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[h]SL 4.4 Linear correlation of bivariate data
[q] Correlation Coefficient
[a] When given a set of x & y values, and we look at their relationship, we can measure how closely it follows a linear relationship, with the Pearson’s product-moment correlation coefficient (r).
Calculation: \(r = \frac{\sum(x-x̄)\sum(y-ȳ)}{\sqrt{\sum(x-x̄)^2\sum(y-ȳ)^2}}\), but like standard deviation, we never need to manually except possibly in an internal assessment.
[q] Regression Line
[a] You may have worked with a line of best fit in the past, although this was most likely done by eye, with the only level of accuracy being that it should pass through the means (x̄, ȳ), if done properly.
The regression line is a more rigorous version – a line that minimises the sum of the squares of the vertical distances between each point and the line. This should only be done with a strong correlation and never needs to be found manually.
[q] Estimation
[a] Once you find the equation of the line (same buttons as finding r), you can use it to estimate values for y, given x-values, but not vice versa. You should also not estimate using x-values that are beyond the range of the given set.
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