In modern terminology, the conditional mean E(Y|X=x) for a continuous distribution is called the regression function of Y on X and the graph of this function of x is known as the regression curve of Y on X or sometimes the regression curve for the mean of Y. Geometrically, the regression function represents the y co- ordinate of the centre of mass of the bivariate probability mass in the infinitesimal vertical strip bounded by x and x+dx.
Similarly, the regression function of X on Y is E(X|Y=y) and the graph of this function of y is called the regression curve of X on Y.
In case a regression curve is a straight line, the corresponding regression is said to be linear. If one of the regression is linear, it does not however follow that the other is also linear.
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