STAT101_Chap10 - 10. Introduction to Multivariate...

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10. Introduction to Multivariate Relationships Bivariate analyses are informative, but we usually need to take into account many variables. Many explanatory variables have an influence on any particular response variable. The effect of an explanatory variable on a response variable may change when we take into account other variables.
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Example : Y = whether admitted into grad school at U. California, Berkeley (for the 6 largest departments) X = gender Whether admitted Gender Yes No Total %yes Female 550 1285 1835 Male 1184 1507 2691 Difference of sample proportions = … There is very strong evidence of a higher probability of admission for men than for women.
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• Now let X 1 = gender and X 2 = department to which the person applied. e.g., for Department A, Whether admitted Gender Yes No Total %yes Female 89 19 108 82% Male 511 314 825 62% Now, a 2 = (df = 1), but difference is …. T he strong evidence is that there is a higher probability of being admitted for than . What happens with other departments?
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Female Male Difference of Dept. Total %admitted Total %admitted proportions a 2 A 108 82% 825 62%
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STAT101_Chap10 - 10. Introduction to Multivariate...

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