1-5次多项式拟合方程

Linear model Poly44: f(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p30*x^3 + p21*x^2*y + p12*x*y^2 + p03*y^3 + p40*x^4 + p31*x^3*y + p22*x^2*y^2 + p13*x*y^3 + p04*y^4 where x is normalized by mean 3478 and std 786.3 and where y is normalized by mean 4239 and std 335.7 Coefficients (with 95% confidence bounds): p00 = 940.5 (930, 950.9) p10 = -52.56 (-65.64, -39.49) p01 = -190.7 (-205.7, -175.6) p20 = -10.19 (-27.41, 7.032) p11 = -20.32 (-44.56, 3.931) p02 = -37.95 (-54.34, -21.56) p30 = -11.3 (-18.7, -3.903) p21 = 25.87 (12.77, 38.98) p12 = -18.89 (-38.19, 0.4014) p03 = 6.006 (-3.927, 15.94) p40 = -0.7479 (-6.189, 4.693) p31 = 4.858 (-5.017, 14.73) p22 = -3.114 (-20.14, 13.91) p13 = 11.81 (-3.784, 27.4) p04 = 5.667 (-0.2945, 11.63) Goodness of fit: SSE: 5.89e+04 R-square: 0.9763 Adjusted R-square: 0.973 RMSE: 24.15 f(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p30*x^3 + p21*x^2*y + p12*x*y^2 + p03*y^3 + p40*x^4 + p31*x^3*y + p22*x^2*y^2 + p13*x*y^3 + p04*y^4 + p50*x^5 + p41*x^4*y + p32*x^3*y^2 + p23*x^2*y^3 + p14*x*y^4 + p05*y^5 where x is normalized by mean 3478 and std 786.3 and where y is normalized by mean 4239 and std 335.7 Coefficients (with 95% confidence bounds): p00 = 923.7 (917.9, 929.5) p10 = -60.56 (-73.45, -47.67) p01 = -169.4 (-181.1, -157.8) p20 = 12.53 (1.772, 23.28) p11 = -20.57 (-37.77, -3.372) p02 = 7.16 (-6.942, 21.26) p30 = -22.46 (-35.37, -9.547) p21 = 14.02 (-6.011, 34.06) p12 = 0.4896 (-22.09, 23.07) p03 = -9.91 (-22.35, 2.532) p40 = -10.01 (-14.15, -5.864) p31 = 16.82 (7.57, 26.07) p22 = -27.6 (-42.85, -12.36) p13 = -8.249 (-24.65, 8.15) p04 = -7.939 (-14.6, -1.273) p50 = 5.87 (2.705, 9.035) p41 = -5.322 (-11.91, 1.268) p32 = 2.738 (-8.493, 13.97) p23 = 14.04 (-0.5119, 28.59) p14 = 3.661 (-7.575, 14.9) p05 = 3.898 (0.2348, 7.562) Goodness of fit: SSE: 1.421e+04 R-square: 0.9943 Adjusted R-square: 0.9931 RMSE: 12.23 f(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p30*x^3 + p21*x^2*y + p12*x*y^2 + p03*y^3 where x is normalized by mean 3478 and std 786.3 and where y is normalized by mean 4239 and std 335.7 Coefficients (with 95% confidence bounds): p00 = 959.9 (947.6, 972.3) p10 = -48.25 (-68.08, -28.41) p01 = -158.7 (-178.2, -139.1) p20 = -31.76 (-42.46, -21.07) p11 = 23.18 (6.424, 39.95) p02 = -29.37 (-43.55, -15.18) p30 = -10.88 (-19.73, -2.027) p21 = 5.731 (-8.245, 19.71) p12 = -17.89 (-37.69, 1.918) p03 = 4.943 (-5.089, 14.98) Goodness of fit: SSE: 1.716e+05 R-square: 0.931 Adjusted R-square: 0.9251 RMSE: 40.23 f(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 where x is normalized by mean 3478 and std 786.3 and where y is normalized by mean 4239 and std 335.7 Coefficients (with 95% confidence bounds): p00 = 921.1 (899.6, 942.7) p10 = -104.3 (-123.8, -84.81) p01 = -122.6 (-144.1, -101.1) p20 = -24.99 (-43.13, -6.858) p11 = 11.54 (-11.98, 35.05) p02 = -0.4705 (-16.55, 15.6) Goodness of fit: SSE: 6.49e+05 R-square: 0.7389 Adjusted R-square: 0.7271 RMSE: 76.81 Linear model Poly11: f(x,y) = p00 + p10*x + p01*y where x is normalized by mean 3478 and std 786.3 and where y is normalized by mean 4239 and std 335.7 Coefficients (with 95% confidence bounds): p00 = 889.6 (874.2, 905) p10 = -120.5 (-139, -102) p01 = -133.2 (-151.8, -114.7) Goodness of fit: SSE: 7.948e+05 R-square: 0.6803 Adjusted R-square: 0.6746 RMSE: 83.87