How to find the variable that minimize the root mean squared error between a known vetor and the multiplication of this variable and an another known vector?
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Supposing that I have a variable
, and two known vectors
, where N is a known number. I want to find the a that minimizes the root mean squared error between
and
. Is there any neat apprach to implement it?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1289910/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1289915/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1289920/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1289925/image.png)
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Accepted Answer
Amal Raj
on 9 Feb 2023
Hi 奥 刘,
You can use linear regression to find a.
Please refer this example below:
N = 100; % Example value for N
x = linspace(0, 10, N)'; % Known vector x
y = sin(x) + 0.1 * randn(N, 1); % Known vector y
X = [ones(N, 1) x]; % Design matrix
a = X \ y; % Solve for a using least squares
y_pred = X * a; % Calculate predicted values of y
rmse = sqrt(mean((y - y_pred) .^ 2)); % Calculate RMSE
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