# How do I perform a linear least squares fit

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Alexander MacFarlane IV on 21 Dec 2018
Edited: Tamas Kis on 26 Jul 2021
Hello.
I would like to perform a linear least squares fit to 3 data points.
The help files are very confusing, to the point where i can't figure out whether this is a base function of Matlab, I need the curve fitting toolbox, optimization toolbox, or both.
Thanks,
Alex

Star Strider on 21 Dec 2018
You don’t need any toolboxes. Use polyfit (link) and polyval functions, or the mldivide (link) operator.

Image Analyst on 21 Dec 2018
Edited: Image Analyst on 21 Dec 2018
See attached polyfit demo. Adapt as needed. All you need is base MATLAB - no toolboxes.
For example
coefficients = polyfit(x, y, 1);
yFitted = polyval(coefficients, x); % yFitted will be at the 3 points where x is. There will be 3 yFitted values.
If you want a lot more points, you can pass in more x to polyval():
xFit = linspace(min(x), max(x), 1000); % 1000 points.
yFitted = polyval(coefficients, xFit);
Alexander MacFarlane IV on 21 Dec 2018
Thanks Star Strider and Image Analyst!
You guys are amazingly fast.

Tamas Kis on 25 Jul 2021
Edited: Tamas Kis on 26 Jul 2021
Function to perform curve fitting using linear least squares:
Linear and polynomial fits are linear least square fits, while the other fits (power, exponential, logarithmic) are approximated by first linearizing the data.

R2018b

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