An Introduction to the Theory of Statistics

Cover An Introduction to the Theory of Statistics
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. („_!, by b^^M . . . („-i) . crl^t . . , („_i)/o-^.34 . . . (n-i).
we have il2.34 . . . n. ir2.31 . . . n = 612.34 . . . (n-l)- 02.34 . . . (n-1) - 6l>i.S4 . . . (n-1). *n2.S4 . (n-1)- 1^2.34 . . . (n-U, or, from (9), 1 _ O12.34 .... (n-1) ~ °lii.34 .... (n-ll ■ "n2.34 . , . (n-1) / 1 1 \ "12.34 . . . . n— 1 A h \'-^/ ■•■ " "211.31 .... (n-1) • ''n2.34 .... (n-1) The student should note that this is an expression of the form I _ O l2 — OiM . On2 "12.n — "i I I 1 - On. . 0„, 238 THEORY OF STATI
...STICS.
with the subscripts 34 ... . (w - 1) ajided throughout. The coefficient 612.34 . . . . „ may therefore be regarded as determined from a regression-equation of the form *'l.S4 . . . (n-l) — "12.34 . . . n • '"iSl . . . |n-l) + "luffl . j . (n-l| • *n.84 . . . (B-l)) i.e. it is the partial regression of ajj.g^ .... („Ii| on a^.^ .... („_,,, *'n.s4 .... (M-ii being given. As any other secondary suffix might have been eliminated in lieu of n, we might also regard it as the partial regression of x^^^ .


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