E-47A Regression Coefficient and Estimated Value CalculationFormula TableThe following table shows the calculation formulas used by the regression coefficient andestimated value commands for each regression calculation type.Linear RegressionCommand Calculation FormulaRegression FormulaConstant Term a a = nΣyi – b.Σx iRegression Coefficient b b = n.Σxi2 – (Σxi)2n.Σxiyi – Σxi.ΣyiCorrelation Coefficient r r ={n.Σxi2 – (Σxi)2}{n.Σyi2 – (Σyi)2}n.Σxiyi – Σxi.ΣyiEstimated Value m m y – ab=Estimated Value ţ n = a + bxQuadratic RegressionCommand Calculation FormulaRegression FormulaConstant Term a a = – b( ) – c( )nΣyinΣxinΣxi2Regression Coefficient b b = Sxx. Sx2x2– (Sxx2)2Sxy.Sx2x2– Sx2y.Sxx2Regression Coefficient c c = Sxx.Sx2x2– (Sxx2)2Sx2y.Sxx – Sxy.Sxx2However,Command Calculation FormulaEstimated Value m1 m1 = 2c– b + b2– 4c(a – y)Estimated Value m2 m2 = 2c– b – b2– 4c(a – y)Estimated Value n n = a + bx + cx2(Σxi )2Sxx = Σxi 2– nSxy = Σxi yi – n(Σxi .Σyi )Sxx2= Σxi 3– n(Σxi .Σx i 2)Sx2x2 = Σxi 4 – n(Σxi 2)2Sx2y = Σxi 2yi – n(Σxi 2.Σy i )(Σxi )2Sxx = Σxi 2– nSxy = Σxi yi – n(Σxi .Σyi )Sxx2= Σxi 3– n(Σxi .Σx i 2)Sx2x2 = Σxi 4 – n(Σxi 2)2Sx2y = Σxi 2yi – n(Σxi 2.Σy i )
