Scaling law: Difference between revisions

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The typical scaling law expression for a (dependent) variable ''y'' as a function of some (independent) system variables ''x<sub>1</sub>'', ''x<sub>2</sub>'',... is:
The typical scaling law expression for a (dependent) variable ''y'' as a function of some (independent) system variables ''x<sub>1</sub>'', ''x<sub>2</sub>'',... is:
:<math>y = e^{\alpha_0} x_1^{\alpha_1} x_2^{\alpha_1} ...</math>
:<math>y = e^{\alpha_0} x_1^{\alpha_1} x_2^{\alpha_2} ...</math>
Here, the &alpha;<sub>i</sub> are the scaling parameters.
Here, the &alpha;<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 and simple (multivariate) linear regression tools can be used to determine the parameters from a set of data.