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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Holt Winter's Method"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[](https://nbviewer.org/github/gautamnaik1994/SalesForecasting_ML_CaseStudy/blob/main/notebooks/modelling/01.HoltWinterMethod.ipynb?flush_cache=true)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"import plotly.io as pio\n",
"pio.renderers.default = \"colab+notebook_connected+vscode\"\n",
"import pandas as pd\n",
"import numpy as np\n",
"import duckdb as db\n",
"import matplotlib.pyplot as plt\n",
"import plotly.express as px\n",
"import plotly.graph_objects as go\n",
"import optuna\n",
"import warnings\n",
"\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"# exponential smoothing\n",
"from statsmodels.tsa.holtwinters import ExponentialSmoothing\n",
"from statsmodels.tsa.exponential_smoothing.ets import ETSModel\n",
"from IPython.display import display, Markdown\n",
"# mape\n",
"from sklearn.metrics import mean_absolute_percentage_error\n",
"optuna.logging.set_verbosity(optuna.logging.ERROR)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"df = pd.read_parquet(\"../../data/processed/train_enhanced.parquet\")\n",
"train_agg = pd.read_parquet(\"../../data/processed/train_agg.parquet\")\n",
"train_region_code_agg = pd.read_parquet(\"../../data/processed/train_region_code_agg.parquet\")\n",
"holiday_df= pd.read_csv(\"../../data/processed/holidays.csv\")"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"def split_train_test(df, test_size=0.2):\n",
" split_idx = int(len(df) * (1 - test_size))\n",
" return df.iloc[:split_idx], df.iloc[split_idx:]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Region 1"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
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" vertical-align: top;\n",
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" .dataframe thead th {\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Region_Code</th>\n",
" <th>Total_Sales</th>\n",
" <th>Avg_Sales</th>\n",
" <th>Total_Orders</th>\n",
" <th>Avg_Orders</th>\n",
" <th>Num_Stores</th>\n",
" <th>Holiday</th>\n",
" <th>Total_Discounts</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Date</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2018-01-01</th>\n",
" <td>R1</td>\n",
" <td>5094374</td>\n",
" <td>41084</td>\n",
" <td>6509</td>\n",
" <td>52</td>\n",
" <td>124</td>\n",
" <td>1</td>\n",
" <td>124</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2018-01-02</th>\n",
" <td>R1</td>\n",
" <td>7050675</td>\n",
" <td>56860</td>\n",
" <td>9738</td>\n",
" <td>79</td>\n",
" <td>124</td>\n",
" <td>0</td>\n",
" <td>124</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2018-01-03</th>\n",
" <td>R1</td>\n",
" <td>6851526</td>\n",
" <td>55254</td>\n",
" <td>9473</td>\n",
" <td>76</td>\n",
" <td>124</td>\n",
" <td>0</td>\n",
" <td>124</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2018-01-04</th>\n",
" <td>R1</td>\n",
" <td>7362648</td>\n",
" <td>59376</td>\n",
" <td>10132</td>\n",
" <td>82</td>\n",
" <td>124</td>\n",
" <td>0</td>\n",
" <td>124</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2018-01-05</th>\n",
" <td>R1</td>\n",
" <td>8153604</td>\n",
" <td>65755</td>\n",
" <td>10883</td>\n",
" <td>88</td>\n",
" <td>124</td>\n",
" <td>0</td>\n",
" <td>124</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Region_Code Total_Sales Avg_Sales Total_Orders Avg_Orders \\\n",
"Date \n",
"2018-01-01 R1 5094374 41084 6509 52 \n",
"2018-01-02 R1 7050675 56860 9738 79 \n",
"2018-01-03 R1 6851526 55254 9473 76 \n",
"2018-01-04 R1 7362648 59376 10132 82 \n",
"2018-01-05 R1 8153604 65755 10883 88 \n",
"\n",
" Num_Stores Holiday Total_Discounts \n",
"Date \n",
"2018-01-01 124 1 124 \n",
"2018-01-02 124 0 124 \n",
"2018-01-03 124 0 124 \n",
"2018-01-04 124 0 124 \n",
"2018-01-05 124 0 124 "
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"train_region_code_agg_R1 = train_region_code_agg[train_region_code_agg['Region_Code'] == 'R1'].set_index('Date')\n",
"train_region_code_agg_R1.head()"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"((412, 8), (104, 8))"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"train_region_code_agg_R1_train, train_region_code_agg_R1_test = split_train_test(train_region_code_agg_R1)\n",
"train_region_code_agg_R1_train.shape, train_region_code_agg_R1_test.shape"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ses = ExponentialSmoothing(train_region_code_agg_R1_train['Total_Sales'], seasonal='add', seasonal_periods=12, freq='D').fit()\n",
"ses.summary()\n",
"\n",
"fig = go.Figure()\n",
"fig.add_trace(go.Scatter(x=train_region_code_agg_R1_train.index, y=train_region_code_agg_R1_train['Total_Sales'], mode='lines', name='Train'))\n",
"fig.add_trace(go.Scatter(x=train_region_code_agg_R1_test.index, y=train_region_code_agg_R1_test['Total_Sales'], mode='lines', name='Test'))\n",
"fig.add_trace(go.Scatter(x=train_region_code_agg_R1_test.index, y=ses.forecast(len(train_region_code_agg_R1_test)), mode='lines', name='Forecast'))\n",
"fig.show()"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.19351601851390085"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mape = mean_absolute_percentage_error(train_region_code_agg_R1_test['Total_Sales'], ses.forecast(len(train_region_code_agg_R1_test)))\n",
"mape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Hyperparameter Tuning"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"def objective(trial):\n",
" seasonal = trial.suggest_categorical('seasonal', ['add', 'mul', 'additive', 'multiplicative'])\n",
" seasonal_periods = trial.suggest_int('seasonal_periods', 7, 100)\n",
" model = ExponentialSmoothing(train_region_code_agg_R1_train['Total_Sales'], seasonal=seasonal, seasonal_periods=seasonal_periods, freq='D').fit()\n",
" forecast = model.forecast(len(train_region_code_agg_R1_test))\n",
" mape = mean_absolute_percentage_error(train_region_code_agg_R1_test['Total_Sales'], forecast)\n",
" return mape\n",
"\n",
"study = optuna.create_study(direction='minimize', study_name='ses')\n",
"study.optimize(objective, n_trials=300)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'seasonal': 'multiplicative', 'seasonal_periods': 12}"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"study.best_params"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ses = ExponentialSmoothing(train_region_code_agg_R1_train['Total_Sales'], seasonal = 'multiplicative', seasonal_periods=12, freq='D').fit()\n",
"\n",
"fig = go.Figure()\n",
"fig.add_trace(go.Scatter(x=train_region_code_agg_R1_train.index, y=train_region_code_agg_R1_train['Total_Sales'], mode='lines', name='Train'))\n",
"fig.add_trace(go.Scatter(x=train_region_code_agg_R1_test.index, y=train_region_code_agg_R1_test['Total_Sales'], mode='lines', name='Test'))\n",
"fig.add_trace(go.Scatter(x=train_region_code_agg_R1_test.index, y=ses.forecast(len(train_region_code_agg_R1_test)), mode='lines', name='Forecast'))\n",
"fig.show()"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.19180792258357673"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mape = mean_absolute_percentage_error(train_region_code_agg_R1_test['Total_Sales'], ses.forecast(len(train_region_code_agg_R1_test)))\n",
"mape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Generalizing the process"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"def plot_forecast(model, train, test):\n",
" fig = go.Figure()\n",
" fig.add_trace(go.Scatter(x=train.index, y=train['Total_Sales'], mode='lines', name='Train'))\n",
" fig.add_trace(go.Scatter(x=test.index, y=test['Total_Sales'], mode='lines', name='Test'))\n",
" fig.add_trace(go.Scatter(x=test.index, y=model.forecast(len(test)), mode='lines', name='Forecast'))\n",
" fig.show()\n",
"\n",
"def tune_parameters(train, test):\n",
" def objective(trial):\n",
" seasonal = trial.suggest_categorical('seasonal', ['add', 'mul', 'additive', 'multiplicative'])\n",
" seasonal_periods = trial.suggest_int('seasonal_periods', 7, 100)\n",
" model = ExponentialSmoothing(train['Total_Sales'], seasonal=seasonal, seasonal_periods=seasonal_periods, freq='D').fit()\n",
" forecast = model.forecast(len(test))\n",
" mape = mean_absolute_percentage_error(test['Total_Sales'], forecast)\n",
" return mape\n",
"\n",
" study = optuna.create_study(direction='minimize')\n",
" study.optimize(objective, n_trials=500)\n",
" return study.best_params"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Region R2"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'seasonal': 'multiplicative', 'seasonal_periods': 12}\n"
]
}
],
"source": [
"train = train_region_code_agg[train_region_code_agg['Region_Code'] == 'R2'].set_index('Date')\n",
"train_train, train_test = split_train_test(train)\n",
"params = tune_parameters(train_train, train_test)\n",
"print(params)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
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"text": [
"MAPE: 0.17683126754833497\n"
]
}
],
"source": [
"ses = ExponentialSmoothing(train_train['Total_Sales'], seasonal = params['seasonal'], seasonal_periods=params[\"seasonal_periods\"], freq='D').fit()\n",
"plot_forecast(ses, train_train, train_test)\n",
"print(\"MAPE: \",mean_absolute_percentage_error(train_test['Total_Sales'], ses.forecast(len(train_test))))"
]
},
{
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"metadata": {},
"source": [
"## Region R3"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'seasonal': 'mul', 'seasonal_periods': 12}\n"
]
}
],
"source": [
"train = train_region_code_agg[train_region_code_agg['Region_Code'] == 'R3'].set_index('Date')\n",
"train_train, train_test = split_train_test(train)\n",
"params = tune_parameters(train_train, train_test)\n",
"print(params)"
]
},
{
"cell_type": "code",
"execution_count": 38,
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"text": [
"MAPE: 0.20489387241933427\n"
]
}
],
"source": [
"ses = ExponentialSmoothing(train_train['Total_Sales'], seasonal = params['seasonal'], seasonal_periods=12, freq='D').fit()\n",
"plot_forecast(ses, train_train, train_test)\n",
"print(\"MAPE: \",mean_absolute_percentage_error(train_test['Total_Sales'], ses.forecast(len(train_test))))"
]
},
{
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"metadata": {},
"source": [
"## Region R4"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{'seasonal': 'multiplicative', 'seasonal_periods': 12}\n"
]
}
],
"source": [
"train = train_region_code_agg[train_region_code_agg['Region_Code'] == 'R4'].set_index('Date')\n",
"train_train, train_test = split_train_test(train)\n",
"params = tune_parameters(train_train, train_test)\n",
"print(params)"
]
},
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"execution_count": 40,
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"text": [
"MAPE: 0.198372394232825\n"
]
}
],
"source": [
"ses = ExponentialSmoothing(train_train['Total_Sales'], seasonal = params['seasonal'], seasonal_periods=12, freq='D').fit()\n",
"plot_forecast(ses, train_train, train_test)\n",
"print(\"MAPE: \",mean_absolute_percentage_error(train_test['Total_Sales'], ses.forecast(len(train_test))))"
]
},
{
"cell_type": "markdown",
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"source": [
"## Global"
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{
"cell_type": "code",
"execution_count": 41,
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" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Total_Sales</th>\n",
" <th>Avg_Sales</th>\n",
" <th>Total_Orders</th>\n",
" <th>Avg_Orders</th>\n",
" <th>Holiday</th>\n",
" <th>Total_Discounts</th>\n",
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" <th>0</th>\n",
" <td>2018-01-01</td>\n",
" <td>15345484</td>\n",
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" <td>54</td>\n",
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" <th>1</th>\n",
" <td>2018-01-02</td>\n",
" <td>19592415</td>\n",
" <td>53678</td>\n",
" <td>25326</td>\n",
" <td>69</td>\n",
" <td>0</td>\n",
" <td>365</td>\n",
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" <tr>\n",
" <th>2</th>\n",
" <td>2018-01-03</td>\n",
" <td>18652527</td>\n",
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" <td>66</td>\n",
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" <th>3</th>\n",
" <td>2018-01-04</td>\n",
" <td>19956267</td>\n",
" <td>54675</td>\n",
" <td>25584</td>\n",
" <td>70</td>\n",
" <td>0</td>\n",
" <td>364</td>\n",
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" <th>4</th>\n",
" <td>2018-01-05</td>\n",
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" <td>78</td>\n",
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" <th>511</th>\n",
" <td>2019-05-27</td>\n",
" <td>17197023</td>\n",
" <td>47115</td>\n",
" <td>25447</td>\n",
" <td>70</td>\n",
" <td>0</td>\n",
" <td>321</td>\n",
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" <th>512</th>\n",
" <td>2019-05-28</td>\n",
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" <td>74</td>\n",
" <td>0</td>\n",
" <td>319</td>\n",
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" <th>513</th>\n",
" <td>2019-05-29</td>\n",
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" <td>24047</td>\n",
" <td>66</td>\n",
" <td>0</td>\n",
" <td>193</td>\n",
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" <tr>\n",
" <th>514</th>\n",
" <td>2019-05-30</td>\n",
" <td>16082139</td>\n",
" <td>44061</td>\n",
" <td>24318</td>\n",
" <td>67</td>\n",
" <td>0</td>\n",
" <td>76</td>\n",
" </tr>\n",
" <tr>\n",
" <th>515</th>\n",
" <td>2019-05-31</td>\n",
" <td>15601825</td>\n",
" <td>42745</td>\n",
" <td>23602</td>\n",
" <td>65</td>\n",
" <td>1</td>\n",
" <td>39</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>516 rows × 7 columns</p>\n",
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" Date Total_Sales Avg_Sales Total_Orders Avg_Orders Holiday \\\n",
"0 2018-01-01 15345484 42042 19666 54 1 \n",
"1 2018-01-02 19592415 53678 25326 69 0 \n",
"2 2018-01-03 18652527 51103 24047 66 0 \n",
"3 2018-01-04 19956267 54675 25584 70 0 \n",
"4 2018-01-05 22902651 62747 28436 78 0 \n",
".. ... ... ... ... ... ... \n",
"511 2019-05-27 17197023 47115 25447 70 0 \n",
"512 2019-05-28 18652065 51102 27184 74 0 \n",
"513 2019-05-29 16213497 44421 24047 66 0 \n",
"514 2019-05-30 16082139 44061 24318 67 0 \n",
"515 2019-05-31 15601825 42745 23602 65 1 \n",
"\n",
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"0 365 \n",
"1 365 \n",
"2 365 \n",
"3 364 \n",
"4 364 \n",
".. ... \n",
"511 321 \n",
"512 319 \n",
"513 193 \n",
"514 76 \n",
"515 39 \n",
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},
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"train_agg"
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"execution_count": 42,
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"name": "stdout",
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"text": [
"{'seasonal': 'multiplicative', 'seasonal_periods': 63}\n"
]
}
],
"source": [
"train = train_agg.set_index('Date')\n",
"train_train, train_test = split_train_test(train)\n",
"params = tune_parameters(train_train, train_test)\n",
"print(params)"
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"text": [
"MAPE: 0.19000567422948877\n"
]
}
],
"source": [
"ses = ExponentialSmoothing(train_train['Total_Sales'], seasonal = params['seasonal'], seasonal_periods=12, freq='D').fit()\n",
"plot_forecast(ses, train_train, train_test)\n",
"print(\"MAPE: \",mean_absolute_percentage_error(train_test['Total_Sales'], ses.forecast(len(train_test))))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"https://stats.stackexchange.com/questions/412276/how-to-handle-many-times-series-simultaneously \n",
"https://stackoverflow.com/questions/61717970/is-there-a-way-to-forecast-sales-for-multiple-products-across-multiple-stores"
]
},
{
"cell_type": "code",
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{
"data": {
"text/plain": [
"┌──────────┬────────────┬─────────────────────┐\n",
"│ Store_id │ t_sales │ pct_sales │\n",
"│ int64 │ double │ double │\n",
"├──────────┼────────────┼─────────────────────┤\n",
"│ 298 │ 32572688.0 │ 0.9229065277013243 │\n",
"│ 346 │ 29651962.0 │ 0.8401514188664002 │\n",
"│ 39 │ 29234458.0 │ 0.8283219444027082 │\n",
"│ 49 │ 28886187.0 │ 0.8184541324856239 │\n",
"│ 278 │ 28776251.0 │ 0.8153392263539905 │\n",
"│ 195 │ 28151748.0 │ 0.7976447046967527 │\n",
"│ 357 │ 28143722.0 │ 0.7974173050680229 │\n",
"│ 201 │ 28051720.0 │ 0.7948105364863556 │\n",
"│ 97 │ 27748247.0 │ 0.7862120033783618 │\n",
"│ 18 │ 27613532.0 │ 0.7823950225152212 │\n",
"│ · │ · │ · │\n",
"│ · │ · │ · │\n",
"│ · │ · │ · │\n",
"│ 51 │ 17388121.0 │ 0.49267074395857163 │\n",
"│ 177 │ 17261487.0 │ 0.489082734397513 │\n",
"│ 187 │ 17158548.0 │ 0.48616608946166706 │\n",
"│ 238 │ 17059578.0 │ 0.48336188674650066 │\n",
"│ 148 │ 16884632.0 │ 0.47840502024680814 │\n",
"│ 46 │ 16698801.0 │ 0.4731397190143569 │\n",
"│ 360 │ 16221385.0 │ 0.4596127378789156 │\n",
"│ 159 │ 15963333.0 │ 0.4523011680927709 │\n",
"│ 142 │ 15932457.0 │ 0.4514263299943258 │\n",
"│ 365 │ 15867221.0 │ 0.44957795203091344 │\n",
"├──────────┴────────────┴─────────────────────┤\n",
"│ 165 rows (20 shown) 3 columns │\n",
"└─────────────────────────────────────────────┘"
]
},
"execution_count": 22,
"metadata": {},
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}
],
"source": [
"db.sql(\"\"\" \n",
"select Store_id, round(sum(Sales),0) t_sales, \n",
" round(sum(Sales)*100,0)/(select sum(Sales) from df where Location_Type = 'L1' ) as pct_sales,\n",
" \n",
" from df where Location_Type = 'L1' group by Store_id order by pct_sales desc\n",
"\"\"\")"
]
}
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