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Correlation, r , measures the direction and strength of the linear relationship between two quantitative variables. We have ( x, y ) data on n individuals. r = .

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## Note that r is calculated by multiplying the z-scores for each individual’s x - and y -values, adding the products,

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**Correlation, r, measures the direction and strength of the**linear relationship between two quantitative variables. We have (x, y) data on n individuals.r =**Note that r is calculated by multiplying the z-scores for**each individual’s x- and y-values, adding the products, and dividing by n-1.**Properties of Correlation:r makes no distinction between**explanatory and response variables. Correlation requires that both variables be quantitative. r does not change if we change the units of measurement. r has no unit of measurement – it is just a number.**r > 0 indicates a positive association;**r < 0 indicates a negative association.**Values near 0 indicate a very weak linear relationship. The**strength of the linear relationship increases as r moves away from zero and toward – 1 or + 1. – 1 ≤ r ≤ + 1 r = – 1 or + 1 only if all the data points are collinear.**Correlation measures only the strength of a linear**relationship between two quantitative variables. Correlation does not describe curved relationships, no matter how strong they may be. ALWAYS visually examine your data!!**Use r with caution when the scatter-plot shows outliers.**r is not a resistant measure.**Correlation is not a complete description of two-variable**data.When describing 2-variable data, give the values of , sx, and sy in addition to r.**Note that the correlation coefficient only measures the**strength of a linear relationship between your variables. It cannot determine causation.A strong linear relationship between two quantities (life expectancy and # people per TV for example) does not guarantee a cause/effect relationship!**Generally, you can NOT conclude that there**is a cause/effect relationship until you have run a carefully designed experiment (discussed in chapter 3). This idea is usually written ASSOCIATION ≠ CAUSATION.

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