Transcription of Standardized Coefficients - University of Notre Dame
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Standardized Coefficients - University of Notre Dame
Standardized Coefficients Task. How do you decide which of the Xs are most important for determining Y? In this handout, we discuss one possible (and controversial) answer to this question - the Standardized regression Coefficients . Formulas. First, we will give the formulas and then explain their rationale: General Case: sx k As this formula shows, it is very bk = bk * easy to go from the metric to the sy Standardized Coefficients . There is no need to actually compute the Standardized variables and run a new regression. Two IV case: ry1 ( r12 * ry 2 ) Compare this to the formula for b1 = the metric Coefficients . Note that 1 r122. correlations take the place of the ry 2 ( r12 * ry1 ) corresponding variances and b2 = covariances. 1 r122. 1 IV case b = ryx In the one IV case, the Standardized coefficient simply equals the correlation between Y.
r b rrr r yy yy 1 112 12 2 2 2121 12 2 1 1 (*) (*) Compare this to the formula for the metric coefficients. Note that correlations take the place of the corresponding variances and covariances. 1 IV case br′= yx In the one IV case, the standardized coefficient simply equals the correlation between Y and X Rationale.
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