How to do a curve fitting for a scatter plot?

Hi everyone,

I have a set of data and I want to plot a curve fitting along these scatter points. I try to use the curve fitting app provided in the MATLAB software but it's not really fitted. What are the codes that I should use to do a curve fitting for this scenerio? The curve doesn't need to fit every single point, an approximation would be fine for these fittings.

The desired curve should be something like on the attached photo.

clc;
close all;
clear all;

x_t = [0.969  0.951  0.938  0.944  0.932  0.926  0.932  0.944  0.951  0.975  0.975  1  0.963  0.957  0.932  0.914  0.87  0.858  0.821  0.772  0.698  0.673  0.66
];
y_t = [35.3  43.2  50.6  56.8  66  71.8  83.4  88  98.4  107  112  116  128  131  141  146  158  162  170  179  186  195  203
];

x_t1 = [1.008  1  0.992  0.983  0.933  0.924  0.933  0.958  0.975  0.992  1  1.008  1  0.975  0.966  0.95  0.941  0.899  0.933  0.908  0.891  0.882  0.849  0.79  0.765
];
y_t1 = [27.6  34.4  44  52.4  59.4  71.8  74.1  84.8  91.2  101  105  115  120  131  136  145  151  161  166  174  182  193  201  210  217
];

x_t2 = [1  0.85  0.9833  0.975  0.9667  0.975  0.9667  0.9583  0.9667  0.9833  0.9667  0.975  1  0.9667  0.975  0.9583  0.9417  0.933  0.8917  0.8333  0.875  0.85  0.8417  0.8167  0.8
];

y_t2 = [27.2  34  44.3  53  60.8  68.9  76  83.9  95.8  102.1  114  117  125  132  141  147  157  163  174  179  186  198  209  217  226
];

figure
plot(x_t,y_t, 'r*','Linewidth', 2);
xlabel('Signal intensity ratio');
ylabel('Temperature');
title('Intensity ratio calibration of 1:4% by mass');
legend('1:4%');
grid on;

figure
plot(x_t1,y_t1, 'g*','Linewidth', 2)
xlabel('Signal intensity ratio');
ylabel('Temperature');
title('Intensity ratio calibration of 1:20% by mass');
legend('1:20%');
grid on;

figure
plot(x_t2,y_t2, 'b*','Linewidth', 2)
xlabel('Signal intensity ratio');
ylabel('Temperature');
title('Intensity ratio calibration of 1:32% by mass');
legend('1:32%');
grid on;

Thanks!

Answer 1

[Rostislav Teryaev]

For approximation use polyfit. For interpolation use interp1. Also when doing approximation it may be helpful to change x and y. For example use not a

polyfit(x,y,7),

but

polyfit(y,x,7).

[Gavin Lo-chindapong]

That gives me some great idea on the curve fitting. Thanks.