diff --git a/skimage/measure/tests/test_fit.py b/skimage/measure/tests/test_fit.py
new file mode 100644
index 00000000..137a6e44
--- /dev/null
+++ b/skimage/measure/tests/test_fit.py
@@ -0,0 +1,43 @@
+import numpy as np
+from numpy.testing import assert_equal, assert_raises, assert_almost_equal
+from skimage.measure import LineModel, CircleModel, EllipseModel
+
+
+def test_line_model_invalid_input():
+    assert_raises(ValueError, LineModel().estimate, np.empty((5, 3)))
+
+
+def test_line_model_predict():
+    model = LineModel()
+    model._params = (10, 1)
+    x = np.arange(-10, 10)
+    y = model.predict_y(x)
+    assert_almost_equal(x, model.predict_x(y))
+
+
+def test_line_model_is_degenerate():
+    assert_equal(LineModel().is_degenerate(np.empty((1, 2))), True)
+
+
+def test_line_model_estimate():
+    # generate original data without noise
+    model0 = LineModel()
+    model0._params = (10, 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)
+
+    # estimate parameters of noisy data
+    model_est = LineModel()
+    model_est.estimate(data)
+
+    # test whether estimated parameters almost equals original parameters
+    assert_almost_equal(model0._params, model_est._params, 1)
+
+
+if __name__ == "__main__":
+    np.testing.run_module_suite()