# How to find the y from given x on fit line?

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### Answers (4)

Jeffrey Clark
on 12 Nov 2022

@kivanc Koca, if you have a fit using spline, pchip, makima, interp1, or the spline utility function mkpp you can use Evaluate piecewise polynomial - MATLAB ppval (mathworks.com).

If you have a polynomial fit using Create and Evaluate Polynomials you can use Polynomial evaluation - MATLAB polyval (mathworks.com).

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John D'Errico
on 12 Nov 2022

Edited: John D'Errico
on 12 Nov 2022

It completely depends on how you perform the fit. For example, with the curve fitting toolbox, just do this:

X = rand(10,1);

Y = cos(X);

mdl = fit(X,Y,'poly2') % quadratic fit to a cosine is probably adequate over a reasonably small interval

Now we can just use the resulting fitted model to predict any point as I do here:

mdl(.3)

Other fitting tools, for example, polyfit, also have evaluation tools provided with them, so you can use polyval to evaluate a polynomial model from polyfit. Read the help for the tool you used to perform the fit.

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Image Analyst
on 12 Nov 2022

You can use polyfit and polyval. Here is a full demo. Don't be afraid, the actual code is only 2 lines. The rest is just code to create the variables and do some fancy plotting.

x = sort(10 * rand(1, 10));

y = 0.5 * x + 0.3 * rand(1, length(x));

% Plot the original points.

plot(x, y, 'b.', 'MarkerSize', 30);

grid on;

xlabel('x', 'FontSize',20)

ylabel('y', 'FontSize',20)

% Fit a line through the points.

coefficients = polyfit(x, y, 1); % YOU NEED THIS LINE!

% Get a fit. Find the fit values everywhere, even between the original points, just for fun.

xFit = linspace(min(x), max(x), 1000);

yFit = polyval(coefficients, xFit);

hold on;

plot(xFit, yFit, 'r-', 'LineWidth', 2)

% Find the y location where x equals exactly 6.

xDesired = 6;

xline(xDesired, 'Color', 'g', 'LineWidth',2)

yDesired = polyval(coefficients, xDesired) % YOU NEED THIS LINE!

% Draw a line from the y axis to the fit line and report what the y value

% is in the title of the graph.

line([0, xDesired], [yDesired, yDesired], 'Color', 'g', 'LineWidth', 2)

caption = sprintf('y = %f when x = %.1f', yDesired, xDesired);

title(caption, 'FontSize',20)

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