It is the sum of the likelihood residuals. At record level, the natural log of the error (residual) is calculated for each record, multiplied by minus one, and those values are totaled. That total is then used as the basis for deviance (2 x ll) and likelihood (exp(ll)).

The same calculation can be applied to a naive model that assumes absolutely no predictive power, and a saturated model assuming perfect predictions.

The likelihood values are used to compare different models, while the deviances (test, naive, and saturated) can be used to determine the predictive power and accuracy. Logistic regression accuracy of the model will always be 100 percent for the development data set, but that is not the case once a model is applied to another data set.

In logistic regression, the log likelihood is a measure used to assess the goodness of fit of the model to the observed data. The likelihood represents the probability of observing the given set of outcomes (dependent variable) given the parameter values of the model. Taking the natural logarithm of the likelihood results in the log likelihood.

In mathematical terms, let $y_{i}$ be the observed outcome for the $i$ -th observation (0 or 1 for binary classification), and let $p_{i}$ be the predicted probability of the same outcome according to the logistic regression model. The log likelihood ( $LL$ ) is given by:

$LL = \sum_{i = 1 n} (y_{i} log (p_{i}) + (1 - y_{i}) log (1 - p_{i}))$

Where $n$ is the number of observations.

In logistic regression, the goal during model training is to maximize the log likelihood. This is equivalent to minimizing the negative log likelihood or, in other words, minimizing the logistic loss or cross-entropy loss. Optimizing the log likelihood helps the model find the parameter values that make the observed outcomes more probable according to the logistic regression model.

During a machine learning interview, you could explain that the log likelihood is a fundamental concept in logistic regression, and optimizing it is a key step in training the model to make accurate predictions.