--------------------------- Linear Regression Functions --------------------------- REGR_* functions analyze relationshitp of the 2 numeric set of data. These functions calculate with records that both of 2 set are not NULL. Syntax: ::= (, ) := { REGR_AVGX | REGR_AVGY | REGR_COUNT | REGR_INTERCEPT | REGR_R2 | REGR_SLOPE | REGR_SXX | REGR_SXY | REGR_SYY } Formula use below variable. Y: ( IS NOT NULL AND IS NOT NULL). X: ( IS NOT NULL AND IS NOT NULL). N: COUNT of recordset except IS NULL OR IS NULL. Formula: REGR_AVGX(Y, X) = SUM(X) / N REGR_AVGY(Y, X) = SUM(Y) / N REGR_COUNT(Y, X) = N REGR_INTERCEPT(Y, X) = REGR_AVGY(Y, X) - REGR_SLOPE(Y, X) * REGR_AVGX(Y, X) REGR_R2(Y, X) = POWER(CORR(Y, X),2) REGR_SLOPE(Y, X) = COVAR_POP(Y, X) / VAR_POP(X) REGR_SXX(Y, X) = N * VAR_POP(X) REGR_SXY(Y, X) = N * COVAR_POP(Y, X) REGR_SYY(Y, X) = N * VAR_POP(Y) Author: Hajime Nakagami Note: Function return NULL if N = 0 except of REGR_COUNT().