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Scaling law: Difference between revisions
→General method
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:<math>y = e^{\alpha_0} x_1^{\alpha_1} x_2^{\alpha_2} ...</math> | :<math>y = e^{\alpha_0} x_1^{\alpha_1} x_2^{\alpha_2} ...</math> | ||
Here, the α<sub>i</sub> are the scaling parameters. | Here, the α<sub>i</sub> are the scaling parameters. | ||
By taking the logarithm of this expression, it becomes linear 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) | * using ''dimensionless'' variables (easily achieved by normalizing all quantities appropriately) | ||