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F04-Correlation - PubH 7405 REGRESSION ANALYSIS Correlation...

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PubH 7405: REGRESSION ANALYSIS Correlation Analysis
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CORRELATION & REGRESSION We have 2 continuous measurements made on each subject, one is the response variable Y, the other predictor X. There are two types of analyses: Correlation : is concerned with the association between them, measuring the strength of the relationship; the aim is to determine if they are correlated – the roles are exchangeable. Regression : To predict response from predictor .
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ROLES OF VAIRABLES In Regression Analysis , each has a well- defined role; we’ll predict “response Y” from a given value of “predictor X” In Correlation Analysis , the roles of “X” and “Y” are exchangeable; in the coefficient of correlation “r” is symmetric with respect to X and Y : we get the same result regardless of which one is X – no special “label”.
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SCATTER DIAGRAM In quarters I and III, For positive association, For stronger relationship most of the dots, being closely clustered around the line, are in these two quarters; the above sum is large. 0 ) )( ( y y x x 0 ) )( ( y y x x ) , ( y x Quarter (I) Quarter (III) (II) (IV)
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SCATTER DIAGRAM In quarters II and IV, For negative association, For stronger relationship most of the dots, being closely clustered around the line, are in these two quarters; the sum is a large negative number. 0 ) )( ( y y x x 0 ) )( ( y y x x ) , ( y x Quarter (II) Quarter (IV) (I) (III)
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SUMMARY The “ sum of products summarizes the “ evidence of the relationship under investigation; It is zero or near zero for weak associations and is large, negative or positive, for stronger associations. The sum of products can be used as a measure of the strength of the association itself. However, it is “ unbounded making it hard to use because we cannot tell if we have a strong association (how large is “large”?). We need to “ standardize it. ) )( ( y y x x
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