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F04-Correlation

# 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 .
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)
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