UV-NIR_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3fe4a4d8",
   "metadata": {},
   "source": [
    "# UV-Near-Infrared Spectra Regression for Urea in Saline\n",
    "UV-NIR spectra were measured for various concentrations of urea in 0.15M NaCl saline on 11/19/2021 using the Cary5000 in the chemistry building from 190-2500 nm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1f45488d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import packages\n",
    "\n",
    "# Pandas library for the pandas dataframes\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd   \n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cross_decomposition import PLSRegression\n",
    "\n",
    "# Set larger fontsize for all plots\n",
    "plt.rcParams.update({'font.size': 14})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0bd598b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import data\n",
    "\n",
    "abs_data = pd.read_csv('Datasets/urea_in_saline_uv_nir.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e3639476",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Urea Conc. (mM)</th>\n",
       "      <th>3000</th>\n",
       "      <th>2999</th>\n",
       "      <th>2998</th>\n",
       "      <th>2997</th>\n",
       "      <th>2996</th>\n",
       "      <th>2995</th>\n",
       "      <th>2994</th>\n",
       "      <th>2993</th>\n",
       "      <th>2992</th>\n",
       "      <th>...</th>\n",
       "      <th>199</th>\n",
       "      <th>198</th>\n",
       "      <th>197</th>\n",
       "      <th>196</th>\n",
       "      <th>195</th>\n",
       "      <th>194</th>\n",
       "      <th>193</th>\n",
       "      <th>192</th>\n",
       "      <th>191</th>\n",
       "      <th>190</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.004525</td>\n",
       "      <td>-0.004511</td>\n",
       "      <td>-0.004733</td>\n",
       "      <td>-0.004982</td>\n",
       "      <td>-0.005159</td>\n",
       "      <td>-0.005245</td>\n",
       "      <td>-0.005385</td>\n",
       "      <td>-0.005520</td>\n",
       "      <td>-0.005835</td>\n",
       "      <td>...</td>\n",
       "      <td>0.053504</td>\n",
       "      <td>0.053560</td>\n",
       "      <td>0.053486</td>\n",
       "      <td>0.053882</td>\n",
       "      <td>0.054544</td>\n",
       "      <td>0.055369</td>\n",
       "      <td>0.055051</td>\n",
       "      <td>0.054595</td>\n",
       "      <td>0.056862</td>\n",
       "      <td>0.052532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.5</td>\n",
       "      <td>0.029535</td>\n",
       "      <td>0.029840</td>\n",
       "      <td>0.029965</td>\n",
       "      <td>0.030102</td>\n",
       "      <td>0.030375</td>\n",
       "      <td>0.030524</td>\n",
       "      <td>0.030621</td>\n",
       "      <td>0.030928</td>\n",
       "      <td>0.030970</td>\n",
       "      <td>...</td>\n",
       "      <td>0.060639</td>\n",
       "      <td>0.060561</td>\n",
       "      <td>0.061145</td>\n",
       "      <td>0.060605</td>\n",
       "      <td>0.061667</td>\n",
       "      <td>0.063021</td>\n",
       "      <td>0.063261</td>\n",
       "      <td>0.062434</td>\n",
       "      <td>0.067644</td>\n",
       "      <td>0.062364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.0</td>\n",
       "      <td>-0.015359</td>\n",
       "      <td>-0.015308</td>\n",
       "      <td>-0.015595</td>\n",
       "      <td>-0.015929</td>\n",
       "      <td>-0.015781</td>\n",
       "      <td>-0.016146</td>\n",
       "      <td>-0.016415</td>\n",
       "      <td>-0.016499</td>\n",
       "      <td>-0.016708</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000318</td>\n",
       "      <td>-0.003270</td>\n",
       "      <td>-0.003912</td>\n",
       "      <td>-0.003808</td>\n",
       "      <td>-0.002543</td>\n",
       "      <td>-0.003404</td>\n",
       "      <td>-0.004041</td>\n",
       "      <td>-0.003729</td>\n",
       "      <td>-0.004644</td>\n",
       "      <td>-0.003760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.0</td>\n",
       "      <td>0.015512</td>\n",
       "      <td>0.015875</td>\n",
       "      <td>0.015960</td>\n",
       "      <td>0.016147</td>\n",
       "      <td>0.016187</td>\n",
       "      <td>0.016439</td>\n",
       "      <td>0.016582</td>\n",
       "      <td>0.016884</td>\n",
       "      <td>0.016985</td>\n",
       "      <td>...</td>\n",
       "      <td>0.006839</td>\n",
       "      <td>0.004705</td>\n",
       "      <td>0.003824</td>\n",
       "      <td>0.003926</td>\n",
       "      <td>0.004741</td>\n",
       "      <td>0.004097</td>\n",
       "      <td>0.003407</td>\n",
       "      <td>0.004785</td>\n",
       "      <td>0.004999</td>\n",
       "      <td>0.003983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>-0.007704</td>\n",
       "      <td>-0.007802</td>\n",
       "      <td>-0.008077</td>\n",
       "      <td>-0.008225</td>\n",
       "      <td>-0.008448</td>\n",
       "      <td>-0.008511</td>\n",
       "      <td>-0.008659</td>\n",
       "      <td>-0.008920</td>\n",
       "      <td>-0.009119</td>\n",
       "      <td>...</td>\n",
       "      <td>0.039463</td>\n",
       "      <td>0.034964</td>\n",
       "      <td>0.034684</td>\n",
       "      <td>0.035229</td>\n",
       "      <td>0.035520</td>\n",
       "      <td>0.036255</td>\n",
       "      <td>0.034981</td>\n",
       "      <td>0.035495</td>\n",
       "      <td>0.036792</td>\n",
       "      <td>0.033767</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.0</td>\n",
       "      <td>0.028715</td>\n",
       "      <td>0.028926</td>\n",
       "      <td>0.029281</td>\n",
       "      <td>0.029247</td>\n",
       "      <td>0.029430</td>\n",
       "      <td>0.029778</td>\n",
       "      <td>0.029832</td>\n",
       "      <td>0.030233</td>\n",
       "      <td>0.030139</td>\n",
       "      <td>...</td>\n",
       "      <td>0.062434</td>\n",
       "      <td>0.058548</td>\n",
       "      <td>0.057964</td>\n",
       "      <td>0.058162</td>\n",
       "      <td>0.059199</td>\n",
       "      <td>0.060019</td>\n",
       "      <td>0.059519</td>\n",
       "      <td>0.059505</td>\n",
       "      <td>0.062893</td>\n",
       "      <td>0.059229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.012563</td>\n",
       "      <td>0.012878</td>\n",
       "      <td>0.012995</td>\n",
       "      <td>0.013099</td>\n",
       "      <td>0.013254</td>\n",
       "      <td>0.013476</td>\n",
       "      <td>0.013582</td>\n",
       "      <td>0.013908</td>\n",
       "      <td>0.014011</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001884</td>\n",
       "      <td>-0.007517</td>\n",
       "      <td>-0.008421</td>\n",
       "      <td>-0.009291</td>\n",
       "      <td>-0.008773</td>\n",
       "      <td>-0.008765</td>\n",
       "      <td>-0.009344</td>\n",
       "      <td>-0.009003</td>\n",
       "      <td>-0.009875</td>\n",
       "      <td>-0.008980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8.0</td>\n",
       "      <td>-0.017267</td>\n",
       "      <td>-0.017460</td>\n",
       "      <td>-0.017426</td>\n",
       "      <td>-0.017700</td>\n",
       "      <td>-0.017883</td>\n",
       "      <td>-0.018200</td>\n",
       "      <td>-0.018312</td>\n",
       "      <td>-0.018487</td>\n",
       "      <td>-0.018711</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.008768</td>\n",
       "      <td>-0.014474</td>\n",
       "      <td>-0.014928</td>\n",
       "      <td>-0.015455</td>\n",
       "      <td>-0.014899</td>\n",
       "      <td>-0.015541</td>\n",
       "      <td>-0.016573</td>\n",
       "      <td>-0.016285</td>\n",
       "      <td>-0.017931</td>\n",
       "      <td>-0.017376</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15.0</td>\n",
       "      <td>0.018503</td>\n",
       "      <td>0.018796</td>\n",
       "      <td>0.018995</td>\n",
       "      <td>0.018857</td>\n",
       "      <td>0.019321</td>\n",
       "      <td>0.019415</td>\n",
       "      <td>0.019655</td>\n",
       "      <td>0.019852</td>\n",
       "      <td>0.019946</td>\n",
       "      <td>...</td>\n",
       "      <td>0.025961</td>\n",
       "      <td>0.018669</td>\n",
       "      <td>0.017207</td>\n",
       "      <td>0.017491</td>\n",
       "      <td>0.017584</td>\n",
       "      <td>0.018018</td>\n",
       "      <td>0.017142</td>\n",
       "      <td>0.017406</td>\n",
       "      <td>0.017559</td>\n",
       "      <td>0.017251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>15.0</td>\n",
       "      <td>0.026297</td>\n",
       "      <td>0.026576</td>\n",
       "      <td>0.026722</td>\n",
       "      <td>0.026661</td>\n",
       "      <td>0.026950</td>\n",
       "      <td>0.027284</td>\n",
       "      <td>0.027349</td>\n",
       "      <td>0.027508</td>\n",
       "      <td>0.027686</td>\n",
       "      <td>...</td>\n",
       "      <td>0.054525</td>\n",
       "      <td>0.047463</td>\n",
       "      <td>0.046284</td>\n",
       "      <td>0.045817</td>\n",
       "      <td>0.047333</td>\n",
       "      <td>0.048565</td>\n",
       "      <td>0.047179</td>\n",
       "      <td>0.047011</td>\n",
       "      <td>0.048968</td>\n",
       "      <td>0.044521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>20.0</td>\n",
       "      <td>-0.010931</td>\n",
       "      <td>-0.010936</td>\n",
       "      <td>-0.011181</td>\n",
       "      <td>-0.011375</td>\n",
       "      <td>-0.011496</td>\n",
       "      <td>-0.011770</td>\n",
       "      <td>-0.012016</td>\n",
       "      <td>-0.012198</td>\n",
       "      <td>-0.012418</td>\n",
       "      <td>...</td>\n",
       "      <td>0.025239</td>\n",
       "      <td>0.016938</td>\n",
       "      <td>0.016293</td>\n",
       "      <td>0.016209</td>\n",
       "      <td>0.016737</td>\n",
       "      <td>0.017252</td>\n",
       "      <td>0.016631</td>\n",
       "      <td>0.015570</td>\n",
       "      <td>0.015058</td>\n",
       "      <td>0.012998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>20.0</td>\n",
       "      <td>0.015716</td>\n",
       "      <td>0.015881</td>\n",
       "      <td>0.016119</td>\n",
       "      <td>0.016120</td>\n",
       "      <td>0.016360</td>\n",
       "      <td>0.016389</td>\n",
       "      <td>0.016595</td>\n",
       "      <td>0.016981</td>\n",
       "      <td>0.016909</td>\n",
       "      <td>...</td>\n",
       "      <td>0.015544</td>\n",
       "      <td>0.007833</td>\n",
       "      <td>0.006397</td>\n",
       "      <td>0.006945</td>\n",
       "      <td>0.006767</td>\n",
       "      <td>0.006785</td>\n",
       "      <td>0.005614</td>\n",
       "      <td>0.005651</td>\n",
       "      <td>0.004806</td>\n",
       "      <td>0.003150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.018728</td>\n",
       "      <td>0.019025</td>\n",
       "      <td>0.019974</td>\n",
       "      <td>0.018634</td>\n",
       "      <td>0.017831</td>\n",
       "      <td>0.016741</td>\n",
       "      <td>0.012298</td>\n",
       "      <td>0.013589</td>\n",
       "      <td>0.012223</td>\n",
       "      <td>0.000271</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.258009</td>\n",
       "      <td>0.263522</td>\n",
       "      <td>0.265619</td>\n",
       "      <td>0.276581</td>\n",
       "      <td>0.277089</td>\n",
       "      <td>0.288269</td>\n",
       "      <td>0.299818</td>\n",
       "      <td>0.294885</td>\n",
       "      <td>0.305267</td>\n",
       "      <td>0.346537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.526411</td>\n",
       "      <td>0.533205</td>\n",
       "      <td>0.537754</td>\n",
       "      <td>0.558487</td>\n",
       "      <td>0.557262</td>\n",
       "      <td>0.581808</td>\n",
       "      <td>0.596001</td>\n",
       "      <td>0.580542</td>\n",
       "      <td>0.628837</td>\n",
       "      <td>0.664575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.389841</td>\n",
       "      <td>0.395944</td>\n",
       "      <td>0.398923</td>\n",
       "      <td>0.415432</td>\n",
       "      <td>0.414669</td>\n",
       "      <td>0.432401</td>\n",
       "      <td>0.446042</td>\n",
       "      <td>0.436558</td>\n",
       "      <td>0.464411</td>\n",
       "      <td>0.508660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.494409</td>\n",
       "      <td>0.500237</td>\n",
       "      <td>0.504528</td>\n",
       "      <td>0.524496</td>\n",
       "      <td>0.523522</td>\n",
       "      <td>0.546210</td>\n",
       "      <td>0.560325</td>\n",
       "      <td>0.546727</td>\n",
       "      <td>0.590858</td>\n",
       "      <td>0.627343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.284347</td>\n",
       "      <td>0.289345</td>\n",
       "      <td>0.291556</td>\n",
       "      <td>0.303814</td>\n",
       "      <td>0.303835</td>\n",
       "      <td>0.316510</td>\n",
       "      <td>0.328385</td>\n",
       "      <td>0.322350</td>\n",
       "      <td>0.335284</td>\n",
       "      <td>0.378498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.391052</td>\n",
       "      <td>0.395970</td>\n",
       "      <td>0.399273</td>\n",
       "      <td>0.415670</td>\n",
       "      <td>0.414930</td>\n",
       "      <td>0.432766</td>\n",
       "      <td>0.445991</td>\n",
       "      <td>0.437282</td>\n",
       "      <td>0.464491</td>\n",
       "      <td>0.508236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.538944</td>\n",
       "      <td>0.544079</td>\n",
       "      <td>0.548836</td>\n",
       "      <td>0.569681</td>\n",
       "      <td>0.568808</td>\n",
       "      <td>0.593077</td>\n",
       "      <td>0.606985</td>\n",
       "      <td>0.591333</td>\n",
       "      <td>0.640818</td>\n",
       "      <td>0.674181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.604671</td>\n",
       "      <td>0.610137</td>\n",
       "      <td>0.615287</td>\n",
       "      <td>0.636820</td>\n",
       "      <td>0.636637</td>\n",
       "      <td>0.664028</td>\n",
       "      <td>0.677853</td>\n",
       "      <td>0.659647</td>\n",
       "      <td>0.718577</td>\n",
       "      <td>0.744512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.591280</td>\n",
       "      <td>0.596302</td>\n",
       "      <td>0.600907</td>\n",
       "      <td>0.622884</td>\n",
       "      <td>0.622226</td>\n",
       "      <td>0.648910</td>\n",
       "      <td>0.662731</td>\n",
       "      <td>0.644063</td>\n",
       "      <td>0.701438</td>\n",
       "      <td>0.730597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.678805</td>\n",
       "      <td>0.684036</td>\n",
       "      <td>0.689481</td>\n",
       "      <td>0.712186</td>\n",
       "      <td>0.711742</td>\n",
       "      <td>0.742293</td>\n",
       "      <td>0.755413</td>\n",
       "      <td>0.733327</td>\n",
       "      <td>0.801067</td>\n",
       "      <td>0.817524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.597779</td>\n",
       "      <td>0.602513</td>\n",
       "      <td>0.607647</td>\n",
       "      <td>0.629037</td>\n",
       "      <td>0.628616</td>\n",
       "      <td>0.654877</td>\n",
       "      <td>0.669157</td>\n",
       "      <td>0.650148</td>\n",
       "      <td>0.708010</td>\n",
       "      <td>0.735733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>15.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.241168</td>\n",
       "      <td>0.245209</td>\n",
       "      <td>0.246798</td>\n",
       "      <td>0.256976</td>\n",
       "      <td>0.257732</td>\n",
       "      <td>0.267668</td>\n",
       "      <td>0.277920</td>\n",
       "      <td>0.273192</td>\n",
       "      <td>0.282122</td>\n",
       "      <td>0.319033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>15.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.517595</td>\n",
       "      <td>0.521871</td>\n",
       "      <td>0.526177</td>\n",
       "      <td>0.546499</td>\n",
       "      <td>0.545774</td>\n",
       "      <td>0.569132</td>\n",
       "      <td>0.583046</td>\n",
       "      <td>0.568071</td>\n",
       "      <td>0.614290</td>\n",
       "      <td>0.649274</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>15.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.222762</td>\n",
       "      <td>0.226195</td>\n",
       "      <td>0.227902</td>\n",
       "      <td>0.236829</td>\n",
       "      <td>0.237518</td>\n",
       "      <td>0.246426</td>\n",
       "      <td>0.255510</td>\n",
       "      <td>0.251953</td>\n",
       "      <td>0.258815</td>\n",
       "      <td>0.293912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.305897</td>\n",
       "      <td>0.310253</td>\n",
       "      <td>0.312452</td>\n",
       "      <td>0.325398</td>\n",
       "      <td>0.325066</td>\n",
       "      <td>0.338144</td>\n",
       "      <td>0.350110</td>\n",
       "      <td>0.343729</td>\n",
       "      <td>0.358601</td>\n",
       "      <td>0.402275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.551370</td>\n",
       "      <td>0.555321</td>\n",
       "      <td>0.560549</td>\n",
       "      <td>0.581112</td>\n",
       "      <td>0.579873</td>\n",
       "      <td>0.604944</td>\n",
       "      <td>0.618454</td>\n",
       "      <td>0.601864</td>\n",
       "      <td>0.652469</td>\n",
       "      <td>0.683623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>0.346636</td>\n",
       "      <td>0.350519</td>\n",
       "      <td>0.353823</td>\n",
       "      <td>0.367575</td>\n",
       "      <td>0.366679</td>\n",
       "      <td>0.380972</td>\n",
       "      <td>0.391134</td>\n",
       "      <td>0.382864</td>\n",
       "      <td>0.405562</td>\n",
       "      <td>0.435067</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>30 rows × 2812 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Urea Conc. (mM)      3000      2999      2998      2997      2996  \\\n",
       "0               0.5 -0.004525 -0.004511 -0.004733 -0.004982 -0.005159   \n",
       "1               0.5  0.029535  0.029840  0.029965  0.030102  0.030375   \n",
       "2               2.0 -0.015359 -0.015308 -0.015595 -0.015929 -0.015781   \n",
       "3               2.0  0.015512  0.015875  0.015960  0.016147  0.016187   \n",
       "4               5.0 -0.007704 -0.007802 -0.008077 -0.008225 -0.008448   \n",
       "5               5.0  0.028715  0.028926  0.029281  0.029247  0.029430   \n",
       "6               8.0  0.012563  0.012878  0.012995  0.013099  0.013254   \n",
       "7               8.0 -0.017267 -0.017460 -0.017426 -0.017700 -0.017883   \n",
       "8              15.0  0.018503  0.018796  0.018995  0.018857  0.019321   \n",
       "9              15.0  0.026297  0.026576  0.026722  0.026661  0.026950   \n",
       "10             20.0 -0.010931 -0.010936 -0.011181 -0.011375 -0.011496   \n",
       "11             20.0  0.015716  0.015881  0.016119  0.016120  0.016360   \n",
       "12              0.5       NaN       NaN       NaN       NaN       NaN   \n",
       "13              0.5       NaN       NaN       NaN       NaN       NaN   \n",
       "14              0.5       NaN       NaN       NaN       NaN       NaN   \n",
       "15              2.0       NaN       NaN       NaN       NaN       NaN   \n",
       "16              2.0       NaN       NaN       NaN       NaN       NaN   \n",
       "17              2.0       NaN       NaN       NaN       NaN       NaN   \n",
       "18              5.0       NaN       NaN       NaN       NaN       NaN   \n",
       "19              5.0       NaN       NaN       NaN       NaN       NaN   \n",
       "20              5.0       NaN       NaN       NaN       NaN       NaN   \n",
       "21              8.0       NaN       NaN       NaN       NaN       NaN   \n",
       "22              8.0       NaN       NaN       NaN       NaN       NaN   \n",
       "23              8.0       NaN       NaN       NaN       NaN       NaN   \n",
       "24             15.0       NaN       NaN       NaN       NaN       NaN   \n",
       "25             15.0       NaN       NaN       NaN       NaN       NaN   \n",
       "26             15.0       NaN       NaN       NaN       NaN       NaN   \n",
       "27             20.0       NaN       NaN       NaN       NaN       NaN   \n",
       "28             20.0       NaN       NaN       NaN       NaN       NaN   \n",
       "29             20.0       NaN       NaN       NaN       NaN       NaN   \n",
       "\n",
       "        2995      2994      2993      2992  ...       199       198       197  \\\n",
       "0  -0.005245 -0.005385 -0.005520 -0.005835  ...  0.053504  0.053560  0.053486   \n",
       "1   0.030524  0.030621  0.030928  0.030970  ...  0.060639  0.060561  0.061145   \n",
       "2  -0.016146 -0.016415 -0.016499 -0.016708  ... -0.000318 -0.003270 -0.003912   \n",
       "3   0.016439  0.016582  0.016884  0.016985  ...  0.006839  0.004705  0.003824   \n",
       "4  -0.008511 -0.008659 -0.008920 -0.009119  ...  0.039463  0.034964  0.034684   \n",
       "5   0.029778  0.029832  0.030233  0.030139  ...  0.062434  0.058548  0.057964   \n",
       "6   0.013476  0.013582  0.013908  0.014011  ... -0.001884 -0.007517 -0.008421   \n",
       "7  -0.018200 -0.018312 -0.018487 -0.018711  ... -0.008768 -0.014474 -0.014928   \n",
       "8   0.019415  0.019655  0.019852  0.019946  ...  0.025961  0.018669  0.017207   \n",
       "9   0.027284  0.027349  0.027508  0.027686  ...  0.054525  0.047463  0.046284   \n",
       "10 -0.011770 -0.012016 -0.012198 -0.012418  ...  0.025239  0.016938  0.016293   \n",
       "11  0.016389  0.016595  0.016981  0.016909  ...  0.015544  0.007833  0.006397   \n",
       "12       NaN       NaN       NaN       NaN  ...  0.018728  0.019025  0.019974   \n",
       "13       NaN       NaN       NaN       NaN  ...  0.258009  0.263522  0.265619   \n",
       "14       NaN       NaN       NaN       NaN  ...  0.526411  0.533205  0.537754   \n",
       "15       NaN       NaN       NaN       NaN  ...  0.389841  0.395944  0.398923   \n",
       "16       NaN       NaN       NaN       NaN  ...  0.494409  0.500237  0.504528   \n",
       "17       NaN       NaN       NaN       NaN  ...  0.284347  0.289345  0.291556   \n",
       "18       NaN       NaN       NaN       NaN  ...  0.391052  0.395970  0.399273   \n",
       "19       NaN       NaN       NaN       NaN  ...  0.538944  0.544079  0.548836   \n",
       "20       NaN       NaN       NaN       NaN  ...  0.604671  0.610137  0.615287   \n",
       "21       NaN       NaN       NaN       NaN  ...  0.591280  0.596302  0.600907   \n",
       "22       NaN       NaN       NaN       NaN  ...  0.678805  0.684036  0.689481   \n",
       "23       NaN       NaN       NaN       NaN  ...  0.597779  0.602513  0.607647   \n",
       "24       NaN       NaN       NaN       NaN  ...  0.241168  0.245209  0.246798   \n",
       "25       NaN       NaN       NaN       NaN  ...  0.517595  0.521871  0.526177   \n",
       "26       NaN       NaN       NaN       NaN  ...  0.222762  0.226195  0.227902   \n",
       "27       NaN       NaN       NaN       NaN  ...  0.305897  0.310253  0.312452   \n",
       "28       NaN       NaN       NaN       NaN  ...  0.551370  0.555321  0.560549   \n",
       "29       NaN       NaN       NaN       NaN  ...  0.346636  0.350519  0.353823   \n",
       "\n",
       "         196       195       194       193       192       191       190  \n",
       "0   0.053882  0.054544  0.055369  0.055051  0.054595  0.056862  0.052532  \n",
       "1   0.060605  0.061667  0.063021  0.063261  0.062434  0.067644  0.062364  \n",
       "2  -0.003808 -0.002543 -0.003404 -0.004041 -0.003729 -0.004644 -0.003760  \n",
       "3   0.003926  0.004741  0.004097  0.003407  0.004785  0.004999  0.003983  \n",
       "4   0.035229  0.035520  0.036255  0.034981  0.035495  0.036792  0.033767  \n",
       "5   0.058162  0.059199  0.060019  0.059519  0.059505  0.062893  0.059229  \n",
       "6  -0.009291 -0.008773 -0.008765 -0.009344 -0.009003 -0.009875 -0.008980  \n",
       "7  -0.015455 -0.014899 -0.015541 -0.016573 -0.016285 -0.017931 -0.017376  \n",
       "8   0.017491  0.017584  0.018018  0.017142  0.017406  0.017559  0.017251  \n",
       "9   0.045817  0.047333  0.048565  0.047179  0.047011  0.048968  0.044521  \n",
       "10  0.016209  0.016737  0.017252  0.016631  0.015570  0.015058  0.012998  \n",
       "11  0.006945  0.006767  0.006785  0.005614  0.005651  0.004806  0.003150  \n",
       "12  0.018634  0.017831  0.016741  0.012298  0.013589  0.012223  0.000271  \n",
       "13  0.276581  0.277089  0.288269  0.299818  0.294885  0.305267  0.346537  \n",
       "14  0.558487  0.557262  0.581808  0.596001  0.580542  0.628837  0.664575  \n",
       "15  0.415432  0.414669  0.432401  0.446042  0.436558  0.464411  0.508660  \n",
       "16  0.524496  0.523522  0.546210  0.560325  0.546727  0.590858  0.627343  \n",
       "17  0.303814  0.303835  0.316510  0.328385  0.322350  0.335284  0.378498  \n",
       "18  0.415670  0.414930  0.432766  0.445991  0.437282  0.464491  0.508236  \n",
       "19  0.569681  0.568808  0.593077  0.606985  0.591333  0.640818  0.674181  \n",
       "20  0.636820  0.636637  0.664028  0.677853  0.659647  0.718577  0.744512  \n",
       "21  0.622884  0.622226  0.648910  0.662731  0.644063  0.701438  0.730597  \n",
       "22  0.712186  0.711742  0.742293  0.755413  0.733327  0.801067  0.817524  \n",
       "23  0.629037  0.628616  0.654877  0.669157  0.650148  0.708010  0.735733  \n",
       "24  0.256976  0.257732  0.267668  0.277920  0.273192  0.282122  0.319033  \n",
       "25  0.546499  0.545774  0.569132  0.583046  0.568071  0.614290  0.649274  \n",
       "26  0.236829  0.237518  0.246426  0.255510  0.251953  0.258815  0.293912  \n",
       "27  0.325398  0.325066  0.338144  0.350110  0.343729  0.358601  0.402275  \n",
       "28  0.581112  0.579873  0.604944  0.618454  0.601864  0.652469  0.683623  \n",
       "29  0.367575  0.366679  0.380972  0.391134  0.382864  0.405562  0.435067  \n",
       "\n",
       "[30 rows x 2812 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "830555ff",
   "metadata": {},
   "source": [
    "#### Specify features (X) and target (y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c3163a21",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = abs_data.iloc[:, 550:1000].values\n",
    "y = abs_data[['Urea Conc. (mM)']].values.reshape(-1, 1)\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.1, random_state=4, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78cb966b",
   "metadata": {},
   "source": [
    "#### Fit principal component analysis (PCA) and partial least squares (PLS) regression models to the POUR data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "aeb4f40e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pcr = make_pipeline(StandardScaler(), PCA(n_components=1), LinearRegression())\n",
    "pcr.fit(X_train, y_train)\n",
    "pca = pcr.named_steps[\"pca\"]  # retrieve the PCA step of the pipeline\n",
    "\n",
    "pls = PLSRegression(n_components=1)\n",
    "pls.fit(X_train, y_train)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 3))\n",
    "axes[0].scatter(pca.transform(X_test), y_test, alpha=0.3, label=\"ground truth\")\n",
    "axes[0].scatter(\n",
    "    pca.transform(X_test), pcr.predict(X_test), alpha=0.3, label=\"predictions\"\n",
    ")\n",
    "axes[0].set(\n",
    "    xlabel=\"Projected data onto first PCA component\", ylabel=\"y\", title=\"PCR / PCA\"\n",
    ")\n",
    "axes[0].legend()\n",
    "axes[1].scatter(pls.transform(X_test), y_test, alpha=0.3, label=\"ground truth\")\n",
    "axes[1].scatter(\n",
    "    pls.transform(X_test), pls.predict(X_test), alpha=0.3, label=\"predictions\"\n",
    ")\n",
    "axes[1].set(xlabel=\"Projected data onto first PLS component\", ylabel=\"y\", title=\"PLS\")\n",
    "axes[1].legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31dba833",
   "metadata": {},
   "source": [
    "#### Print the R-squared values for each regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "103f3b70",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PCR r-squared -2.244\n",
      "PLS r-squared -2.249\n"
     ]
    }
   ],
   "source": [
    "print(f\"PCR r-squared {pcr.score(X_test, y_test):.3f}\")\n",
    "print(f\"PLS r-squared {pls.score(X_test, y_test):.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02e32ce0",
   "metadata": {},
   "source": [
    "#### Find best wavelength range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "09051e9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 311.        ,  322.23595506,  333.47191011,  344.70786517,\n",
       "        355.94382022,  367.17977528,  378.41573034,  389.65168539,\n",
       "        400.88764045,  412.12359551,  423.35955056,  434.59550562,\n",
       "        445.83146067,  457.06741573,  468.30337079,  479.53932584,\n",
       "        490.7752809 ,  502.01123596,  513.24719101,  524.48314607,\n",
       "        535.71910112,  546.95505618,  558.19101124,  569.42696629,\n",
       "        580.66292135,  591.8988764 ,  603.13483146,  614.37078652,\n",
       "        625.60674157,  636.84269663,  648.07865169,  659.31460674,\n",
       "        670.5505618 ,  681.78651685,  693.02247191,  704.25842697,\n",
       "        715.49438202,  726.73033708,  737.96629213,  749.20224719,\n",
       "        760.43820225,  771.6741573 ,  782.91011236,  794.14606742,\n",
       "        805.38202247,  816.61797753,  827.85393258,  839.08988764,\n",
       "        850.3258427 ,  861.56179775,  872.79775281,  884.03370787,\n",
       "        895.26966292,  906.50561798,  917.74157303,  928.97752809,\n",
       "        940.21348315,  951.4494382 ,  962.68539326,  973.92134831,\n",
       "        985.15730337,  996.39325843, 1007.62921348, 1018.86516854,\n",
       "       1030.1011236 , 1041.33707865, 1052.57303371, 1063.80898876,\n",
       "       1075.04494382, 1086.28089888, 1097.51685393, 1108.75280899,\n",
       "       1119.98876404, 1131.2247191 , 1142.46067416, 1153.69662921,\n",
       "       1164.93258427, 1176.16853933, 1187.40449438, 1198.64044944,\n",
       "       1209.87640449, 1221.11235955, 1232.34831461, 1243.58426966,\n",
       "       1254.82022472, 1266.05617978, 1277.29213483, 1288.52808989,\n",
       "       1299.76404494, 1311.        ])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "start_wl = np.linspace(311, 1311, num=90)\n",
    "start_wl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "eb12b6e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max principal components regression (PCR) score: -0.05920524019386009\n",
      "Max PCR score starting wavelength: 1\n",
      "Max PCR score stopping wavelength: 11\n",
      "Max partial least squasres (PLS) regression score: -0.059236813895465534\n",
      "Max PLS score starting wavelength: 1\n",
      "Max PLS score stopping wavelength: 11\n"
     ]
    }
   ],
   "source": [
    "# Create integer lists of starting wavelengths and stopping wavelengths to probe\n",
    "start_wl = np.linspace(1, 10, num=10)\n",
    "start_wl = [round(x) for x in start_wl]\n",
    "stop_wl = np.linspace(11, 100, num=90)\n",
    "stop_wl = [round(x) for x in stop_wl]\n",
    "\n",
    "# Initiate lists for results\n",
    "starting_wavelength = []\n",
    "stopping_wavelength = []\n",
    "pcr_r_squared = []\n",
    "pls_r_squared = []\n",
    "\n",
    "for start in start_wl:\n",
    "    for stop in stop_wl:\n",
    "        X = abs_data.iloc[:, start:stop].values\n",
    "        y = abs_data[['Urea Concentration (mM)']].values.reshape(-1, 1)\n",
    "\n",
    "        X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=4, shuffle=True)\n",
    "        \n",
    "        pcr = make_pipeline(StandardScaler(), PCA(n_components=1), LinearRegression())\n",
    "        pcr.fit(X_train, y_train)\n",
    "        pca = pcr.named_steps[\"pca\"]  # retrieve the PCA step of the pipeline\n",
    "\n",
    "        pls = PLSRegression(n_components=1)\n",
    "        pls.fit(X_train, y_train)\n",
    "        \n",
    "        starting_wavelength.append(start)\n",
    "        stopping_wavelength.append(stop)\n",
    "        pcr_r_squared.append(pcr.score(X_test, y_test))\n",
    "        pls_r_squared.append(pls.score(X_test, y_test))\n",
    "        \n",
    "# Choose the highest pcr and pls scores and report\n",
    "pcr_array = np.array(pcr_r_squared)\n",
    "pcr_max_index = pcr_array.argmax()\n",
    "\n",
    "pls_array = np.array(pls_r_squared)\n",
    "pls_max_index = pls_array.argmax()\n",
    "\n",
    "print(f'Max principal components regression (PCR) score: {pcr_r_squared[pcr_max_index]}')\n",
    "print(f'Max PCR score starting wavelength: {starting_wavelength[pcr_max_index]}')\n",
    "print(f'Max PCR score stopping wavelength: {stopping_wavelength[pcr_max_index]}')\n",
    "\n",
    "print(f'Max partial least squasres (PLS) regression score: {pls_r_squared[pls_max_index]}')\n",
    "print(f'Max PLS score starting wavelength: {starting_wavelength[pls_max_index]}')\n",
    "print(f'Max PLS score stopping wavelength: {stopping_wavelength[pls_max_index]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52209ba3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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