Linear Regression(2).py

    # -*- coding: utf-8 -*-
"""
Created on Mon Jun 24 15:45:40 2024
Implementation of Linear Regression using Ordinary Least Squares Fitting
@author: SROTOSHI GHOSH
"""

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

def lin_reg(xi,yi):
     N=len(xi)
     xi2=[]
     xiyi=[]
     for i in range (0,N):
        xi2.append(xi[i]**2)
        xiyi.append(xi[i]*yi[i])
     s_xi2=np.sum(xi2)
     s_xiyi=np.sum(xiyi)
    #slope (m)
     m=s_xiyi/s_xi2
    #calculation of errors
     ei=[]
     ei2=[]
     for i in range (0,N):
        term=yi[i]-m*xi[i]
        ei.append(term)
        ei2.append(term**2)
     meanxi=np.sum(xi)/N
     exi=[]
     for i in range (0,N):
        term=(xi[i]-meanxi)**2
        exi.append(term)
     er_slope=np.sqrt(np.sum(ei2)/((N-2)*(np.sum(exi))))
    
     return m,er_slope,xi2,xiyi,ei,ei2,exi

cl=3*(10**8)
#importing the csv file as a data frame
df=pd.read_csv('data.csv')
#storing the necessary data
ri=df['NASA dist'] #stores distance of galaxies from earth
u_ri=df['sigma dist'] #stores uncertainty in distance
zi=df['NASA z'] 
vi=[] #stores velocity of recession of galaxies, evaluated from redshift 
for i in range (0,len(zi)):
     vi.append(zi[i]*cl)
u_zi=df['sigma z'] #stores uncertainty in redshift and in turn in velocity
u_vi=[]
for i in range (0,len(u_zi)):
     u_vi.append(cl*u_zi[i])
    
m,errm,xi2,xiyi,ei,ei2,exi=lin_reg(vi,ri)

yfit=[]
for i in range (0,len(vi)):
     yfit.append((m*vi[i]))

plt.plot(vi,yfit,label="fitted data")
plt.errorbar(vi,ri,u_ri,u_vi,fmt='.',capsize=2,label="observed data with error bars")
plt.ylabel("distance in Mpc")
plt.xlabel("velocity in m/s")
plt.grid()
plt.legend()

print (" The slope of the fitted line is : ",m," with an uncertainty of : ",errm)
  

#evaluation of fractional errors 
N=len(ri)
fx=[]
fy=[]
for i in range (0,N):
     fy.append(u_ri[i]/ri[i])
     fx.append(u_vi[i]/vi[i])
mfx=np.sum(fx)/N
mfy=np.sum(fy)/N
print (" The mean fractional error in velocity is : ",mfx)
print (" The mean fractional error in distance is : ",mfy)


#creating data frame to store as csv
data={'xi':vi, 'sigma xi':u_vi, 'frac err in x':fx, 'yi':ri, 'sigma yi':u_ri, 'frac err in y':fy, 
      'xi^2':xi2, 'xi*yi':xiyi, 'yi(fitted)':yfit, 'residue ei':ei, 'ei^2':ei2 }

df2=pd.DataFrame(data)
df2.to_csv('Lin Reg Data4.csv')