# LCT23 - Introduction to Business Statistics Lecture 23...

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1 Introduction to Business Statistics L e c t u r e 2 3 Correlation Analysis Correlation coefficient: It measures the strength of the relationship between independent variable X and dependent variable Y . SSY SSX SSXY S Y Y S X X n r Y i n i X i = = = ) ( ) ( 1 1 1 z 1 1 r z Positive (negative) r indicates a positive (negative) association: Increasing X tends to increase (decrease) Y . z 1 = r or 1 = r occur only in the case of perfect linear association. z The value of r does not change when the unit of measurement of X or Y or both are changed.

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2 z r measures only the strength of linear relationship between two variables. z The least-square slope estimate 1 b can be calculated from r via X Y S S r b = 1 , where Y X S S , is the sample s.d. for X and Y , respectively. z The preceding equation implies that Y X rS b S = 1 , indicating that a change of one standard deviation in X corresponds to a change of r standard deviations in Y .
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## This note was uploaded on 02/13/2012 for the course ISOM 111 taught by Professor Hu,inchi during the Fall '10 term at HKUST.

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LCT23 - Introduction to Business Statistics Lecture 23...

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