dataset.
- Finding the equation of the line of best fit (slope and intercept) using the least-squares method.
- Using the line of best fit to interpolate a predicted value.
- Recognising the danger of extrapolating far beyond the range of the original data, and of a low r masking a non-linear relationship.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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