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Scaling law: Difference between revisions
→General method
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By taking the logarithm of this expression, it becomes linear in the parameters and simple (multivariate) linear regression tools can be used to determine the parameters from a set of data. | By taking the logarithm of this expression, it becomes linear in the parameters and simple (multivariate) linear regression tools can be used to determine the parameters from a set of data. | ||
However, a proper analysis requires: | However, a proper analysis requires: | ||
* using ''dimensionless'' variables (easily achieved by normalizing all quantities appropriately)<ref> | * using ''dimensionless'' variables (easily achieved by normalizing all quantities appropriately)<ref>T.C. Luce, C.C. Petty, and J.G. Cordey,''Application of dimensionless parameter scaling techniques to the design and interpretation of magnetic fusion experiments'', [[doi:10.1088/0741-3335/50/4/043001|Plasma Phys. Control. Fusion, '''50''', 4 (2008) 043001]]</ref> | ||
* guaranteeing the (linear) ''statistical independence'' of the independent variables (applying, e.g., [[:Wikipedia:Principal component analysis|Principal Component Analysis]]) | * guaranteeing the (linear) ''statistical independence'' of the independent variables (applying, e.g., [[:Wikipedia:Principal component analysis|Principal Component Analysis]]) | ||