Spurious Correlation Due to Deflating Variables

This Memorandum shows that when a homogeneous linear regression of a normally distributed variable Y on two nromally distributed variables X and Z is deflated by Z, then when X and Y are uncorrelated the deflated dependent variable Y/Z and independent variable X/Z are either uncorrelated or perfectly correlated. Thus, existing approximations to the covariance of these deflated variables are poor. A new approximation to this covariance is given which has the same defect for normally distributed variables, but which could otherwise be better than existing ones. (Author)