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I have a hundred time series, all sampled at the same time interval. I did an FFT of all of these time series and arranged them row by row in a matrix ($\mathbf{X}$). I have a target variable ($\mathbf{y}$) for each time series. I then solve the multiple linear regression equation:

$$ \mathbf{y} = \mathbf{X}\,\boldsymbol{\beta} + \boldsymbol{\varepsilon} $$

I want to plot the $\boldsymbol{\beta}$ back on the FFT spectrum to see which FFT spectrum is the most useful in predicting $\mathbf{y}$.

Does this make any sense?

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  • $\begingroup$ No, it doesn't make sense because each FFT spectrum predicts only one component of y, if I understand your formula correctly. Now, if your formula was written as $\mathbf{y} = \boldsymbol{\beta}\,\mathbf{X} + \boldsymbol{\varepsilon}$, then it would make sense because each weight would correspond to one FFT spectrum, and the FFT spectrum with the higher weight (in absolute sense) would contribute more to predicting $\mathbf{y}$. $\endgroup$ Commented Oct 3 at 12:55

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