Editing Logistic regression (section)

===Parameter estimation===
Since ''ℓ'' is nonlinear in {{tmath|\beta_0}} and {{tmath|\beta_1}}, determining their optimum values will require numerical methods. One method of maximizing  ''ℓ'' is to require the derivatives of ''ℓ'' with respect to {{tmath|\beta_0}} and {{tmath|\beta_1}} to be zero:

:<math>0 = \frac{\partial \ell}{\partial \beta_0} = \sum_{k=1}^K(y_k-p_k)</math>

:<math>0 = \frac{\partial \ell}{\partial \beta_1} = \sum_{k=1}^K(y_k-p_k)x_k</math>

and the maximization procedure can be accomplished by solving the above two equations for {{tmath|\beta_0}} and {{tmath|\beta_1}}, which, again, will generally require the use of numerical methods.

The values of {{tmath|\beta_0}} and {{tmath|\beta_1}} which maximize ''ℓ'' and ''L'' using the above data are found to be:

:<math>\beta_0 \approx -4.1</math>
:<math>\beta_1 \approx 1.5</math>

which yields a value for ''μ'' and ''s'' of:

:<math>\mu = -\beta_0/\beta_1 \approx 2.7</math>
:<math>s = 1/\beta_1 \approx 0.67</math>