diff --git a/skimage/measure/fit.py b/skimage/measure/fit.py
index c6b6864b..b227d59f 100644
--- a/skimage/measure/fit.py
+++ b/skimage/measure/fit.py
@@ -15,6 +15,11 @@ def _check_data_atleast_2D(data):
         raise ValueError('Input data must be at least 2D.')
 
 
+def _norm_along_axis(x, axis):
+    """NumPy < 1.8 does not support the `axis` argument for `np.linalg.norm`."""
+    return np.sqrt(np.einsum('ij,ij->i', x, x))
+
+
 class BaseModel(object):
 
     def __init__(self):
@@ -239,8 +244,9 @@ class LineModelND(BaseModel):
         """
 
         X0, u = self.params
-        return np.linalg.norm((data - X0) -
-                              np.dot(data - X0, u)[..., np.newaxis] * u, axis=1)
+        return _norm_along_axis((data - X0) -
+                                np.dot(data - X0, u)[..., np.newaxis] * u,
+                                axis=1)
 
     def predict(self, x, axis=0, params=None):
         """Predict intersection of the estimated line model with a hyperplane