diff --git a/Orange/widgets/evaluate/owpredictions.py b/Orange/widgets/evaluate/owpredictions.py
index 0fd3a5085af..3d57d9c5727 100644
--- a/Orange/widgets/evaluate/owpredictions.py
+++ b/Orange/widgets/evaluate/owpredictions.py
@@ -56,7 +56,12 @@ class Warning(OWWidget.Warning):
         empty_data = Msg("Empty data set")
 
     class Error(OWWidget.Error):
-        predictor_failed = Msg("One or more predictors failed (see more...)\n{}")
+        predictor_failed = \
+            Msg("One or more predictors failed (see more...)\n{}")
+        predictors_target_mismatch = \
+            Msg("Predictors do not have the same target.")
+        data_target_mismatch = \
+            Msg("Data does not have the same target as predictors.")
 
     settingsHandler = settings.ClassValuesContextHandler()
     #: Display the full input dataset or only the target variable columns (if
@@ -182,13 +187,11 @@ def set_data(self, data):
 
         self.data = data
         if data is None:
-            self.class_var = class_var = None
             self.dataview.setModel(None)
             self.predictionsview.setModel(None)
             self.predictionsview.setItemDelegate(PredictionsItemDelegate())
         else:
             # force full reset of the view's HeaderView state
-            self.class_var = class_var = data.domain.class_var
             self.dataview.setModel(None)
             model = TableModel(data, parent=None)
             modelproxy = TableSortProxyModel()
@@ -196,18 +199,6 @@ def set_data(self, data):
             self.dataview.setModel(modelproxy)
             self._update_column_visibility()
 
-        discrete_class = class_var is not None and class_var.is_discrete
-        self.classification_options.setVisible(discrete_class)
-
-        self.closeContext()
-        if discrete_class:
-            self.class_values = list(class_var.values)
-            self.selected_classes = list(range(len(self.class_values)))
-            self.openContext(self.class_var)
-        else:
-            self.class_values = []
-            self.selected_classes = []
-
         self._invalidate_predictions()
 
     def set_predictor(self, predictor=None, id=None):
@@ -221,7 +212,36 @@ def set_predictor(self, predictor=None, id=None):
             self.predictors[id] = \
                 PredictorSlot(predictor, predictor.name, None)
 
+    def set_class_var(self):
+        pred_classes = set(pred.predictor.domain.class_var
+                           for pred in self.predictors.values())
+        self.Error.predictors_target_mismatch.clear()
+        self.Error.data_target_mismatch.clear()
+        self.class_var = None
+        if len(pred_classes) > 1:
+            self.Error.predictors_target_mismatch()
+        if len(pred_classes) == 1:
+            self.class_var = pred_classes.pop()
+            if self.data is not None and \
+                    self.data.domain.class_var is not None and \
+                    self.class_var != self.data.domain.class_var:
+                self.Error.data_target_mismatch()
+                self.class_var = None
+
+        discrete_class = self.class_var is not None \
+                         and self.class_var.is_discrete
+        self.classification_options.setVisible(discrete_class)
+        self.closeContext()
+        if discrete_class:
+            self.class_values = list(self.class_var.values)
+            self.selected_classes = list(range(len(self.class_values)))
+            self.openContext(self.class_var)
+        else:
+            self.class_values = []
+            self.selected_classes = []
+
     def handleNewSignals(self):
+        self.set_class_var()
         if self.data is not None:
             self._call_predictors()
         self._update_predictions_model()
@@ -232,14 +252,9 @@ def handleNewSignals(self):
 
     def _call_predictors(self):
         for inputid, pred in self.predictors.items():
-            if pred.results is None:
+            if pred.results is None or numpy.isnan(pred.results[0]).all():
                 try:
-                    predictor_class = pred.predictor.domain.class_var
-                    if predictor_class != self.class_var:
-                        results = "{}: mismatching target ({})".format(
-                            pred.predictor.name, predictor_class.name)
-                    else:
-                        results = self.predict(pred.predictor, self.data)
+                    results = self.predict(pred.predictor, self.data)
                 except ValueError as err:
                     results = "{}: {}".format(pred.predictor.name, err)
                 self.predictors[inputid] = pred._replace(results=results)
@@ -285,12 +300,16 @@ def _invalidate_predictions(self):
             self.predictors[inputid] = pred._replace(results=None)
 
     def _valid_predictors(self):
-        return [p for p in self.predictors.values()
-                if p.results is not None and not isinstance(p.results, str)]
+        if self.class_var is not None and \
+                self.data is not None:
+            return [p for p in self.predictors.values()
+                    if p.results is not None and not isinstance(p.results, str)]
+        else:
+            return []
 
     def _update_predictions_model(self):
         """Update the prediction view model."""
-        if self.data is not None:
+        if self.data is not None and self.class_var is not None:
             slots = self._valid_predictors()
             results = []
             class_var = self.class_var
@@ -323,7 +342,7 @@ def _update_predictions_model(self):
 
     def _update_column_visibility(self):
         """Update data column visibility."""
-        if self.data is not None:
+        if self.data is not None and self.class_var is not None:
             domain = self.data.domain
             first_attr = len(domain.class_vars) + len(domain.metas)
 
@@ -415,12 +434,12 @@ def commit(self):
         self._commit_evaluation_results()
 
     def _commit_evaluation_results(self):
-        class_var = self.class_var
         slots = self._valid_predictors()
-        if not slots:
+        if not slots or self.data.domain.class_var is None:
             self.send("Evaluation Results", None)
             return
 
+        class_var = self.class_var
         nanmask = numpy.isnan(self.data.get_column_view(class_var)[0])
         data = self.data[~nanmask]
         N = len(data)
@@ -442,15 +461,15 @@ def _commit_predictions(self):
             self.send("Predictions", None)
             return
 
-        class_var = self.class_var
-        if class_var and class_var.is_discrete:
+        if self.class_var and self.class_var.is_discrete:
             newmetas, newcolumns = self._classification_output_columns()
         else:
             newmetas, newcolumns = self._regression_output_columns()
 
         attrs = list(self.data.domain.attributes) if self.output_attrs else []
         metas = list(self.data.domain.metas) + newmetas
-        domain = Orange.data.Domain(attrs, class_var, metas=metas)
+        domain = \
+            Orange.data.Domain(attrs, self.data.domain.class_var, metas=metas)
         predictions = self.data.from_table(domain, self.data)
         if newcolumns:
             newcolumns = numpy.hstack(
@@ -506,7 +525,7 @@ def merge_data_with_predictions():
                       [data_model.data(data_model.index(i, j))
                        for j in iter_data_cols]
 
-        if self.data is not None:
+        if self.data is not None and self.class_var is not None:
             text = self.infolabel.text().replace('\n', '<br>')
             if self.show_probabilities and self.selected_classes:
                 text += '<br>Showing probabilities for: '
diff --git a/Orange/widgets/evaluate/tests/test_owpredictions.py b/Orange/widgets/evaluate/tests/test_owpredictions.py
index 8f366b7d2cd..bbae03bf3d8 100644
--- a/Orange/widgets/evaluate/tests/test_owpredictions.py
+++ b/Orange/widgets/evaluate/tests/test_owpredictions.py
@@ -5,7 +5,7 @@
 from Orange.widgets.tests.base import WidgetTest
 from Orange.widgets.evaluate.owpredictions import OWPredictions
 
-from Orange.data import Table
+from Orange.data import Table, Domain
 from Orange.classification import MajorityLearner
 from Orange.evaluation import Results
 
@@ -47,6 +47,8 @@ def test_nan_target_input(self):
         self.assertEqual(len(evres.data), 0)
 
     def test_mismatching_targets(self):
+        error = self.widget.Error
+
         titanic = Table("titanic")
         majority_titanic = MajorityLearner()(titanic)
         majority_iris = MajorityLearner()(self.iris)
@@ -54,35 +56,66 @@ def test_mismatching_targets(self):
         self.send_signal("Data", self.iris)
         self.send_signal("Predictors", majority_iris, 1)
         self.send_signal("Predictors", majority_titanic, 2)
-        self.assertTrue(self.widget.Error.predictor_failed.is_shown())
-        output = self.get_output("Predictions")
-        self.assertEqual(len(output.domain.metas), 4)
+        self.assertTrue(error.predictors_target_mismatch.is_shown())
+        self.assertIsNone(self.get_output("Predictions"))
 
         self.send_signal("Predictors", None, 1)
-        self.assertTrue(self.widget.Error.predictor_failed.is_shown())
+        self.assertFalse(error.predictors_target_mismatch.is_shown())
+        self.assertTrue(error.data_target_mismatch.is_shown())
         self.assertIsNone(self.get_output("Predictions"))
 
         self.send_signal("Data", None)
-        self.assertFalse(self.widget.Error.predictor_failed.is_shown())
+        self.assertFalse(error.predictors_target_mismatch.is_shown())
+        self.assertFalse(error.data_target_mismatch.is_shown())
         self.assertIsNone(self.get_output("Predictions"))
 
         self.send_signal("Predictors", None, 2)
-        self.assertFalse(self.widget.Error.predictor_failed.is_shown())
+        self.assertFalse(error.predictors_target_mismatch.is_shown())
+        self.assertFalse(error.data_target_mismatch.is_shown())
         self.assertIsNone(self.get_output("Predictions"))
 
         self.send_signal("Predictors", majority_titanic, 2)
-        self.assertFalse(self.widget.Error.predictor_failed.is_shown())
+        self.assertFalse(error.predictors_target_mismatch.is_shown())
+        self.assertFalse(error.data_target_mismatch.is_shown())
         self.assertIsNone(self.get_output("Predictions"))
 
         self.send_signal("Data", self.iris)
-        self.assertTrue(self.widget.Error.predictor_failed.is_shown())
+        self.assertFalse(error.predictors_target_mismatch.is_shown())
+        self.assertTrue(error.data_target_mismatch.is_shown())
         self.assertIsNone(self.get_output("Predictions"))
 
         self.send_signal("Predictors", majority_iris, 2)
-        self.assertFalse(self.widget.Error.predictor_failed.is_shown())
+        self.assertFalse(error.predictors_target_mismatch.is_shown())
+        self.assertFalse(error.data_target_mismatch.is_shown())
+        output = self.get_output("Predictions")
         self.assertEqual(len(output.domain.metas), 4)
 
         self.send_signal("Predictors", majority_iris, 1)
         self.send_signal("Predictors", majority_titanic, 3)
-        output = self.get_output("Predictions")
-        self.assertEqual(len(output.domain.metas), 8)
+        self.assertTrue(error.predictors_target_mismatch.is_shown())
+        self.assertFalse(error.data_target_mismatch.is_shown())
+        self.assertIsNone(self.get_output("Predictions"))
+
+    def test_no_class_on_test(self):
+        """Allow test data with no class"""
+        error = self.widget.Error
+
+        titanic = Table("titanic")
+        majority_titanic = MajorityLearner()(titanic)
+        majority_iris = MajorityLearner()(self.iris)
+
+        no_class = Table(Domain(titanic.domain.attributes, None), titanic)
+        self.send_signal("Predictors", majority_titanic, 1)
+        self.send_signal("Data", no_class)
+        out = self.get_output("Predictions")
+        np.testing.assert_allclose(out.get_column_view("majority")[0], 0)
+
+        self.send_signal("Predictors", majority_iris, 2)
+        self.assertTrue(error.predictors_target_mismatch.is_shown())
+        self.assertFalse(error.data_target_mismatch.is_shown())
+        self.assertIsNone(self.get_output("Predictions"))
+
+        self.send_signal("Predictors", None, 2)
+        self.send_signal("Data", titanic)
+        out = self.get_output("Predictions")
+        np.testing.assert_allclose(out.get_column_view("majority")[0], 0)