ECON 120B Lecture Notes - Covariance
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Sample covariance sxy= (x x) ( y y) ; 1 rxy +(see appendix) n 1 sxy sx s y: note symmetry: sxy = syx and rxy = ryx, these estimators are unbiased, but not robust, correlation is unit free; it remains the same if the units of measurement of the variables are changed. rxy is called pearson"s correlation coefficient. =22. 81 smg= gi mi n g m n 1 r mg= =0. 901: hypothesis testing (correlation), assume that x and y are jointly normally distributed with correlation r, typical hypothesis specification, ho: = 0; h1: 0 (h0 (cid:222) x and y are stat. independent, test procedure, compute test statistic. Ec 120b intro correlation & regression page 3 of 8 y x x x x rxy = 1 rxy = -0. 9 rxy = 0. 1 rxy = 0: correlation does not imply causation!.
