# 1 x i x 2 n n yi y 2 i 1 r is

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Unformatted text preview: ) 2 i =1 ◊ r is unaffected by the units of measurements ◊ The sign of r ◊ The magnitude of r NUS/FOS/DSAP 6 GEM2900 Semester 1, 2009/1010 Evaluate Strength of a Relationship Through Correlation √ Some features of correlation coefficient, r… –1 ≤ r ≤ 1 A positive correlation indicates the values of the two variables changes towards the same direction . A negative correlation indicates the values of the two variables changes towards the opposite directions. When r = ± 1… there is a perfect linear relationship between the two variables; (i.e.) All paired values fall on the same straight line. When r = 0… there is no linear relationship between the two variables; or the best straight line through the paired values is horizontal. NUS/FOS/DSAP 7 GEM2900 Semester 1, 2009/1010 Evaluate Strength of a Relationship Through Correlation Examples: √ In an article, Marsh and Hand et al. reported that the data on the heights of a random sample of 200 married couples in Britain showed a correlation coefficient of 0.36. The ages of 200 couples were also collected. The correlation between husbands’ and wives’ age is 0.94. √ A study was conducted by Sport Illustrated magazine to study the success rates at putting versus the distance of putt among professional golfers. The correlation was found to be –0.94. NUS/FOS/DSAP 8 GEM2900 Semester 1, 2009/1010 Relationships Can Be Deceiving √ Illegitimate Correlations: Outliers can substantially inflate or deflate the correlations Groups combined inappropriately may mask the relationships √ Correlation Does Not Imply Causation: Relationships found from observational studies can not be reported as causal relationships A causal relationship between two variables may be established if an experimental design is possible. NUS/FOS/DSAP 9 GEM2900 Semester 1, 2009/1010 Relationships Can Be Deceiving Example: Pages vs. Prices of Books... A college student recorded the number of pages and the prices for a randomly selected books from the university bookstore. The correlation was found to be –0.312. The fewer the pages, the more expensive the books? Pages 104 188 220 264 336 Price 32.95 24.95 49.95 79.95 4.50 Type H H H H S Pages 342 378 385 415 417 Price 49.95 4.95 5.99 12.50 32.95 Type H S S S H Pages 436 458 466 469 585 Price 5.95 60.95 49.95 6.95 5.95 Type S H H S S Missing link… A third variable NUS/FOS/DSAP 10 GEM2900 Semester 1, 2009/1010 Relationships Can Be Deceiving Example: Dental Health vs. Heart Disease... An article from Straits Time posted discussed the relationship between dental health and heart disease. It was implied that some of the bacteria living in our mouth can cause the heart disease. The article discussed how infrequently that many Singaporean visit the dentists, with implication that if they did this more often they would be less likely to suffer from heart disease. A causal link is doubtful though not impossible. An experimental design must be conducted to reach the conclusion of possible causal relationship NUS/FOS/DSAP 11...
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## This note was uploaded on 09/12/2013 for the course SCIENCE GEM2900 taught by Professor Chen during the Fall '10 term at National University of Singapore.

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