correclation - <Correlation coefficient> Descriptive...

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<Correlation coefficient> Descriptive study of bivariate data Univariate: score, height, number of heads,… Bivariate: (height, weight), (age, income),… Data: 11 2 2 (,) , ,, ( ,) nn X YX Y XY K Purpose of collecting bivariate data - Are the variables related? - What form of relationship is indicated by the data?: linear, quadratic,… - Can we quantify the strength of their relationship?: strong, weak - Can we predict one variable from the other? Scatter diagram - provides a visual display of a relationship Ex) (2,5) (1,3) (5,6) (0,2) <Correlation: a measure of linear relationship> Book: 11.7 (p.590-593), Note: p.12-13 (Sample) Correlation coefficient r = measure of strength of the linear relation between x and y based on data (= ˆ ρ ) - Figure 11.19 (p.591) - The value of r is always between -1 and +1 - r>0: the pattern of (x,y) values is a band that runs from lower left to upper right - r<0: the pattern of (x,y) values is a band that runs from upper left to lower right - r=+1: all (x,y) values lie exactly on a straight line with a positive slope (perfect positive linear
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correclation - &lt;Correlation coefficient&gt; Descriptive...

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