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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奥刘 2023-2-9

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https://ww2.mathworks.cn/matlabcentral/answers/1909340-how-to-find-the-variable-that-minimize-the-root-mean-squared-error-between-a-known-vetor-and-the-mul

评论：奥刘 2023-2-10

采纳的回答： Amal Raj

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?

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采纳的回答

Amal Raj 2023-2-9

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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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Torsten 2023-2-9

编辑：Torsten 2023-2-9

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@Amal Raj

You mustn't include the constant term in the calculation of the regression coefficients because you are to regress

y = a*x

not

y = a*x + b

The results for "a" will differ for the two cases.

奥刘 2023-2-10

@Torsten Yes, that's right. I think @Amal Raj just gave me an example but didn't mean that I should include the constant. Anyway, thanks for reminding me!

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