%matplotlib inline

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from scipy import stats

# Initial Data
time = np.array([0.008333334,0.508333325,1.008333325,1.508333325,2.008333445,2.508333445,3.008333445,3.508333445,4.008333206,4.508333206,5.008333206,5.508333206,6.008333206,6.508333206,7.008333206,7.508333206,8.008333206])
absorbance = np.array([0.417830259,0.346029699,0.290778458,0.243839279,0.205080524,0.171536624,0.144038409,0.120138422,0.101258248,0.083564349,0.069462888,0.059087373,0.04753048,0.039430205,0.032463193,0.027355824,0.021077819])
e = 70939.0

# Calculate concentration, ln[CV], 1/[CV]
CV_molar = absorbance/e
CV_ln = np.log(CV_molar)
#Calculate the equation of the trendline for ln[CV]
line_fit = np.polyfit(time, CV_ln,1)

#Create trendline array
trendline_2 = np.empty(CV_ln.size)
for k in range(0, CV_ln.size):
    trendline_2[k] = time[k]*line_fit[0]+line_fit[1]
slope, intercept, r_value, p_value, std_err = stats.linregress(time, trendline_2)

#PLOT
fig= plt.figure(figsize = (9,5))
ax = plt.axes()

ax.plot(time, CV_ln,'-', label = 'Data')
ax.plot(time, trendline_2,'.', label = 'trendline')

ax.set(xlabel='Time', ylabel = 'ln[CV+]',title='ln[CV+] vs time')

ax.text(0, -14.8,'The equation of the trendline is y={a}x - {b}'.format(a=round(line_fit[0],2), b=0-round(line_fit[1],2)))
ax.text(0, -15,'The R^2 value of the trendline is R^2 ={k}'.format(k= r_value**2))
ax.legend(['Data', 'Trendline'])

fig.savefig('my_figure_2.png')