May 16 - Multiple Regression Controlling for a third...

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May 16, 2008 Multiple Regression Controlling for a third variable o We compare only similar groups o We remove the influence of a second independent variable o We can control for several variables at the same time Multiple regression equation o There are several slopes, or regression coefficients o Each tells you the average change in Y as X increase by 1, while holding each other variable constant Example: age, family attachments, and delinquency o Y = a +b1x1 +b2x2 + e Delinquency = a + b1(age) + b2(family attachments) + e o Using the correlations we could find b1 and b2 o Then: a = - b 11 – b 22 b 1 = 3.9, b 2 = -2.05; a 23.1 delinquency = 23.1 + 3.9(age) – 2.05(attachment) o For an 18 year-old with an attachment score of 15, predicted delinquency=23.1+70.2-30.75=62.55 Standardized slopes: Beta weights o One problem with regression coefficient is the it is not standardized It varies based on the measurement scale
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Unformatted text preview: We cannot compare two coefficients in the same model o The standardized slope, or beta weight, is standardized we can use this to compare relative influence of different variables Standardized slope: Beta weights o b* x1 = b x1 (s x1 /s y ) o The standardized slope tells us how many standard deviations y will change with a 1 standard deviation increase in x. o In the delinquency equation: b1 = 3.9; b*1=0.23 b2 = -2.05; b*2 = -0.579 Though the slope for age (b1) is larger, family attachment (b2) has a larger effect on delinquency Multiple coefficient of determination: R 2 o R 2 is just like Bivariate regression The proportion of variance in the dependent variable that is explained by all the independent variable Varies from 0 to 1 It tells us how good out model is, overall...
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