make_harmony_output_calibrated_value.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "773ade2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "325d10c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"data/mcelroy_cosine_correlation.csv\", sep=\"\\t\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "264cf697",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>text_1</th>\n",
       "      <th>text_2</th>\n",
       "      <th>y</th>\n",
       "      <th>cosine</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Felt down or depressed for most of the day?</td>\n",
       "      <td>Felt nervous or anxious?</td>\n",
       "      <td>0.719539</td>\n",
       "      <td>0.611496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Felt down or depressed for most of the day?</td>\n",
       "      <td>Worried a lot about different things?</td>\n",
       "      <td>0.719244</td>\n",
       "      <td>0.445721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Felt down or depressed for most of the day?</td>\n",
       "      <td>Felt physically tense or agitated?</td>\n",
       "      <td>0.731183</td>\n",
       "      <td>0.711875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Felt down or depressed for most of the day?</td>\n",
       "      <td>Felt your heart racing, difficulty breathing, ...</td>\n",
       "      <td>0.665979</td>\n",
       "      <td>0.571581</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Felt down or depressed for most of the day?</td>\n",
       "      <td>Felt “on edge”?</td>\n",
       "      <td>0.703581</td>\n",
       "      <td>0.511956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>736</th>\n",
       "      <td>Experienced reduced energy or fatigue?</td>\n",
       "      <td>Having powerful images or memories that someti...</td>\n",
       "      <td>0.530528</td>\n",
       "      <td>0.194023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>737</th>\n",
       "      <td>Experienced reduced energy or fatigue?</td>\n",
       "      <td>Avoiding internal reminders of the experience ...</td>\n",
       "      <td>0.544454</td>\n",
       "      <td>0.284540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>738</th>\n",
       "      <td>Experienced reduced energy or fatigue?</td>\n",
       "      <td>Avoiding external reminders of the experience ...</td>\n",
       "      <td>0.542928</td>\n",
       "      <td>0.190842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>739</th>\n",
       "      <td>Experienced reduced energy or fatigue?</td>\n",
       "      <td>Being “super-alert”, watchful, or on guard?</td>\n",
       "      <td>0.519665</td>\n",
       "      <td>0.355699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>740</th>\n",
       "      <td>Experienced reduced energy or fatigue?</td>\n",
       "      <td>Feeling jumpy or easily startled?</td>\n",
       "      <td>0.594313</td>\n",
       "      <td>0.330957</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>741 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                          text_1   \n",
       "0    Felt down or depressed for most of the day?  \\\n",
       "1    Felt down or depressed for most of the day?   \n",
       "2    Felt down or depressed for most of the day?   \n",
       "3    Felt down or depressed for most of the day?   \n",
       "4    Felt down or depressed for most of the day?   \n",
       "..                                           ...   \n",
       "736       Experienced reduced energy or fatigue?   \n",
       "737       Experienced reduced energy or fatigue?   \n",
       "738       Experienced reduced energy or fatigue?   \n",
       "739       Experienced reduced energy or fatigue?   \n",
       "740       Experienced reduced energy or fatigue?   \n",
       "\n",
       "                                                text_2         y    cosine  \n",
       "0                             Felt nervous or anxious?  0.719539  0.611496  \n",
       "1                Worried a lot about different things?  0.719244  0.445721  \n",
       "2                   Felt physically tense or agitated?  0.731183  0.711875  \n",
       "3    Felt your heart racing, difficulty breathing, ...  0.665979  0.571581  \n",
       "4                                      Felt “on edge”?  0.703581  0.511956  \n",
       "..                                                 ...       ...       ...  \n",
       "736  Having powerful images or memories that someti...  0.530528  0.194023  \n",
       "737  Avoiding internal reminders of the experience ...  0.544454  0.284540  \n",
       "738  Avoiding external reminders of the experience ...  0.542928  0.190842  \n",
       "739        Being “super-alert”, watchful, or on guard?  0.519665  0.355699  \n",
       "740                  Feeling jumpy or easily startled?  0.594313  0.330957  \n",
       "\n",
       "[741 rows x 4 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c23d2ade",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2a0e1aca",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0c38aeb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.fit(df[[\"cosine\"]], df.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f75f24ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.27562271])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fea93837",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5374678271626451"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a7e611e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2dc5be79",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/thomas/anaconda3/lib/python3.11/site-packages/sklearn/base.py:493: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "xs = sorted(df.cosine)\n",
    "ys= m.predict([[x] for x in xs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "646a19ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x728d49df0050>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df.cosine, df.y)\n",
    "plt.plot(xs, ys, color=\"red\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9b742601",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/thomas/anaconda3/lib/python3.11/site-packages/sklearn/base.py:493: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.53746783])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.predict([[0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a5b39ec7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/thomas/anaconda3/lib/python3.11/site-packages/sklearn/base.py:493: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0.81309054])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.predict([[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "08be38d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"residual\"] = df.cosine - df.y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0205f8c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.sort_values(\"residual\", inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "81c261d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.naive_bayes import MultinomialNB\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.feature_extraction.text import CountVectorizer, TfidfTransformer\n",
    "\n",
    "vectoriser = CountVectorizer(lowercase=True)\n",
    "transformer = TfidfTransformer()\n",
    "\n",
    "nb = MultinomialNB()\n",
    "model = make_pipeline(vectoriser, transformer, nb)\n",
    "\n",
    "y = [\"harmony false positive\"] * len(df)\n",
    "for i in range(len(df)//2):\n",
    "    y[i] = \"harmony missed\"\n",
    "    \n",
    "for i in range(len(df)//4, len(df)//4 * 3):\n",
    "    y[i] = \"neither\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "bc68511a",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"over_or_under\"] = y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "9d054360",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"concat\"] = df.text_1 + \" \" + df.text_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "c4c62111",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "2977947d",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train, df_test = train_test_split(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "da29f79e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-3 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-3 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-3 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-3 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-3 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-3 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-3 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-3 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-3 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-3 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;countvectorizer&#x27;, CountVectorizer()),\n",
       "                (&#x27;tfidftransformer&#x27;, TfidfTransformer()),\n",
       "                (&#x27;multinomialnb&#x27;, MultinomialNB())])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" ><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;Pipeline<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.pipeline.Pipeline.html\">?<span>Documentation for Pipeline</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>Pipeline(steps=[(&#x27;countvectorizer&#x27;, CountVectorizer()),\n",
       "                (&#x27;tfidftransformer&#x27;, TfidfTransformer()),\n",
       "                (&#x27;multinomialnb&#x27;, MultinomialNB())])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-7\" type=\"checkbox\" ><label for=\"sk-estimator-id-7\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;CountVectorizer<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.feature_extraction.text.CountVectorizer.html\">?<span>Documentation for CountVectorizer</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>CountVectorizer()</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-8\" type=\"checkbox\" ><label for=\"sk-estimator-id-8\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;TfidfTransformer<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.feature_extraction.text.TfidfTransformer.html\">?<span>Documentation for TfidfTransformer</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>TfidfTransformer()</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-9\" type=\"checkbox\" ><label for=\"sk-estimator-id-9\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;MultinomialNB<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.naive_bayes.MultinomialNB.html\">?<span>Documentation for MultinomialNB</span></a></label><div class=\"sk-toggleable__content fitted\"><pre>MultinomialNB()</pre></div> </div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('countvectorizer', CountVectorizer()),\n",
       "                ('tfidftransformer', TfidfTransformer()),\n",
       "                ('multinomialnb', MultinomialNB())])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(df_train[\"concat\"], df_train.over_or_under)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a7256d02",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = model.predict(df_test[\"concat\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "ef69739b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import accuracy_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "a69e2196",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.521505376344086"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(df_test.over_or_under, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "582c6461",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Strongest predictors for class 0 harmony false positive\n",
      "\n",
      "0\tmoving\n",
      "1\tstaying\n",
      "2\tfalling\n",
      "3\tasleep\n",
      "4\tsleeping\n",
      "5\topposite\n",
      "6\tspeaking\n",
      "7\taround\n",
      "8\tusual\n",
      "9\tthan\n",
      "10\tnoticed\n",
      "11\tslowly\n",
      "12\tother\n",
      "13\tfidgety\n",
      "14\tcould\n",
      "15\tnervous\n",
      "16\tanxious\n",
      "Strongest predictors for class 1 harmony missed\n",
      "\n",
      "0\tdisturbances\n",
      "1\tfatigue\n",
      "2\treduced\n",
      "3\twatching\n",
      "4\tnewspaper\n",
      "5\treading\n",
      "6\ttelevision\n",
      "7\tsuch\n",
      "8\tguilt\n",
      "9\tworthlessness\n",
      "10\tsleep\n",
      "11\tovereating\n",
      "12\tpoor\n",
      "13\tconcentrating\n",
      "14\tobjects\n",
      "15\tplaces\n",
      "16\tsituations\n",
      "Strongest predictors for class 2 neither\n",
      "\n",
      "0\trelaxing\n",
      "1\tif\n",
      "2\tafraid\n",
      "3\tmight\n",
      "4\thappen\n",
      "5\tawful\n",
      "6\tsomething\n",
      "7\trelated\n",
      "8\tdreams\n",
      "9\tpart\n",
      "10\tupsetting\n",
      "11\tclearly\n",
      "12\treplay\n",
      "13\tnot\n",
      "14\tcontrol\n",
      "15\table\n",
      "16\tstop\n"
     ]
    }
   ],
   "source": [
    "\n",
    "fake_document = \" \".join(vectoriser.vocabulary_)\n",
    "vectorised_document = vectoriser.transform([fake_document])\n",
    "transformed_document = transformer.transform(vectorised_document)\n",
    "probas = np.zeros((transformed_document.shape[1]))\n",
    "\n",
    "for prediction_idx in range(3):\n",
    "    print(f\"Strongest predictors for class {prediction_idx} {model.classes_[prediction_idx]}\\n\")\n",
    "    for i in range(transformed_document.shape[1]):\n",
    "        zeros = np.zeros(transformed_document.shape)\n",
    "        zeros[0, i] = transformed_document[0, i]\n",
    "        proba = nb.predict_log_proba(zeros)\n",
    "        probas[i] = proba[0, prediction_idx]\n",
    "\n",
    "    for ctr, j in enumerate(np.argsort(-probas)):\n",
    "        for w, i in vectoriser.vocabulary_.items():\n",
    "            if i == j:\n",
    "                print(f\"{ctr}\\t{w}\")\n",
    "        if ctr > 15:\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "e3fe4eef",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"sleep\"] = df[\"concat\"].str.contains(\"sleep\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "e62eee58",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[\"dream\"] = df[\"concat\"].str.contains(\"dream\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "e8d73c4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-5 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-5 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-5 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-5 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-5 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-5 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-5 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-5 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-5 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-5 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-5 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-5 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-5 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-5 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-5 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-5\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-11\" type=\"checkbox\" checked><label for=\"sk-estimator-id-11\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;LinearRegression<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.fit(df[[\"cosine\", \"sleep\", \"dream\"]], df.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "f98a1eab",
   "metadata": {},
   "outputs": [],
   "source": [
    "pred = m.predict(df[[\"cosine\", \"sleep\", \"dream\"]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "f1c92e31",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5498936116442322\n",
      "0.3023829841271377\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "actual = df.y\n",
    "predict = pred\n",
    "\n",
    "corr_matrix = numpy.corrcoef(actual, predict)\n",
    "corr = corr_matrix[0,1]\n",
    "print (corr)\n",
    "R_sq = corr**2\n",
    "\n",
    "print(R_sq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "8cf79c38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.25260324, -0.03738961, -0.05534086])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21efe828",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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