Oracle Regression - Slope, Intercept Functions ```-- Oracle Regression - Slope, Intercept Functions -- The query table is non-null data and computation of Slope and Intercept -- is as computed in [1.1]. The query table [2] has a null value row -- and computation of Slope and Intercept is as computed in [2.1]. -- [1] Query Table WITH q_stat AS (SELECT 1 x, 2 y FROM DUAL UNION SELECT 2 x, 6 y FROM DUAL UNION SELECT 9 x, 3 y FROM DUAL UNION SELECT 4 x, 7 y FROM DUAL) SELECT AVG(x) avg_x, AVG(y) avg_y, COVAR_POP(x ,y) covar_pop, VAR_POP(y) var_pop_y, ROUND(REGR_SLOPE(x, y),4) regr_slope, ROUND(REGR_INTERCEPT(x, y),4) regr_intercept, REGR_COUNT(x ,y) regr_cnt FROM q_stat; ``` Oracle Regression - Slope, Intercept Computation ```-- [1.1] Slope, Intercept Formula COVAR_POP = (SUM(expr1 * expr2) - SUM(expr2) * SUM(expr1)/n)/n = (SUM(1x2+2x6+9x3+4x7) - (2+6+3+7) x (1+2+9+4)/4)/4 = (69 - 288/4)/4 = -0.75 VAR_POP = SUM((expr-(SUM(expr)/COUNT(expr)))2)/COUNT(expr) = SUM((Xi - Avg)2)/n = SUM((2-4.5)2+(6-4.5)2+(3-4.5)2+(7-4.5)2)/4 = (6.25 + 2.25 + 2.25 + 6.25)/4 = 4.25 REGR_SLOPE = COVAR_POP(expr1, expr2)/VAR_POP(expr2) = COVAR_POP(x, y)/VAR_POP(y) = -0.75/4.25 = -0.1765 REGR_INTERCEPT = AVG(expr1) - REGR_SLOPE(expr1, expr2) * AVG(expr2) = AVG(x) - REGR_SLOPE(x, y) * AVG(y) = 4 - (-0.1765 * 4.5) = 4.7941 ``` Oracle Regression - Slope, Intercept Functions With Null Value Data ```-- [2] Query Table with a Null value row WITH q_stat AS (SELECT 1 x, 2 y FROM DUAL UNION SELECT 2 x, 6 y FROM DUAL UNION SELECT 9 x, NULL y FROM DUAL UNION SELECT 4 x, 7 y FROM DUAL) SELECT AVG(x) avg_x, AVG(y) avg_y, ROUND(COVAR_POP(x ,y),4) covar_pop, ROUND(VAR_POP(y),4) var_pop_y, ROUND(REGR_SLOPE(x, y),4) regr_slope, ROUND(REGR_INTERCEPT(x, y),4) regr_intercept, REGR_COUNT(x ,y) regr_cnt FROM q_stat; ``` Oracle Regression - Slope, Intercept Functions ```-- [2.1] Slope, Intercept Formula -- With a Null value, the third row having the Null value is skipped in -- computation of average values as shown below, -- Avg(x) = (1+2+4)/3 = 2.3333 and -- Avg(y) = (2+6+7)/3 = 5 -- with corresponding changes to slope and intercept computation COVAR_POP = (SUM(expr1 * expr2) - SUM(expr2) * SUM(expr1)/n)/n = (SUM(1x2+2x6+null+4x7) - (2+6+null+7) x (1+2+null+4)/3)/3 = (42 - 15 x (7/3))/3 = (42 - 35)/3 = 2.3333 VAR_POP = SUM((expr-(SUM(expr)/COUNT(expr)))2)/COUNT(expr) = SUM((Xi - Avg)2)/n = SUM((2-5)2+(6-5)2+(Null-5)2+(7-5)2)/3 = (9 + 1 + Null + 4)/3 = 14/3 = 4.6667 REGR_SLOPE = COVAR_POP(expr1, expr2)/VAR_POP(expr2) = COVAR_POP(x, y)/VAR_POP(y) = 2.3333/4.6667 = 0.5 REGR_INTERCEPT = AVG(expr1) - REGR_SLOPE(expr1, expr2) * AVG(expr2) = AVG(x) - REGR_SLOPE(x, y) * AVG(y) = (7/3) - 0.5 * 5 = -0.1667 ```

Oracle Covariance
Oracle Variance

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Last Revised On: September 20, 2014

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