May 12 - Are b or r significantly greater than 0? o For...

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May 12, 2008 Regression and Correlation Adding an error term o Our prediction helps, but is far from perfect – there is always error involved o A different version of the same equation is: y=a+bx+e o This acknowledges the error involved Comparing b and r o Similarities: Will always be the same sign ( + or - ) Both tell us about the strength of the relationship between X and Y r yx = b yx (S x /S y ) o Differences r is standardized, it can only for from -1 to 1; b is not b lets us predict values of y based on x; r does not b becomes more important with multiple regression Significance test o
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Unformatted text preview: Are b or r significantly greater than 0? o For now, we only need one test- If r is significantly greater than 0, then b will be too o Null and alternative hypotheses H : =0 H 1 : o We use a t-test, so find t critical , with df=n-2 o Calculate t: t = r r2 1 / 2--n <- r 2 o If t calculated >t critical , reject H o Example 2 tailed n = 500 H0: =0 r = .40 H1: df = n-2 = 498 t = r 2 / 2 r q n--t critical = 1.96 = .4 84 . / 498 = .4(24.3) = 9.7 REJECT the null hypothesis; the correlation is statistically significant...
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