Hello, Quadratic and power curve fitting

pressure=[10 15 25 40 50 55];
flow=[94 116 147 183 215 220];

a = -0.0170 ; b = 3.8870 ; c = 59.0062 ;

p = 5 : 60 ;

f = 5 : 300 ;

f_par = a* p.^ 2 +b * p + c

alpha = 72.0144 ; beta = 2.7842 ;

f_exp = alpha * p.^beta;

plot (pressure,flow,'o',p,f_par,p,f_exp,'--')
legend ('eperimental data','parabolic fit','exponential fit')
xlabel ('pressure psi') , ylabel ('flow gpm'),grid

Could some one correct my code where Y axis (f = flow rate) would stop plotting at value 400. currently it plots to 7*10^6.

thank you very much

Answer 1

[John D'Errico]

What do you expect? As you generated it, we see:

f_exp
f_exp =
Columns 1 through 13
     6360.5        10567        16231        23540        32675        43815        57130        72791        90962   1.1181e+05   1.3549e+05   1.6215e+05   1.9197e+05
Columns 14 through 26
 2.2509e+05   2.6165e+05   3.0182e+05   3.4573e+05   3.9354e+05   4.4539e+05   5.0142e+05   5.6178e+05    6.266e+05   6.9602e+05   7.7019e+05   8.4923e+05    9.333e+05
Columns 27 through 39
 1.0225e+06    1.117e+06   1.2169e+06   1.3224e+06   1.4336e+06   1.5505e+06   1.6734e+06   1.8024e+06   1.9376e+06   2.0791e+06   2.2271e+06   2.3816e+06   2.5429e+06
Columns 40 through 52
 2.7109e+06    2.886e+06   3.0681e+06   3.2574e+06   3.4541e+06   3.6582e+06   3.8698e+06   4.0892e+06   4.3163e+06   4.5514e+06   4.7946e+06   5.0459e+06   5.3055e+06
Columns 53 through 56
 5.5735e+06     5.85e+06   6.1352e+06   6.4291e+06

The problem is NOT the plot. The problem is that somehow, you generated a garbage model.

ALWAYS look at what you got from a computation. Plotting garbage and expecting to magically see what you want to see is a good path to failure.

And since we have not been shown where those coefficients came from, how can we realistically help you?

Perhaps you wanted to do this:

mdl = fittype('power1')
mdl = 
     General model Power1:
     mdl(a,b,x) = a*x^b

fittedmdl = fit(pressure',flow',mdl)
fittedmdl = 
     General model Power1:
     fittedmdl(x) = a*x^b
     Coefficients (with 95% confidence bounds):
       a =       29.17  (23.95, 34.4)
       b =      0.5049  (0.456, 0.5538)

f_exp = fittedmdl.a*p.^fittedmdl.b;
plot (pressure,flow,'o',p,f_par,p,f_exp,'--')
legend ('eperimental data','parabolic fit','exponential fit')
xlabel ('pressure psi') , ylabel ('flow gpm'),grid

That presumes the Curve fitting TB.

[Charitha Heshan]

Thank you for your response ,

if true
  % code
function [a2,a1,a0] = QuadraticRegression (x,y)

x=[10 15 25 40 50 55]; y=[94 116 147 183 215 220];

n = length (x) sx = sum(x) sy = sum(y) sx2 = sum(x.^2) sx3 = sum(x.^3) sx4 = sum(x.^4) sxy = sum(x.*y) sx2y= sum(x.*x.*y)

A = [ n sx sx2; sx sx2 sx3;sx2 sx3 sx4] b = [sy;sxy;sx2y]

w= A\b

a2 = w(3) a1 = w(2) a0 = w(1)

end

This is the model i used to find the coefficients a0 a1 a3 .

if true
  % code
function [a1 , a0] = linearRegression (x,y)

x=[10 15 25 40 50 55]; y=[94 116 147 183 215 220];

n=length(x) sx= sum(x) sy= sum(y) sxx= sum(x.*x) sxy= sum(x.*y) den = n*sxx - sx^2 a1 = (n*sxy - sx*sy) /den a0 = (sxx*sy - sxy*sx) /den

l = zeros (n,1) for i = 1:n, l(i) = a1*x(i) + a0; plot (x,y,'o') hold on plot (x,l) end

end

the above model was used to obtain a linear equation y= n0x+n1 and converted it to a power function as follows = alpha = 72.0144 ; beta = 2.7842 ;

function = alpha * p.^beta;

so i'm suppose to plot both quadratic and power functions on the same graph .

the original plot model was provided to me by the professor, i honestly lack knowledge to come up with by my self.

thank you for your time