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handout_2_2_fall11(1)

handout_2_2_fall11(1) - 2.2 Correlation linear relationship...

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2.2 Correlation linear relationship is strong if points lie close to a straight line linear relationship is weak if points are widely scattered about a line problem with scatterplot- our eyes can be fooled about the strength of the relationship need numerical measure of strength of linear relationship- correlation The correlation r measures the strength and direction of the linear relationship between two quantitative variables. Suppose that we have data on variables x and y for n individuals. The mean and standard deviation of the x -values are x and s x . The mean and standard deviation of the y -values are y and s y . The correlation r between x and y is: r = 1 1 - n - ) ( x i s x x ) ( y i s y y - Suppose that x is height in centimeters and y is weight in kilograms and that we have height and weight measurements for n people. ) ( x i s x x - is the standardized height for the i th person ) ( y i s y y - is the standardized weight for the i th person ) ( x i s x x - = - cm cm cm = # with no unit of measurement ) ( y i s y y - = - kg kg kg = # with no unit of measurement ●Standardized values have no units of measurement. Hence, the correlation r has no unit of measurement. The correlation r is just a number.
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