MATLAB: How to predict x values for a dataset of y values using a fitted polynomial model of y/x values

curve fitting

I have immunoassay data with OD values for different concentration of antigen. I fitted a polynomial function (2 degree) to the data (y=OD, x=concentration). Now I need to predict concentrations based on measured ODs (which are on a collumn vector). How can I do that?

Thanks

Best Answer

Get the equation:

coeffs = polyfit(x, y, 2);

Then get the x values for any particular y value with roots():

a = coeffs(1);
b = coeffs(2);
c = coeffs(3) - y;
x = roots([a, b, c]) % Will be vector of two values.

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MATLAB: Not Really sure how to go about plotting this

Try using roots() - the function meant for doing that:

x = linspace(-6, 6, 1000);
y = x.^2 + 2 * x - 10;
plot(x, y, 'b-', 'LineWidth', 2);
grid on;
r = roots([1,2,-10])
% Make black line for x axis;
yline(0, 'LineWidth', 2);
% Make vertical lines at roots
xline(r(1), 'LineWidth', 2, 'Color', 'r');
xline(r(2), 'LineWidth', 2, 'Color', 'r');
xlabel('x', 'FontSize', 18);
ylabel('t', 'FontSize', 18);
caption = sprintf('Roots at %.2f and %.2f', r(1), r(2));
title(caption, 'FontSize', 18);

MATLAB: How to plot a tangent line of specific point (x,y) of function y=x^2+2

Try this:

x = linspace(-2, 2, 500);
y = x .^ 2 + 2;
plot(x, y, 'b-', 'LineWidth', 2);
grid on;
fontSize = 20;
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
ylim([0, 7]);
% Pick a point at -1 (or wherever) and plot the tangent
xTangent = -1;
% Equation of the tangent is y = slope*x + offset
% From the equation y=x^2 we know the slope is 2*x.
% Find the slope at x = xTangent.
slope = 2 * xTangent;
% We want to plot the tangent line where it just touches the curve,
% so we need to know the y value at xTangent.
yTangent = xTangent .^ 2 + 2;  % Y value of curve at x = xTangent.
hold on;
plot(xTangent, yTangent, 'r*', 'LineWidth', 2, 'MarkerSize', 10);
% Use point slope formula of a line to get equation for y
% y-y0 = slope*(x-x0).
% y = slope * (x - xTangent) + yOffset
yTangentLine = slope * (x - xTangent) + yTangent;
plot(x, yTangentLine, 'b-', 'LineWidth', 2);

Best Answer

Related Solutions

MATLAB: Not Really sure how to go about plotting this

MATLAB: How to plot a tangent line of specific point (x,y) of function y=x^2+2

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