diff --git a/src/glum/_glm.py b/src/glum/_glm.py
index e7f221de..dde0bfbc 100644
--- a/src/glum/_glm.py
+++ b/src/glum/_glm.py
@@ -2466,7 +2466,10 @@ def _set_up_and_check_fit_args(
                 )
 
         if y is None:
-            raise ValueError("y cannot be None when not using a two-sided formula.")
+            raise ValueError(
+                f"Unless using a two-sided formula, {self.__class__.__name__} "
+                "requires y to be passed, but the target y is None."
+            )
 
         if not _is_contiguous(X):
             if self.copy_X is not None and not self.copy_X: