A new physically based thermal noise model for MESFET``s has been proposed, which is compatible with small signal equivalent circuit and large signal current-voltage characteristics. Specifically, the static feedback effect is taken into account to model noise characteristics correctly especially in low current regime. The gate and drain bias dependence of the gate noise voltage, the drain noise current, and the correlation coefficient between them has been investigated thoroughly, showing good agreement with experimental results from 0.5 {SYMBOL 109 \f "Symbol"}m gate length MESFET. As a result, our formulation is successfully used to model bias dependence of the four noise parameters with reasonably good accuracy. A new extraction method for noise sources and correlation coefficient in the noise equivalent circuit of GaAs MESFET is proposed. It is based on the linear regression, which allows us to extract physically meaningful parameters from the measurement in a systematic and straightforward way. The confidence level of the measured data can also be easily examined from the linearity, y-intercept of the linear regression, and the scattering from the regression line. Furthermore, it is found that the time delay of correlation coefficient whose value is almost the same as that of the transconductance should be considered to model noise parameters accurately. The calculated values of minimum noise figure, optimum impedance, and noise resistance both at high and at low drain current bias using above approach, show excellent agreement with measurement for a typical MESFET device studied in this paper.