Back to: Chapter 16: Simple linear regression and correlation

2 thoughts on “The Coefficient of Determination (Preview)

  1. How do you know when to square the formula and when not to? I mean like why is sxy squared not x and y

    1. The formula I’m using here for the coefficient of determination is

      Coefficient of Determination

      This formula calls for three quantities to be used:
      • the covariance (Sxy)
      • the variance of X (Sx2)
      • the variance of Y (Sy2)

      Notice that the covariance is unlike the other two variances listed here in that it is not a squared quantity… in other words, we did not square anything to calculate it, and so the symbol (Sxy) does not show that it is squared. The formula for the coefficient of determination requires that it be squared, so this is why we square the coefficient of variation when calculating R2, but not the variance of x or the variance of y (since they already ARE squared quantities).

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