How to use regression to find equation of data set?

Dear All,

I would like to ask for some help.

I am trying to find the equation present my data.

But io stuck when use regression method.

could someone help me?

i assume my equation is:

z = a*x^n +b*y+c

Thanks so much!

Han

x = [12	12.5	13	13.5	14
]

x = 1×5

12.0000 12.5000 13.0000 13.5000 14.0000

y = [61	61.5	62	62.5	63
]

y = 1×5

61.0000 61.5000 62.0000 62.5000 63.0000

z = [120	114	103	93	80
124	120	109	97	85
128	121	113	101	88
130	125	116	105	92
134	128	119	109	96
]

z = 5×5

120 114 103 93 80 124 120 109 97 85 128 121 113 101 88 130 125 116 105 92 134 128 119 109 96

surf(x,y,z)

Answer 1

[KSSV]

x = [12	12.5	13	13.5	14] ;
y = [61	61.5	62	62.5	63] ;

[X,Y] = meshgrid(x,y) ; 
Z = [120	114	103	93	80
124	120	109	97	85
128	121	113	101	88
130	125	116	105	92
134	128	119	109	96] ;

x = X(:) ;
y = Y(:) ;
z = Z(:) ; 

sf = fit([x, y],z,'poly22') 

     Linear model Poly22:
     sf(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2
     Coefficients (with 95% confidence bounds):
       p00 =       -3160  (-6274, -46.38)
       p10 =       55.49  (9.233, 101.7)
       p01 =       90.67  (-8.557, 189.9)
       p20 =      -4.514  (-5.311, -3.717)
       p11 =        0.68  (0.01303, 1.347)
       p02 =     -0.7429  (-1.54, 0.05432)

plot(sf,[x y],z)

[Jenifer NG]

Thanks you!

Is there anyway to find best fit equation of my data? or just base on RMSE value

[KSSV]

This is fine enough.

[Jenifer NG]

Could you help me to modify grid that display only 4x4 ?

[KSSV]

x = [12	12.5	13	13.5	14] ;
y = [61	61.5	62	62.5	63] ;

[X,Y] = meshgrid(x,y) ; 
Z = [120	114	103	93	80
124	120	109	97	85
128	121	113	101	88
130	125	116	105	92
134	128	119	109	96] ;

x = X(:) ;
y = Y(:) ;
z = Z(:) ; 

sf = fit([x, y],z,'poly22') 

     Linear model Poly22:
     sf(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2
     Coefficients (with 95% confidence bounds):
       p00 =       -3160  (-6274, -46.38)
       p10 =       55.49  (9.233, 101.7)
       p01 =       90.67  (-8.557, 189.9)
       p20 =      -4.514  (-5.311, -3.717)
       p11 =        0.68  (0.01303, 1.347)
       p02 =     -0.7429  (-1.54, 0.05432)

zi = sf(x,y) ;

figure
hold on
surf(X,Y,Z)
plot3(x,y,zi,'*b')
view(3)

[Jenifer NG]

thanks you!

I got it