Intrinsically Linear Variables

Intrinsically Linear Variables

• Can a least-squares linear regression analysis be used to determine the best fit of (F,V) data to the nonlinear expression V = k + bFc, where k is V when F = 0 ?

MATLAB’s polyfit Command

• Using MATLAB, x,y data can be fit and evaluated using least-squares regression analysis.

Example: Fitting Ideal Gas DataFor an ideal gas, pV=C, where p is pressure, V is volume, is the specific heatratio, and C is a constant. Determine the best-fit value for given the data:

Example: Fitting Hot-Wire Data• Hot-wire anemometry can be used to measure local flow velocity. The relationship between the flow velocity, U, and the anemometer circuit’s voltage, E, is given by King’s Law (a form of the conservation of energy).

sensor

• For the following data, determine

A, B and n using LSLRA.

Example: Fitting Hot-Wire Data• King’s Law can be transformed into linear intrinsic variables, where

Example: Fitting Hot-Wire Data