Covariance, Regression, and Correlation Covariance Consider a set of paired variables, ((x,y)). The Covariance of (x) and (y) is: [\sigma(x,y)=E[(x-\mu_x)(y-\mu_y)]=E(xy)-\mu_x\mu_y] Regression [y=\alpha+\beta x+e] [\hat y=\alpha+\beta x] [a=\bar y-b\bar x] [b=\frac{Cov(x,y)}{Var(x)}] The least-squares estimators for the intercept and slope of a linear regression are simple functions of the observed means, variances, and covariances. This property is exceedingly useful for quantitative genetics, since such statistics are readily obtainable from phenotypic …