diff --git a/linearmodels/shared/hypotheses.py b/linearmodels/shared/hypotheses.py
index 462e3e071c..ddf3dc35cd 100644
--- a/linearmodels/shared/hypotheses.py
+++ b/linearmodels/shared/hypotheses.py
@@ -196,13 +196,12 @@ def _parse_single(constraint: str) -> tuple[str, float]:
     except Exception as exc:
         raise TypeError(_constraint_error.format(cons=constraint)) from exc
     expr = "=".join(parts[:-1])
-    return expr, value
+    return expr.strip(), value
 
 
 def _reparse_constraint_formula(
     formula: str | list[str] | dict[str, float],
 ) -> str | dict[str, float]:
-    # TODO: Test against variable names constaining , or =
     if isinstance(formula, Mapping):
         return dict(formula)
     if isinstance(formula, str):
@@ -227,6 +226,11 @@ def quadratic_form_test(
     if formula is not None and restriction is not None:
         raise ValueError("restriction and formula cannot be used simultaneously.")
     if formula is not None:
+        if not isinstance(params, Series):
+            raise TypeError(
+                "params must be a pandas Series when using formula= to specify "
+                "linear restrictions (indexed by parameter names)."
+            )
         assert isinstance(params, Series)
         param_names = [str(p) for p in params.index]
         rewritten_constraints = _reparse_constraint_formula(formula)
diff --git a/linearmodels/tests/shared/test_hypotheses_constraints.py b/linearmodels/tests/shared/test_hypotheses_constraints.py
new file mode 100644
index 0000000000..4f3f3adbf6
--- /dev/null
+++ b/linearmodels/tests/shared/test_hypotheses_constraints.py
@@ -0,0 +1,95 @@
+import numpy as np
+import pandas as pd
+import pytest
+
+from linearmodels.shared.hypotheses import (
+    _parse_single,
+    _reparse_constraint_formula,
+    quadratic_form_test,
+)
+
+
+def test_parse_single_simple():
+    expr, val = _parse_single("x1 = 1")
+    assert expr == "x1"
+    assert val == 1.0
+
+
+def test_parse_single_expression_with_plus():
+    expr, val = _parse_single("x1 + x2 = 2.5")
+    assert expr == "x1 + x2"
+    assert val == 2.5
+
+
+def test_parse_single_multiple_equals():
+    expr, val = _parse_single("a = b = 1")
+    assert expr == "a = b"
+    assert val == 1.0
+
+
+def test_parse_single_no_equals_raises():
+    with pytest.raises(ValueError, match="required syntax"):
+        _parse_single("x1")
+
+
+def test_parse_single_non_float_rhs_raises():
+    with pytest.raises(TypeError, match="required syntax"):
+        _parse_single("x1 = not_a_number")
+
+
+def test_reparse_dict_passthrough():
+    spec = {"x1": 0.0, "x2": 1.0}
+    out = _reparse_constraint_formula(spec)
+    assert out == spec
+
+
+def test_reparse_single_constraint_string_unchanged():
+    s = "x1 + x2 = 1"
+    assert _reparse_constraint_formula(s) is s
+
+
+def test_reparse_multiple_equals_without_comma():
+    out = _reparse_constraint_formula("x1 = x2 = 0")
+    assert out == {"x1": 0.0, "x2": 0.0}
+
+
+def test_reparse_comma_separated():
+    out = _reparse_constraint_formula("x1 = 1, x2 = 2")
+    assert out == {"x1": 1.0, "x2": 2.0}
+
+
+def test_reparse_list_of_strings():
+    out = _reparse_constraint_formula(["x1 = 1", "x2 = 2"])
+    assert out == {"x1": 1.0, "x2": 2.0}
+
+
+def test_reparse_comma_with_multiple_equals():
+    out = _reparse_constraint_formula("a=b=1,c=2")
+    assert out == {"a=b": 1.0, "c": 2.0}
+
+
+def test_quadratic_form_formula_end_to_end():
+    params = pd.Series([0.0, 1.0], index=["x0", "x1"])
+    cov = np.eye(2)
+    res = quadratic_form_test(params, cov, formula="x0=0")
+    assert res.stat == 0.0
+    assert res.df == 1
+
+
+def test_quadratic_form_formula_and_restriction_exclusive():
+    params = pd.Series([0.0, 0.0], index=["a", "b"])
+    cov = np.eye(2)
+    r = np.array([[1.0, 0.0]])
+    with pytest.raises(ValueError, match="cannot be used simultaneously"):
+        quadratic_form_test(params, cov, restriction=r, formula="a=0")
+
+
+def test_quadratic_form_formula_requires_series_params():
+    with pytest.raises(TypeError, match="pandas Series"):
+        quadratic_form_test(np.array([0.0, 1.0]), np.eye(2), formula="x0=0")
+
+
+def test_reparse_name_with_comma_single_equals():
+    # One "=" in the string: pass through to formulaic as a single constraint.
+    out = _reparse_constraint_formula("my,var = 1")
+    assert out == "my,var = 1"