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Notes on Multiple Regression

Notes on Multiple Regression - Notes on Multiple Regression...

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Unformatted text preview: Notes on Multiple Regression Cxy = ([x(score) X(mean)][y Y]) / (N 1) rxy = Cxy/(sx * sy) rxy = (zx * zy)/N 1 Y(estimating) = b0 + b1x1 + b2x2 + ... + bnxn The more two factors' scores covary, the higher the result of (x X)(y Y), because you need the highest positive differences in x to be multiplied with the highest positive differences in y along with the highest negative differences in both x and y to produce the highest resulting score. To get the highest possible score, x and y must vary exactly (which would produce the same results as [x X]2/[N 1] ). So, the resulting rxy is closer to one as (x X) and (y Y) get infinitely more similar. What you are doing here is getting the standard deviation for xy and if x and y are perfectly similar, then their standard deviation should equal 1. You get the standard deviation of x and y by taking the root of (x X)2/(N 1). Cxy is a covariance score that approaches (x X)2 as x covaries more similarly with y so if x and y are perfectly similar than dividing them by their standard deviations would equal one. Conversely, if x and y were perfect opposites, then you would still yield a very high Cxy but it would be negative (because the highest positive scores would now be multiplied with the highest negative scores). If you then divided this by the standard deviations of x and y, then you would get a score of 1. ...
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