Project: s41467-024-49339-1 | Function: Linear_regression_bootstrap_coordinates (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
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user: Complete this Python function:

**DESCRIPTION:** Implements bootstrap statistical analysis to determine topographic organization of cerebellar nuclear neurons based on their spatial coordinates and connectivity patterns. Uses linear regression with 50,000 random samples to calculate statistical significance of R² values for different zone connectivity groups.

**KEY TERMS:** {
  "nShuffles": "number of bootstrap samples (50,000)",
  "fourzone_r2": "observed R² for 4-zone cells",
  "sample_of_3_i": "bootstrap sample of equivalent size",
  "stats.linregress": "linear regression calculation",
  "samplesof3_pvalue": "bootstrap p-value calculation"
}

**CONTEXT CODE:** import numpy as np
import matplotlib.pyplot as plt
import scipy as sp
import pandas as pd
import random
import numpy.random as random
from numpy import genfromtxt
from scipy import stats
from scipy.stats import norm
from scipy.stats import sem
import csv
from scipy.stats import percentileofscore



# using SciPy stats models for linear regression

def Linear_regression_bootstrap_coordinates(axis1, axis2, axis, nZones, nShuffles):
    """Implements bootstrap statistical analysis to determine topographic organization of cerebellar nuclear neurons based on their spatial coordinates and connectivity patterns."""
    raise NotImplementedError("Function has been masked for testing purposes")

    ###n4 = number of cells with n=4 zones
    n0 = 34
    n1 = 26
    n2 = 6
    n3 = 6
    n4 = 3

    ### Creating a pandas dataframe from .csv file
    pd_coordinates = pd.read_csv(file) 
    pd_coordinates_RC = pd_coordinates['Original_all_x']
    pd_coordinates_VD = pd_coordinates['Original_all_y']
    pd_coordinates_LM = pd_coordinates['Original_all_x']
    pd_coordinates_nZones = pd_coordinates['Original_coordinates_nZone']
    
    coordinates_RC = pd_coordinates_RC.to_numpy()
    coordinates_VD = pd_coordinates_VD.to_numpy()
    coordinates_LM = pd_coordinates_LM.to_numpy()
    
    x = coordinates_RC
    y = coordinates_VD
    z = coordinates_LM
    
    np_xy = np.dstack((x,y))
    np_xz = np.dstack((x,z))
    np_yz = np.dstack((y,z))


    ### Manually inputting coordinates in numpy array format 
    
    n0_x = np.array([12107,11923,11977,11925,12005,11921,11890,11752,12019,12022,12116,11926,12068,12040,11995,11995,11967,11995,11965,12056,11861,11844,11980,11716,11965,11851,11838,12008,12068,12046,11302,11365,11839,12006])
    n0_y = np.array([3378,3456,3476,3465,3537,3479,3445,3558,3463,3487,3465,3636,3510,3516,3585,3560,3516,3481,3491,3690,3628,3401,3440,3476,3725,3631,3645,3595,3619,3609,3845,3925,3755,3645])
    n0_z = np.array([4240,4240,4240,4240,4240,4240,4360,4360,4360,4360,4360,4360,4360,4360,4360,4540,4540,4540,4540,4540,4540,4540,4540,4660,4660,4660,4840,4840,4840,4840,4840,4840,4840,4960])
    
    n1_x = np.array([11751,11375,11715,11795,11789,11874,12003,11758,12135,12095,11912,12067,12059,11927,12040,12053,12058,12101,11777,11479,11485,12012,12045,11896,11862,12133])
    n1_y = np.array([3455,3707,3535,3465,3624,3545,3555,3450,3436,3544,3505,3560,3472,3562,3480,3454,3564,3647,3521,3904,3930,3761,3564,3656,3525,3581]) 
    n1_z = np.array([4660,4960,4960,4540,4540,4960,4400,4240,4240,4840,4540,4540,4240,4660,4360,4360,4540,4540,4660,4840,4840,4660,4960,4240,4540,4840])
    
    n2_x = np.array([11997,11878,11546,12105,11839,12080])
    n2_y = np.array([3535,3587,3889,3675,3743,3570]) 
    n2_z = np.array([4360,4960,4840,4960,4840,4840])
    
    n3_x = np.array([11846,11881,11798,11985,11920,11896])
    n3_y = np.array([3641,3624,3800,3479,3654,3615]) 
    n3_z = np.array([4360,4360,4840,4540,4660,4660])
    
    
    fourzone_x = np.array([11985,11761,11968])
    fourzone_y = np.array([3608,3760,3611])
    fourzone_z = np.array([4540,4960,4840])

    nOutliers = 0
    j = 0
    i = 0
    
    rng = np.random.default_rng()
    
    samples_of_34_nShuffles_times = []
    samples_of_26_nShuffles_times = []
    samples_of_6_nShuffles_times = []
    samples_of_6_nShuffles_times = []
    samples_of_3_nShuffles_times = []
    
    
    if nZones == "n4":
        if axis == "xy":

            fourzone_results = stats.linregress(fourzone_x,fourzone_y)

            fourzone_r2 = fourzone_results.rvalue**2
            fourzone_slope = fourzone_results.slope
            fourzone_yintercept = fourzone_results.intercept
            fourzone_pvalue = fourzone_results.pvalue

            fourzone_stats = ([fourzone_r2,fourzone_slope,fourzone_yintercept,fourzone_pvalue])


            for i in range(nShuffles):
                sample_of_3_i = pd.DataFrame()
                sample_of_3_i = pd_coordinates.sample(n4)
                sample_of_3_i_xy = sample_of_3_i[['Original_all_x','Original_all_y']].to_numpy()
                sample_of_3_i_xz = sample_of_3_i[['Original_all_x','Original_all_z']].to_numpy()
                sample_of_3_i_yz = sample_of_3_i[['Original_all_y','Original_all_z']].to_numpy()

                sample_of_3_i_x = sample_of_3_i_xy[:,0]
                sample_of_3_i_y = sample_of_3_i_xy[:,1]
                sample_of_3_i_z = sample_of_3_i_xz[:,1]

                sample_of_3_i_xy_linear_reg = stats.linregress(sample_of_3_i_x,sample_of_3_i_y)
                sample_of_3_i_xy_r = sample_of_3_i_xy_linear_reg.rvalue
                sample_of_3_i_xy_r2 = sample_of_3_i_xy_linear_reg.rvalue**2

                sample_of_3_i_xy_r_np = np.corrcoef(sample_of_3_i_x, sample_of_3_i_y)

                sample_of_3_i_xy_slope = sample_of_3_i_xy_linear_reg.slope
                sample_of_3_i_xy_yintercept = sample_of_3_i_xy_linear_reg.intercept
                sample_of_3_i_xy_pvalue = sample_of_3_i_xy_linear_reg.pvalue


Complete the function implementation replacing "raise NotImplementedError".