In logistic regression, is there an official term for the value you get when you multiply feature values with coefficients? I am currently calling it the effect, so I can report on the impact of the feature values for each observation. But is there an official term for it? That is, to understand why someone is getting a prediction, I multiply feature values by the relevant coefficient and rankorder them based on the absolute value, and then list the top features in terms of absolute effect (along with the actual effect).
 A: For simplicity, let's say you have a (binary) logistic regression model where you regress the binary outcome variable $Y$ on the predictors $X_1$ and $X_2$. $Y$ takes the value 1 for the event of interest (e.g., student is admitted into the program) and 0 otherwise (e.g., student is not admitted into the program).
The (binary) logistic regression model is then formulated like this:
$log(p/(1-p)) = \beta_0 + \beta_1 X_1 + \beta_2 X_2$
where p is the conditional probability that Y = 1 given $X_1$ and $X_2$. For the student admission program example, let's say that $X_1$ is the student age (in years) and $X_2$ is student gender (male/female); in this case, p represents the probability of admission given a students's age and their gender.
As Demetri pointed out in his answer, the right-hand side (RHS) of the model is referred to as the linear predictor. Because $log(p/(1-p))$ represents the log odds of $Y = 1$ given $X_1$ and $X_2$, the RHS of the model can also be referred to as a log odds value or, equivalently, a logit value (see https://en.m.wikipedia.org/wiki/Logit).
Note that you can re-express the model as:
$p = exp(lp)/(1 + exp(lp))$
where $lp =  \beta_0 + \beta_1 X_1 + \beta_2 X_2$ is the linear predictor. This allows you to compute a probability (which has a more natural interpretation) rather than a log odds as a function of input values for the predictors $X_1$ and $X_2$.
