1-5次多项式拟合方程

1-5次多项式拟合方程

2023年8月3日发(作者:)

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

Linear model Poly55:

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

Linear model Poly33:

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

Linear model Poly22:

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

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