class_docstr: Check if new LOO PPM computed using closed form formulas is the same as
  computing the values manually.
code: def manual_LOO_coefs(
      self, model, return_intercepts=False, center=False
  ):
      loo_coefs = []
      loo_intercepts = []
      for i in range(self.n):
          train_indices = [j != i for j in range(self.n)]
          if center:
              X = self.X - self.X.mean(axis=0)
          else:
              X = self.X
          X_partial = X[train_indices, :]
          y_partial = self.y[train_indices]
          model.fit(X_partial, y_partial)
          loo_coefs.append(model.coef_)
          loo_intercepts.append(model.intercept_)
      if return_intercepts:
          return np.array(loo_coefs), np.array(loo_intercepts)
      else:
          return np.array(loo_coefs)
  
imports: import copy
  import numpy
  import random
  import scipy
  from sklearn.linear_model import Ridge, LinearRegression
  from sklearn.tree import DecisionTreeRegressor
  from sklearn.ensemble import RandomForestRegressor, RandomForestClassifier
  from sklearn.metrics import r2_score, log_loss, roc_auc_score, mean_squared_error
  from imodels.importance.block_transformers import IdentityTransformer, TreeTransformer, CompositeTransformer, MDIPlusDefaultTransformer
  from imodels.importance.ppms import RidgeRegressorPPM, LogisticClassifierPPM, RobustRegressorPPM
  from imodels.importance.mdi_plus import TreeMDIPlus, ForestMDIPlus
  from imodels.importance.rf_plus import RandomForestPlusClassifier
label_desc: Use image node_id 2 for calling the TestLOOParams obj's underlying member method code with example usage: obj.manual_LOO_coefs(model, return_intercepts, center) and returns: np,  np, np