diff --git a/tests/test_loss.py b/tests/test_loss.py
new file mode 100644
index 0000000..ef252c8
--- /dev/null
+++ b/tests/test_loss.py
@@ -0,0 +1,41 @@
+import numpy as np
+
+from tricycle_v2.loss import mean_squared_error
+from tricycle_v2.tensor import to_tensor
+from tricycle_v2.ops import repeat 
+
+
+def test_can_mean_square_error():
+    y_true = to_tensor([[0, 0, 1], [0, 1, 0], [1 / 3, 1 / 3, 1 / 3]])
+    y_pred = to_tensor([[0, 0, 1], [0, 0, 1], [0, 0, 1]])
+
+    mse = mean_squared_error(y_true, y_pred)
+
+    assert mse.shape == (3,)
+    assert np.allclose(mse, np.array([0, 2 / 3, 2 / 9]))
+
+
+def test_can_linear_regression():
+    np.random.seed(42)
+
+    x = np.linspace(-10, 10, 201)
+    y = x * 2 + 1 + np.random.normal(loc=0, scale=0.01, size=201)
+
+    x = to_tensor(x.reshape(-1, 1))
+    y = to_tensor(y)
+
+    slope = to_tensor([0.01])
+    intercept = to_tensor(0.01)
+
+    for _ in range(100):
+        repeated_slope = repeat("i->ji", slope, (x.shape[0],))
+        repeated_intercept = repeat("i->ji", intercept, (x.shape[0],))
+
+        y_pred = x * repeated_slope + repeated_intercept
+        loss = mean_squared_error(y, y_pred)
+
+        loss.backward()
+        breakpoint()
+
+        slope -= slope.grad
+        intercept -= intercept.grad