Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Stat 312: Lecture 21 Correlations Moo K. Chung [email protected] April 10, 2003 Concepts 1. The coefficient of determination r 2 = S 2 xy /S xx S yy . 2. The sample correlation coefficient r is defined as r = S xy / p S xx S yy . In Lecture 20, we showed that 0 r 2 1. Hence - 1 r 1. 3. r = 0 if and only if paired observations ( x j , y j ) pass through the same straight line. From Lec- ture 20 example 2, if ( x j , y j ) pass through a cir- cle, r = 0. So r can be used to measure if the paired observations show linear relationship. 4. Population correlation coefficient ρ ( X, Y ) = Cov ( X, Y ) p Var ( X ) Var ( Y ) . In-class problems Example 1. Is there any linear relationship betweenthe mathematical achievement test scores (xi) andcalculus grades (yi) for 10 college freshmen?xk39,43,21,64,57,47,

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