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Scatter graphs and correlation
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A scatter graph shows whether two things are linked, such as hours of revision and test scores.
Bivariate data and correlation
Bivariate data has two values for each item. Plot each pair as a point.
Positive correlation: as one goes up, the other goes up.
Negative correlation: as one goes up, the other goes down.
No correlation: no clear pattern.
Positive correlation: as one goes up, the other goes up.
Negative correlation: as one goes up, the other goes down.
No correlation: no clear pattern.
Line of best fit
Draw a straight line through the middle of the points, with roughly as many above as below. Ignore outliers.
Use it to estimate a value. Estimates inside the range of the data (interpolation) are more reliable than estimates outside it (extrapolation).
Use it to estimate a value. Estimates inside the range of the data (interpolation) are more reliable than estimates outside it (extrapolation).
Careful conclusions
Correlation does not prove that one thing causes the other.
Ice cream sales and sunburn cases both rise in hot weather: they are linked by a third factor, not by each other.
Ice cream sales and sunburn cases both rise in hot weather: they are linked by a third factor, not by each other.
A line of best fit passes through (2, 30) and (6, 50). Estimate y when x = 4.
- x = 4 is halfway between 2 and 6
- So y is halfway between 30 and 50
Answer: 40
Positive correlation: both increase. Negative: one up, the other down. Use a line of best fit to estimate within the data, and remember correlation is not causation.
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