Neocis.ipynb

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   "cell_type": "code",
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   "metadata": {
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   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy\n",
    "import plotly.graph_objects as go\n",
    "from plotly.graph_objs import FigureWidget\n",
    "from plotly.callbacks import Points, InputDeviceState\n",
    "from ipywidgets import HBox, VBox, Button, interact\n",
    "from functools import partial\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cross_decomposition import PLSRegression\n",
    "from sklearn import linear_model\n",
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neocis data##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('https://raw.githubusercontent.com/bevi-rosso/Neocis/master/Neocis.csv', sep=';')\n",
    "X = np.array(df.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
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      },
      "text/plain": [
       "interactive(children=(Dropdown(description='variabile', options=('Tingresso', 'Solvente', 'Nd_on_PBu', 'Al_on_…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(variabile=df.columns)\n",
    "def sel(variabile):\n",
    "    fig=go.Figure()\n",
    "    fig.add_trace(go.Scatter(x=np.arange(len(df.index)),y=df[variabile], mode='markers+lines', marker_color = 'green'))\n",
    "    fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# PCA\n",
    "pca = PCA()\n",
    "xs = scale(df)\n",
    "x_red = pca.fit_transform(xs)\n",
    "V = pca.components_\n",
    "nPC = np.arange(len(V)) + 1\n",
    "dfV = pd.DataFrame(V, columns=[df.columns], index=[nPC])\n",
    "EV_cum = pd.DataFrame(np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100),\n",
    "                  columns =['% Explained Variance'], index=[nPC])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PCs =  7\n"
     ]
    },
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>Tingresso</th>\n",
       "      <th>Solvente</th>\n",
       "      <th>Nd_on_PBu</th>\n",
       "      <th>Al_on_Nd</th>\n",
       "      <th>Sty_on_Bde</th>\n",
       "      <th>Mooney</th>\n",
       "      <th>VEI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.358783</td>\n",
       "      <td>-0.418246</td>\n",
       "      <td>0.329424</td>\n",
       "      <td>-0.414178</td>\n",
       "      <td>-0.363168</td>\n",
       "      <td>0.350172</td>\n",
       "      <td>0.402206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.449975</td>\n",
       "      <td>-0.174692</td>\n",
       "      <td>-0.563403</td>\n",
       "      <td>-0.084179</td>\n",
       "      <td>-0.372736</td>\n",
       "      <td>0.516521</td>\n",
       "      <td>-0.191753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.408843</td>\n",
       "      <td>0.140916</td>\n",
       "      <td>0.443297</td>\n",
       "      <td>-0.407815</td>\n",
       "      <td>0.503850</td>\n",
       "      <td>0.408207</td>\n",
       "      <td>-0.172243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.138822</td>\n",
       "      <td>-0.080493</td>\n",
       "      <td>-0.410253</td>\n",
       "      <td>0.182902</td>\n",
       "      <td>0.587020</td>\n",
       "      <td>0.312900</td>\n",
       "      <td>0.574447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.668456</td>\n",
       "      <td>-0.284311</td>\n",
       "      <td>0.290850</td>\n",
       "      <td>0.317304</td>\n",
       "      <td>-0.121018</td>\n",
       "      <td>-0.221395</td>\n",
       "      <td>0.472649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.010482</td>\n",
       "      <td>0.799333</td>\n",
       "      <td>0.124231</td>\n",
       "      <td>0.161756</td>\n",
       "      <td>-0.340413</td>\n",
       "      <td>0.301865</td>\n",
       "      <td>0.335195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.188228</td>\n",
       "      <td>-0.220116</td>\n",
       "      <td>0.330470</td>\n",
       "      <td>0.703390</td>\n",
       "      <td>0.013905</td>\n",
       "      <td>0.453771</td>\n",
       "      <td>-0.325653</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Tingresso  Solvente Nd_on_PBu  Al_on_Nd Sty_on_Bde    Mooney       VEI\n",
       "1 -0.358783 -0.418246  0.329424 -0.414178  -0.363168  0.350172  0.402206\n",
       "2  0.449975 -0.174692 -0.563403 -0.084179  -0.372736  0.516521 -0.191753\n",
       "3  0.408843  0.140916  0.443297 -0.407815   0.503850  0.408207 -0.172243\n",
       "4 -0.138822 -0.080493 -0.410253  0.182902   0.587020  0.312900  0.574447\n",
       "5  0.668456 -0.284311  0.290850  0.317304  -0.121018 -0.221395  0.472649\n",
       "6  0.010482  0.799333  0.124231  0.161756  -0.340413  0.301865  0.335195\n",
       "7 -0.188228 -0.220116  0.330470  0.703390   0.013905  0.453771 -0.325653"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print ('PCs = ', len(V))\n",
    "dfV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>% Explained Variance</th>\n",
       "      <td>73.34</td>\n",
       "      <td>87.23</td>\n",
       "      <td>92.85</td>\n",
       "      <td>96.04</td>\n",
       "      <td>98.3</td>\n",
       "      <td>99.38</td>\n",
       "      <td>100.01</td>\n",
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      "text/plain": [
       "                          1      2      3      4     5      6       7\n",
       "% Explained Variance  73.34  87.23  92.85  96.04  98.3  99.38  100.01"
      ]
     },
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   "source": [
    "EV_cum.T"
   ]
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   "cell_type": "code",
   "execution_count": 45,
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   "source": [
    "# Calculate ellipse bounds and plot with scores\n",
    "theta = np.concatenate((np.linspace(-np.pi, np.pi, 50), np.linspace(np.pi, -np.pi, 50)))\n",
    "circle = np.array((np.cos(theta), np.sin(theta)))\n",
    "sigma = np.cov(np.array((x_red[:, 0], x_red[:, 1])))\n",
    "ed = np.sqrt(scipy.stats.chi2.ppf(0.95, 2))\n",
    "ell = np.transpose(circle).dot(np.linalg.cholesky(sigma) * ed)\n",
    "a, b = np.max(ell[: ,0]), np.max(ell[: ,1]) #95% ellipse bounds\n",
    "t = np.linspace(0, 2 * np.pi, 100)"
   ]
  },
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       "                        {\"responsive\": true}\n",
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       "            Plotly.purge(gd);\n",
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       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Score plot\n",
    "col = [x for x in range(len(X))]\n",
    "xtit = 'PC1 - explained variance = '+str(np.round(100*pca.explained_variance_ratio_[0],decimals=2))+'%'\n",
    "ytit = 'PC2 - explained variance = '+str(np.round(100*pca.explained_variance_ratio_[1],decimals=2))+'%'\n",
    "fig=go.Figure()\n",
    "fig.add_trace(go.Scatter(x=x_red[:,0], y=x_red[:,1], mode='markers', marker=dict(symbol=[200], \n",
    "             color=col, line_width=2, size=10, colorscale='Viridis', showscale=True)))\n",
    "fig.add_trace(go.Scatter(x=a * np.cos(t),y=b * np.sin(t),mode='lines',\n",
    "                        line=dict(color='lightgreen', width=2, dash='dash')))\n",
    "fig.update_layout(height=600, width=800, title='PCA - Score plot', \n",
    "                  xaxis_title=xtit,yaxis_title=ytit, showlegend=False, xaxis_zeroline=True, yaxis_zeroline=True, \n",
    "                  xaxis_zerolinecolor='blue', yaxis_zerolinecolor='blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4811829a46a24e34a668f71f3b715ced",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='PCa', options=('1', '2', '3', '4', '5', '6', '7'), value='1'), Dro…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "score=pd.DataFrame(x_red)\n",
    "index = np.linspace(1,len(V),num=len(V))\n",
    "index = index.astype('int')\n",
    "index = index.astype('str')\n",
    "score.columns=index\n",
    "@interact(PCa=score.columns, PCb=score.columns)\n",
    "def sel(PCa, PCb):\n",
    "    fig=go.Figure()\n",
    "    fig.add_trace(go.Scatter(x=np.arange(len(df.index)),y=score[PCa], name=PCa, mode='lines', marker_color = 'green'))\n",
    "    fig.add_trace(go.Scatter(x=np.arange(len(df.index)),y=score[PCb], name=PCb, mode='lines', marker_color = 'red'))\n",
    "    fig.update_layout(height=600, width=800, title='PCA - components plot',\n",
    "                     xaxis_title='n° samples', yaxis_title='PCs',\n",
    "                     xaxis_zeroline=True, yaxis_zerolinecolor='blue')\n",
    "    fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9634028481257921"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr=np.array(dfV)\n",
    "min(arr[1,:])-0.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
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        "plotlyServerURL": "https://plot.ly"
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           201
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         "text": [
          "Tingresso",
          "Solvente",
          "Nd_on_PBu",
          "Al_on_Nd",
          "Sty_on_Bde",
          "Mooney",
          "VEI"
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\"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"title\": {\"text\": \"PCA - Loadings plot\"}, \"width\": 800, \"xaxis\": {\"range\": [-0.6182460001283813, 0.6022064933061736], \"title\": {\"text\": \"PC1 - explained variance = 73.34%\"}, \"zeroline\": true, \"zerolinecolor\": \"blue\"}, \"yaxis\": {\"range\": [-0.7634028481257922, 0.7165213164939015], \"title\": {\"text\": \"PC2 - explained variance = 13.89%\"}, \"zeroline\": true, \"zerolinecolor\": \"blue\"}},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('25514ce1-8cfc-4121-88fd-15bf667ecf55');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Loadings plot\n",
    "arr = np.array(dfV)\n",
    "label = np.array(df.columns)\n",
    "plot = go.Scatter(x=arr[0,:], y=arr[1,:], mode='markers+text', marker=dict(symbol=[201],color='darkred', size=10), \n",
    "              text = label, textposition=\"middle left\")\n",
    "fig=go.Figure()\n",
    "fig.add_trace(plot)\n",
    "fig.update_layout(height=600, width=800, title='PCA - Loadings plot', xaxis_title=xtit,yaxis_title=ytit, \n",
    "                  xaxis_zeroline=True, yaxis_zeroline=True, xaxis_zerolinecolor='blue', yaxis_zerolinecolor='blue')\n",
    "fig.update_xaxes(range=[min(arr[0,:])-0.2, max(arr[0,:])+0.2])\n",
    "fig.update_yaxes(range=[min(arr[1,:])-0.2, max(arr[1,:])+0.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = len(df)\n",
    "f1 = FigureWidget(**{\n",
    "    'data': [{'marker': {'cmax': 2, 'cmin': 0, 'color': np.zeros(N), 'size': 8},\n",
    "              'mode': 'markers', 'type': 'scatter', 'x': x_red[:,0], 'y': x_red[:,1]}],\n",
    "    'layout': {'dragmode': 'lasso', 'xaxis': {'title': 'PC1'}, 'yaxis': {'title': 'PC2'}}})\n",
    "scatt1 = f1.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "f2 = FigureWidget(**{\n",
    "    'data': [{'marker': {'cmax': 2, 'cmin': 0, 'color': np.zeros(N), 'size': 8},\n",
    "              'mode': 'markers+lines', 'type': 'scatter', 'x': X, 'y': x_red[:,0]}],\n",
    "    'layout': {'dragmode': 'lasso', 'xaxis': {'title': 'n°sample'}, 'yaxis': {'title': 'PC1'}}})\n",
    "scatt2 = f2.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "f3 = FigureWidget(**{\n",
    "    'data': [{'marker': {'cmax': 2, 'cmin': 0, 'color': np.zeros(N), 'size': 8},\n",
    "              'mode': 'markers+lines', 'type': 'scatter', 'x': X, 'y': x_red[:,1]}],\n",
    "    'layout': {'dragmode': 'lasso', 'xaxis': {'title': 'n°sample'}, 'yaxis': {'title': 'PC2'}}})\n",
    "scatt3 = f3.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure brush on both plots to update both plots\n",
    "def brush(trace, points, state):\n",
    "    inds = np.array(points.point_inds)\n",
    "    if inds.size:\n",
    "        selected = scatt1.marker.color.copy()\n",
    "        selected[inds] = 1\n",
    "        scatt1.marker.color = selected\n",
    "        scatt2.marker.color = selected\n",
    "        scatt3.marker.color = selected\n",
    "    \n",
    "scatt1.on_selection(brush)\n",
    "scatt2.on_selection(brush)\n",
    "scatt3.on_selection(brush)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reset brush\n",
    "def reset_brush(btn):\n",
    "    selected = np.zeros(N)\n",
    "    scatt1.marker.color = selected\n",
    "    scatt2.marker.color = selected\n",
    "    scatt3.marker.color = selected\n",
    "    \n",
    "# Create reset button\n",
    "button = Button(description=\"RESET\")\n",
    "button.on_click(reset_brush)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c6f3ae2f3b5f47dfb274fab2a7afcc1d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(HBox(children=(FigureWidget({\n",
       "    'data': [{'marker': {'cmax': 2,\n",
       "                         'cmi…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "upper=HBox([f1, button])\n",
    "lower=HBox([f2,f3])\n",
    "dashboard = VBox([upper, lower])\n",
    "dashboard"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PLS ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Separa x e y\n",
    "x = df.drop(['Mooney','VEI'],axis=1)         # elimina colonne y\n",
    "y = df.Mooney\n",
    "# PLS (https://scikit-learn.org/stable/modules/generated/sklearn.cross_decomposition.PLSRegression.html)\n",
    "pls2 = PLSRegression(n_components=5)\n",
    "pls2.fit(x, y)\n",
    "Y_pred=pd.DataFrame(pls2.predict(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "marker": {
          "color": "darkgreen",
          "size": 10,
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           201
          ]
         },
         "mode": "markers+text",
         "text": [
          "Tingresso",
          "Solvente",
          "Nd_on_PBu",
          "Al_on_Nd",
          "Sty_on_Bde"
         ],
         "textposition": "top left",
         "type": "scatter",
         "x": [
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         "y": [
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         "marker": {
          "color": "darkred",
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         "text": "Mooney",
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         "y": [
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        "height": 600,
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          "heatmapgl": [
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       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "# Loadings plot\n",
    "\n",
    "label_x = np.array(x.columns)\n",
    "plot_x = go.Scatter(x=pls2.x_loadings_[:,0], y=pls2.x_loadings_[:,1], \n",
    "                  mode='markers+text', marker=dict(symbol=[201],color='darkgreen', size=10), \n",
    "                  text = label_x, textposition=\"top left\")\n",
    "plot_y = go.Scatter(x=pls2.y_loadings_[:,0], y=pls2.y_loadings_[:,1], \n",
    "                  mode='markers+text', marker=dict(symbol=[201],color='darkred', size=10), \n",
    "                  text = 'Mooney', textposition=\"top left\")\n",
    "\n",
    "fig=go.Figure()\n",
    "fig.add_trace(plot_x)\n",
    "fig.add_trace(plot_y)\n",
    "fig.update_layout(height=600, width=800, title='PLS - Loadings plot', xaxis_title='PC1',yaxis_title='PC2', \n",
    "                  xaxis_zeroline=True, yaxis_zeroline=True, xaxis_zerolinecolor='blue', yaxis_zerolinecolor='blue',\n",
    "                  showlegend=False)\n",
    "fig.update_xaxes(range=[min(pls2.x_loadings_[:,0])-0.2, max(pls2.x_loadings_[:,1])+0.2])\n",
    "fig.update_yaxes(range=[min(pls2.x_loadings_[:,0])-0.2, max(pls2.x_loadings_[:,1])+0.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create linear regression object\n",
    "y_exp=np.array(y)                 # Dataframe to array\n",
    "y_exp=y_exp[:,np.newaxis]         # Add 2nd dimension\n",
    "y_pls=np.array(Y_pred[0])         # Dataframe to array\n",
    "\n",
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(y_exp, y_pls)\n",
    "y_regr = regr.predict(y_exp)\n",
    "\n",
    "rmse=mean_squared_error(y_exp,y_pls,squared=False)\n",
    "r2=r2_score(y_exp,y_pls)"
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  },
  {
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    "# Regression plot\n",
    "title_pls= 'PLS regression: r^2 = '+str(np.round(r2, decimals=5))+','+' RMSE = '+str(np.round(rmse, decimals=5))\n",
    "fig=go.Figure()\n",
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