correlation of data

correlation of data - random errors. r=0: there is no...

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Regression and Correlation of Data Correlation: Correlation is a measure of the association between random variables, say X and Y. No assumption that one of these variables is known without error. Assume that X and Y are related linearly, so the usual correlation coefficient gives a measure of the linear association between X and Y, determined by yy xx xy xy S S S r = This coefficient is often denoted simply by r.
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Regression and Correlation of Data Correlation Coefficient: yy xx xy S S S r = r =1: the points (xi,yi) are in a perfect straight line and the slope of that line is positive; r =-1: the points (xi,yi) are in a perfect straight line and the slope of that line is negative; r close to +1 or -1: X and Y follow a linear relation affected by
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Unformatted text preview: random errors. r=0: there is no systematic linear relation between X and Y. Regression and Correlation of Data Coefficient of determination: form linear for the ) ( ) ( 2 1 2 1 2 2 = = = = yy xx xy n i i n i i S S S y y y y r The coefficient of determination is the fraction of this sum of squares which is explained by the linear relation between and x given by regression of y on x. e.g. r 2 =0.997, which means 0.03% of the sum of squares of deviations in the y-direction from y bar is not explained by the regression. y Example 43...
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This note was uploaded on 02/13/2012 for the course MATH 2320 taught by Professor Glyn during the Fall '11 term at Minnesota.

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correlation of data - random errors. r=0: there is no...

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