diff --git a/skimage/measure/fit.py b/skimage/measure/fit.py
index 5ab66251..c6b6864b 100644
--- a/skimage/measure/fit.py
+++ b/skimage/measure/fit.py
@@ -275,7 +275,7 @@ class LineModelND(BaseModel):
         l = (x - X0[axis]) / u[axis]
         return X0 + l[..., np.newaxis] * u
 
-    def predict_x(self, y, params=None, new_params=None):
+    def predict_x(self, y, params=None):
         """Predict x-coordinates for 2D lines using the estimated model.
 
         Alias for::
diff --git a/skimage/measure/tests/test_fit.py b/skimage/measure/tests/test_fit.py
index af34cc29..794d173e 100644
--- a/skimage/measure/tests/test_fit.py
+++ b/skimage/measure/tests/test_fit.py
@@ -1,18 +1,18 @@
 import numpy as np
 from numpy.testing import assert_equal, assert_raises, assert_almost_equal
-from skimage.measure import LineModel, LineModelND, CircleModel, EllipseModel, ransac
+from skimage.measure import LineModelND, CircleModel, EllipseModel, ransac
 from skimage.transform import AffineTransform
 from skimage.measure.fit import _dynamic_max_trials
 from skimage._shared._warnings import expected_warnings
 
 
 def test_line_model_invalid_input():
-    assert_raises(ValueError, LineModel().estimate, np.empty((5, 3)))
+    assert_raises(ValueError, LineModelND().estimate, np.empty((1, 3)))
 
 
 def test_line_model_predict():
-    model = LineModel()
-    model.params = (10, 1)
+    model = LineModelND()
+    model.params = ((0, 0), (1, 1))
     x = np.arange(-10, 10)
     y = model.predict_y(x)
     assert_almost_equal(x, model.predict_x(y))
@@ -20,38 +20,36 @@ def test_line_model_predict():
 
 def test_line_model_estimate():
     # generate original data without noise
-    model0 = LineModel()
-    model0.params = (10, 1)
+    model0 = LineModelND()
+    model0.params = ((0, 0), (1, 1))
     x0 = np.arange(-100, 100)
     y0 = model0.predict_y(x0)
-    data0 = np.column_stack([x0, y0])
 
-    # add gaussian noise to data
-    np.random.seed(1234)
-    data = data0 + np.random.normal(size=data0.shape)
+    data = np.column_stack([x0, y0])
 
     # estimate parameters of noisy data
-    model_est = LineModel()
+    model_est = LineModelND()
     model_est.estimate(data)
 
     # test whether estimated parameters almost equal original parameters
-    assert_almost_equal(model0.params, model_est.params, 1)
+    x = np.random.rand(100, 2)
+    assert_almost_equal(model0.predict(x), model_est.predict(x), 1)
 
 
 def test_line_model_residuals():
-    model = LineModel()
-    model.params = (0, 0)
-    assert_equal(abs(model.residuals(np.array([[0, 0]]))), 0)
-    assert_equal(abs(model.residuals(np.array([[0, 10]]))), 0)
-    assert_equal(abs(model.residuals(np.array([[10, 0]]))), 10)
-    model.params = (5, np.pi / 4)
-    assert_equal(abs(model.residuals(np.array([[0, 0]]))), 5)
-    assert_almost_equal(abs(model.residuals(np.array([[np.sqrt(50), 0]]))), 0)
+    model = LineModelND()
+    model.params = (np.array([0, 0]), np.array([0, 1]))
+    assert_equal(model.residuals(np.array([[0, 0]])), 0)
+    assert_equal(model.residuals(np.array([[0, 10]])), 0)
+    assert_equal(model.residuals(np.array([[10, 0]])), 10)
+    model.params = (np.array([-2, 0]), np.array([1, 1])  / np.sqrt(2))
+    assert_equal(model.residuals(np.array([[0, 0]])), np.sqrt(2))
+    assert_almost_equal(model.residuals(np.array([[-4, 0]])), np.sqrt(2))
 
 
 def test_line_model_under_determined():
     data = np.empty((1, 2))
-    assert_raises(ValueError, LineModel().estimate, data)
+    assert_raises(ValueError, LineModelND().estimate, data)
 
 
 def test_line_modelND_invalid_input():
@@ -60,7 +58,7 @@ def test_line_modelND_invalid_input():
 
 def test_line_modelND_predict():
     model = LineModelND()
-    model.params = (np.array([0,0]), np.array([0.2,0.98]))
+    model.params = (np.array([0, 0]), np.array([0.2, 0.98]))
     x = np.arange(-10, 10)
     y = model.predict_y(x)
     assert_almost_equal(x, model.predict_x(y))
@@ -99,10 +97,10 @@ def test_line_modelND_estimate():
 
 def test_line_modelND_residuals():
     model = LineModelND()
-    model.params = (np.array([0,0,0]), np.array([0,0,1]))
-    assert_equal(abs(model.residuals(np.array([[0, 0,0]]))), 0)
-    assert_equal(abs(model.residuals(np.array([[0,0,1]]))), 0)
-    assert_equal(abs(model.residuals(np.array([[10, 0,0]]))), 10)
+    model.params = (np.array([0, 0, 0]), np.array([0, 0, 1]))
+    assert_equal(abs(model.residuals(np.array([[0, 0, 0]]))), 0)
+    assert_equal(abs(model.residuals(np.array([[0, 0, 1]]))), 0)
+    assert_equal(abs(model.residuals(np.array([[10, 0, 0]]))), 10)
 
 
 def test_line_modelND_under_determined():
@@ -245,7 +243,7 @@ def test_ransac_is_data_valid():
     np.random.seed(1)
 
     is_data_valid = lambda data: data.shape[0] > 2
-    model, inliers = ransac(np.empty((10, 2)), LineModel, 2, np.inf,
+    model, inliers = ransac(np.empty((10, 2)), LineModelND, 2, np.inf,
                             is_data_valid=is_data_valid)
     assert_equal(model, None)
     assert_equal(inliers, None)
@@ -256,7 +254,7 @@ def test_ransac_is_model_valid():
 
     def is_model_valid(model, data):
         return False
-    model, inliers = ransac(np.empty((10, 2)), LineModel, 2, np.inf,
+    model, inliers = ransac(np.empty((10, 2)), LineModelND, 2, np.inf,
                             is_model_valid=is_model_valid)
     assert_equal(model, None)
     assert_equal(inliers, None)
@@ -304,8 +302,8 @@ def test_ransac_invalid_input():
 
 
 def test_deprecated_params_attribute():
-    model = LineModel()
-    model.params = (10, 1)
+    model = LineModelND()
+    model.params = ((0, 0), (1, 1))
     x = np.arange(-10, 10)
     y = model.predict_y(x)
     with expected_warnings(['`_params`']):