I. On a General Method of determining the successive terms in a Skew Regreuion Line
Year: 1921
Type: article
Abstract: Let x aud y be the two variates.Suppose tho x-ntnge divided up into any not necessarily equal intervals A, giving arrays of y of which the mean of those which centre at x (lying somewhere in Ax) in y x and the array total *,.Let x, y, c I , <r, be the means and standard deviations of the total pnpulatinu Af of the two variatcs.Assume the form of tie regression line of y on J to be: ^-a e f,+a 1 + 1 + ...+a.f a (i), where do, a,...a, are absolute constants to be determined and if-, i« an orthogonal function of --, Le. in subject to the oondition that: .O-O, < and «' unequal (ii), if the summation S be taken for all values of x corresponding to the arbitrary system of arrays.Further let us supposet thai : in the usual product-moment notation. .Clearly if the ^,'s can be determined we must hare by virtue of (ii) from (i) »• Now if i^, be determined as an integral function af-(s -x)/<r m of the nth degree, the left-hand side of (iii) in expressible in terms of the fu'a, or the product-moments of the correlation distribution.Thus o» will be detenuiued.Let us write: _ /*' \ Civ).and * Bepiodaeed from leoture notes.*t * & denotes tanunstfon of all array*, Z denotes fTrmTnatitTTi
Source: Biometrika
Author: K. PEARSON
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2082880424