Non uniform relationship between predictors and response variable I aim to determine the relation between Y (a dichotomous variable, Y/N) and  multiple Xs (Continuous variables). In the following charts, X axis represents the binned value of an X, while Y axis represents the frequency of positive cases. The average frequency of positives is ~11%.
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You may notice that the relationship between Frequency and a X values is not uniform across all values of X, e.g., in chart 1, the frequency is almost constant till x= 1.0 , followed by somewhat of an linear rise till x=2.0 , beyond which the frequency plateaus once again.
My question is how to use these Xs to create a predictive model for Y, as e.g., including these X's as-is as predictors in logistic regression would clearly not be appropriate.

The canonical way of modeling such nonlinear relationships would be to use splines.
