On a problem connected with quadratic regression

E(Y) = flo +/3lE(X) + ... +4kE(Xk). (1.2) If k 2 and f2 t 0 (k = 1 and Ih1 + 0) then we speak of quadratic (linear) regression. If k = 0, that is if E( YjX) = E( Y) almost everywhere, then we say that Y has constant regression on X. The coefficients ,80, ,l1, . . , Ak are called the regression coefficients. Let X1, X2, .. ., Xn be a sample of size n (independently and identically distributed random variables) from a population with distribution function F(x). We write