diff --git a/cobra/model_building/forward_selection.py b/cobra/model_building/forward_selection.py
index 29e06b3..50961f9 100644
--- a/cobra/model_building/forward_selection.py
+++ b/cobra/model_building/forward_selection.py
@@ -31,6 +31,12 @@ class ForwardFeatureSelection:
         selection.
     pos_only : bool
         Whether or not the model coefficients should all be positive (no sign flips).
+    model_kwargs: dict, optional
+        An optional dictionary of hyperparameters and their values to
+        override the default hyperparameters that Cobra uses when
+        constructing the model during forward selection.
+        For more info, see the documentation of kwargs in the documentation
+        of the model that is used (e.g. LinearRegressionModel).
     self._fitted_models : list
         List of fitted models.
     """
@@ -38,7 +44,8 @@ class ForwardFeatureSelection:
     def __init__(self,
                  model_type: str="classification",
                  max_predictors: int=50,
-                 pos_only: bool=True):
+                 pos_only: bool=True,
+                 model_kwargs: Optional[dict]=None):
 
         self.model_type = model_type
         if model_type == "classification":
@@ -49,6 +56,8 @@ def __init__(self,
         self.max_predictors = max_predictors
         self.pos_only = pos_only
 
+        self.model_kwargs = model_kwargs
+
         self._fitted_models = []
 
     def get_model_from_step(self, step: int):
@@ -347,7 +356,10 @@ def _train_model(self, train_data: pd.DataFrame, target_column_name: str,
         self.MLModel
             Trained model.
         """
-        model = self.MLModel()
+        if self.model_kwargs is None:
+            model = self.MLModel()
+        else:
+            model = self.MLModel(**self.model_kwargs)
 
         model.fit(train_data[predictors], train_data[target_column_name])
 
diff --git a/cobra/model_building/models.py b/cobra/model_building/models.py
index 3a921c0..1977b54 100644
--- a/cobra/model_building/models.py
+++ b/cobra/model_building/models.py
@@ -25,14 +25,29 @@ class LogisticRegressionModel:
         scikit-learn logistic regression model.
     predictors : list
         List of predictors used in the model.
+    kwargs: dict, optional
+        Pass a dictionary here (optional!), to override Cobra's default
+        choice of hyperparameter values for the scikit-learn
+        LogisticRegression model that is used behind the scenes.
+        Cobra's defaults are: fit_intercept=True, C=1e9, solver='liblinear',
+        random_state=42.
+        See scikit-learn's documentation of the possible hyperparameters and
+        values that can be set:
+        https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html
     """
 
-    def __init__(self):
-        self.logit = LogisticRegression(fit_intercept=True, C=1e9,
-                                        solver='liblinear', random_state=42)
+    def __init__(self, **kwargs):
+        # Initialize a scikit-learn linear regression model,
+        # with custom arguments passed by the data scientist (if any),
+        # supplemented with Cobra's default arguments, if a custom value was
+        # not provided by the data scientist for overriding purposes:
+        model_kwargs = dict(fit_intercept=True, C=1e9, solver='liblinear',
+                              random_state=42)
+        model_kwargs.update(kwargs)
+        self.logit = LogisticRegression(**model_kwargs)
+
         self._is_fitted = False
-        # placeholder to keep track of a list of predictors
-        self.predictors = []
+        self.predictors = []  # placeholder to keep track of a list of predictors
         self._eval_metrics_by_split = {}
 
     def serialize(self) -> dict:
@@ -104,7 +119,12 @@ def get_intercept(self) -> float:
         float
             Intercept of the model.
         """
-        return self.logit.intercept_[0]
+        if self.logit.fit_intercept:
+            return self.logit.intercept_[0]
+        else:
+            raise ValueError("An intercept cannot be returned: this "
+                             "LogisticRegressionModel was created with "
+                             "the hyperparameter fit_intercept set to False.")
 
     def get_coef_by_predictor(self) -> dict:
         """Returns a dictionary mapping predictor (key) to coefficient (value).
@@ -258,10 +278,26 @@ class LinearRegressionModel:
         scikit-learn linear regression model.
     predictors : list
         List of predictors used in the model.
+    kwargs: dict, optional
+        Pass a dictionary here (optional!), to override Cobra's default
+        choice of hyperparameter values for the scikit-learn
+        LinearRegression model that is used behind the scenes.
+        Cobra's only default setting is fit_intercept=True, but there are
+        other hyperparmeters that can be set too.
+        See scikit-learn's documentation of the possible hyperparameters and
+        values that can be set:
+        https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html
     """
 
-    def __init__(self):
-        self.linear = LinearRegression(fit_intercept=True)
+    def __init__(self, **kwargs):
+        # Initialize a scikit-learn linear regression model,
+        # with custom arguments passed by the data scientist (if any),
+        # supplemented with Cobra's default arguments, if a custom value was
+        # not provided by the data scientist for overriding purposes:
+        model_kwargs = dict(fit_intercept=True)
+        model_kwargs.update(kwargs)
+        self.linear = LinearRegression(**model_kwargs)
+
         self._is_fitted = False
         self.predictors = []  # placeholder to keep track of a list of predictors
         self._eval_metrics_by_split = {}