I have the following problem.
A bank wants to decide whether a customer can be given a loan, based on two features related to (i) the monthly salary of the customer, and (ii) his/her account balance. For simplicity, we model the two features with two binary variables $X1$, $X2$ and the class $Y$ (all of which can be either 0 or 1). $Y=1$ indicates that the customer can be given loan, and Y=0 indicates otherwise.
Consider the following dataset having four instances:
($X1 = 0$, $X2 = 0$, $Y = 0$)
($X1 = 0$, $X2 = 1$, $Y = 0$)
($X1 = 1$, $X2 = 0$, $Y = 0$)
($X1 = 1$, $X2 = 1$, $Y = 1$)
Can there be any logistic regression classifier using X1 and X2 as features, that can perfectly classify the given data?
The approach followed in the question was to calculate respective probabilities for Y=0 and Y=1 respectively. The value of $p$ obtained was $0.25$ and $(1-p)$ as $0.75$. The $\log(p/1-p)$ is coming as negative.
However, I don't understand what I need to do to understand whether there is a Logistic Regression classifier that can perfectly classify the given data.