diff --git a/pyerrors/fits.py b/pyerrors/fits.py
index 377246a8..6db0b1dc 100644
--- a/pyerrors/fits.py
+++ b/pyerrors/fits.py
@@ -252,7 +252,7 @@ def total_least_squares(x, y, func, silent=False, **kwargs):
         new_jac = np.concatenate((fused_row1, fused_row2), axis=1)
 
         A = W @ new_jac
-        P_phi = A @ np.linalg.inv(A.T @ A) @ A.T
+        P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
         expected_chisquare = np.trace((np.identity(P_phi.shape[0]) - P_phi) @ W @ cov @ W)
         if expected_chisquare <= 0.0:
             warnings.warn("Negative expected_chisquare.", RuntimeWarning)
@@ -531,7 +531,7 @@ def _standard_fit(x, y, func, silent=False, **kwargs):
             W = np.diag(1 / np.asarray(dy_f))
             cov = covariance(y)
             A = W @ jacobian(func)(fit_result.x, x)
-            P_phi = A @ np.linalg.inv(A.T @ A) @ A.T
+            P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
             expected_chisquare = np.trace((np.identity(x.shape[-1]) - P_phi) @ W @ cov @ W)
             output.chisquare_by_expected_chisquare = chisquare / expected_chisquare
             if not silent:
diff --git a/tests/fits_test.py b/tests/fits_test.py
index da43b4ec..cc958dbc 100644
--- a/tests/fits_test.py
+++ b/tests/fits_test.py
@@ -319,6 +319,23 @@ def test_prior_fit():
     fitp = pe.fits.least_squares([0, 1], y, f, priors=y, resplot=True, qqplot=True)
 
 
+def test_correlated_fit_covobs():
+    x1 = pe.cov_Obs(1.01, 0.01 ** 2, 'test1')
+    x2 = pe.cov_Obs(2.01, 0.01 ** 2, 'test2')
+    x3 = pe.cov_Obs(2.99, 0.01 ** 2, 'test3')
+
+    [o.gamma_method() for o in [x1, x2, x3]]
+
+    def func(a, x):
+        return a[0] * x + a[1]
+
+    fit_res = pe.fits.least_squares(np.arange(1, 4), [x1, x2, x3], func, expected_chisquare=True)
+    assert np.isclose(fit_res.chisquare_by_dof, fit_res.chisquare_by_expected_chisquare)
+
+    fit_res_corr = pe.fits.least_squares(np.arange(1, 4), [x1, x2, x3], func, correlated_fit=True)
+    assert np.isclose(fit_res.chisquare_by_dof, fit_res_corr.chisquare_by_dof)
+
+
 def test_error_band():
     def f(a, x):
         return a[0] + a[1] * x