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How do I plot a polynomial equation and set of x-y coordinates on the same graph?

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I am trying to plot a polynmial and some x-y coordinates on the same graph. I need the coordinates to be visible and the lines to be distingushable from one another (eg. different colors).
Here is the measured data.
coefficients = [0.6252 -0.4165 0.1311 -0.0163 0.0009,-0.0000]
x = [2 5 8 11 14 20];
y = [0.20 0.29 0.44 0.50 0.66 0.56];

Accepted Answer

Sam Chak
Sam Chak on 10 May 2024
Edited: Sam Chak on 10 May 2024
Edit: Your original polynomial coefficients are truncated. So, the polynomial cannot produce an accurate result.
%% data
x = [2 5 8 11 14 20];
y = [0.20 0.29 0.44 0.50 0.66 0.56];
%% polynomial coefficients
coefficients = [0.6252 -0.4165 0.1311 -0.0163 0.0009 -0.0000];
p = fliplr(coefficients)
p = 1x6
0 0.0009 -0.0163 0.1311 -0.4165 0.6252
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
format long
p = polyfit(x, y, numel(x)-1)
p = 1x6
-0.000018175582990 0.000901920438957 -0.016287722908091 0.131052812071305 -0.416499314128809 0.625240054869418
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
%% points generated by polynomial
xx = linspace(x(1), x(end), 181);
yy = polyval(p, xx);
%% plot results
plot(x, y, 'o', 'markersize', 10), hold on
plot(xx, yy), grid on, xlabel('x'), xlabel('y')
legend('data', 'polynomial', 'location', 'northwest')
  9 Comments
Deleted User
Deleted User on 11 May 2024
Thank you for that! Sorry to bother you, but I have another question. I’m trying to plot another point on the polynomial. I know the x coordinate is 17.5, but I don’t know the y coordinate. Is there a way I could plot the x coordinate on the polynomial and use the information from the graph to figure out the y coordinate? This coordinate needs to be distinguished from the points (eg. different colour).
Sam Chak
Sam Chak on 11 May 2024
Edited: John Kelly on 20 May 2024
Hi
You can use the polyval() command in this case.
%% data
x = [2 5 8 11 14 20];
y = [0.20 0.29 0.44 0.50 0.66 0.56];
%% polynomial coefficients
p = polyfit(x, y, numel(x)-1)
p = 1x6
-0.0000 0.0009 -0.0163 0.1311 -0.4165 0.6252
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
%% points generated by polynomial
xx = linspace(x(1), x(end), 181);
yy = polyval(p, xx);
%% find y coordinate with given x coordinate
xpt = 17.5;
ypt = polyval(p, xpt)
ypt = 0.9379
%% plot results
plot(x, y, 'o', 'markersize', 10), hold on
plot(xx, yy), grid on, xlabel('x'), ylabel('y')
plot(xpt, ypt, 'p', 'markersize', 10, 'color', "#7E2F8E"), hold off
legend('data', 'polynomial', 'point', 'location', 'northwest')

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More Answers (1)

KSSV
KSSV on 10 May 2024
x = [2 5 8 11 14 20];
y = [0.20 0.29 0.44 0.50 0.66 0.56];
p = polyfit(x,y,3) ;
yi = polyval(p,x) ;
figure
hold on
plot(x,y,'r')
plot(x,yi,'b')
legend('data points','polynomial fit')

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