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Refers to a general estimation technique that selects the parameter value to minimize the squared difference between two quantities, such as the observed value of a variable, and the expected value of that observation conditioned on the parameter value. Gaussian linear models are fit by least squares and least squares is the idea underlying the use of mean-squared-error (MSE) as a way of evaluating an estimator.

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What regression analysis should I perform on my data and why?

Your situation is a bit complicated. We just need to take a step back. In order for us to run this regression we need to know what your research question / hypothesis is? You might not have to use t …
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