Interpretation of Logistic Regression output in Credit Scoring Currently I'm working on a project involving loan data where I am trying to build a model that will predict a probability of an individual defaulting on a loan. I have binary dependent variable where defaulted loans are denoted with 1. I decided to use logistic regression for this task, but However, I have difficulty interpreting the results of the regression and would greatly appreciate some clarification.
Namely, I would like to know, whether the probabilities calculated by logistic regression should be interpreted as a probability of default? For example, if for some observation, the predicted value is 0.8, should I assume that according to the model, this individual has 80% chance of default?

For the sake of notation, I am using the model with only one independent variable $X$. All of the results hold true with more independent variables as well.
In logistic regression, we use the logistic function
$$ p(X) = \frac{e^{\beta_0 + \beta_1 X}}{1 + e^{\beta_0 + \beta_1 X}}$$
to model the relationship between $p(X) = \mathbb{P}(Y = 1|X)$ and $X$. In your case, $p(X)$ denotes the probability of the default conditional on $X$.
For the predictions, for an individual with the value of the independent variable $x_0$, we predict the probability of default by just plugging it in the estimated function:
$$ \hat{p}(x_0) = \frac{e^{\hat{\beta}_0 + \hat{\beta}_1 x_0}}{1 + e^{\hat{\beta}_0 + \hat{\beta}_1 x_0}}.$$
If you get $\hat{p}(x_0) = 0.8$, then you predict the probability of default for this individual to be $0.8$.
