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I have several temporal signals of different dimensions, for example the motion of a point throughout time which would be of dimension 3, and the value of a temperature sensor, of dimension 1.

I would like to find out if these signals are correlated. Is there a measure of correlation that works for signals that do not have the same dimensionality?

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Yes, you can use multiple regression, with temperature as the dependent variable and the three space dimensions as the independent variables.

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