mmm.ipynb

mmm.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/WHU-Chair-of-Digital-Marketing/ee05482d39317561ac610a8f6ce72026/mmm.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IiKPNryt-EVj"
      },
      "source": [
        "# **JUPYTER/R-CODE for Integrating Brand Equity in MMM for a Long-term Ad Effectiveness Measurement**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7QySOVKh-RIW"
      },
      "source": [
        "The methodology of this project is based on the paper \"Integrating Brand Equity in MMM for a Long-term Ad Effectiveness Measurement\" published by Meta and WHU (Reh et al., 2022).\n",
        "In this code a marekting mix model in multiplicative form with 14 variables is displayed, two clustered media channels and four control variables are used.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4toiqCbt-Loj"
      },
      "source": [
        "**SET UP**\n",
        "\n",
        "To be able to use the R-code in Jupyter, it is recommended to use the package \"R magic\" to convert R code into Python."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#This version is recommended as newer versions could cause errors\n",
        "!pip install rpy2==3.5.1"
      ],
      "metadata": {
        "id": "4rYPP5LnPbzN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "oN0NuPvV_Eb-"
      },
      "outputs": [],
      "source": [
        "#Activate R magic in colab notebook\n",
        "%load_ext rpy2.ipython"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K8X6Q-Ut8q1O"
      },
      "source": [
        "**1. INTRODUCTION**\n",
        "\n",
        "Marketing mix modeling (MMM) has become a powerful and trustworthy tool for marketers in supporting them in optimizing advertising mix and promotional tactics for sales revenue. Typically, MMMs build on weekly sales, the various channels' ad spends, and other marketing mix data to capture a statistical link between the marketing activities and sales. \n",
        "This code stems from a MMM-case with fictive data recently analysed in the Working Paper available on SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4103941. This study highlights the relevance to incorporate brand equity - measured as ad awareness- into MMM. \n",
        "In the following, we concentrate on the results of a pragmatic multiplicative regression model. The main finding is that by integrating brand mindset metrics into MMM, we can enhance the diagnosticity of the advertising effectiveness analysis.\n",
        "\n",
        "**Data Upload & Preparation**\n",
        "\n",
        "First, R packages that will be used are installed."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Install and import R packages in colab notebook\n",
        "%%R \n",
        "library(readr) \n",
        "library(tidyverse)\n",
        "library(readxl)\n",
        "library(ggplot2)\n",
        "install.packages(\"caret\")\n",
        "library(caret)\n",
        "install.packages(\"vars\")\n",
        "library(vars)"
      ],
      "metadata": {
        "id": "iVgN2EyIdkvS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HQ_um9v1VHmd"
      },
      "source": [
        "Second, the MMM raw data from our workspace that is stored in a .csv-sheet is uploaded. Therefore a fictive \"mmm_data.csv\"-input inspired by real-world data, that can be found in this shared link, shall serve as an exemplary dataset: https://drive.google.com/file/d/1g7gVL2f63tKXuKcJo8hcpAyi_7HMqg5g/view?usp=share_link\n",
        "\n",
        "You can download this dataset and upload it into the Colab environment - please execute the next code chunk.\n",
        "Some summary statistics will be displayed then to be able to have a first look into the data."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import file via data-upload\n",
        "from google.colab import files\n",
        "uploaded = files.upload()\n",
        "import io\n",
        "import pandas as pd\n",
        "Final_dataset_weekly = pd.read_csv(io.BytesIO(uploaded['mmm_data.csv']))\n",
        "# Dataset is now stored in a Pandas Dataframe"
      ],
      "metadata": {
        "id": "Aqo6xkycQ84H",
        "outputId": "39bdff25-216f-43ad-b03f-618dd3489a0b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 73
        }
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-bb008a2d-5663-423f-9f19-bd055a21b852\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-bb008a2d-5663-423f-9f19-bd055a21b852\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script>// Copyright 2017 Google LLC\n",
              "//\n",
              "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
              "// you may not use this file except in compliance with the License.\n",
              "// You may obtain a copy of the License at\n",
              "//\n",
              "//      http://www.apache.org/licenses/LICENSE-2.0\n",
              "//\n",
              "// Unless required by applicable law or agreed to in writing, software\n",
              "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
              "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
              "// See the License for the specific language governing permissions and\n",
              "// limitations under the License.\n",
              "\n",
              "/**\n",
              " * @fileoverview Helpers for google.colab Python module.\n",
              " */\n",
              "(function(scope) {\n",
              "function span(text, styleAttributes = {}) {\n",
              "  const element = document.createElement('span');\n",
              "  element.textContent = text;\n",
              "  for (const key of Object.keys(styleAttributes)) {\n",
              "    element.style[key] = styleAttributes[key];\n",
              "  }\n",
              "  return element;\n",
              "}\n",
              "\n",
              "// Max number of bytes which will be uploaded at a time.\n",
              "const MAX_PAYLOAD_SIZE = 100 * 1024;\n",
              "\n",
              "function _uploadFiles(inputId, outputId) {\n",
              "  const steps = uploadFilesStep(inputId, outputId);\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  // Cache steps on the outputElement to make it available for the next call\n",
              "  // to uploadFilesContinue from Python.\n",
              "  outputElement.steps = steps;\n",
              "\n",
              "  return _uploadFilesContinue(outputId);\n",
              "}\n",
              "\n",
              "// This is roughly an async generator (not supported in the browser yet),\n",
              "// where there are multiple asynchronous steps and the Python side is going\n",
              "// to poll for completion of each step.\n",
              "// This uses a Promise to block the python side on completion of each step,\n",
              "// then passes the result of the previous step as the input to the next step.\n",
              "function _uploadFilesContinue(outputId) {\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  const steps = outputElement.steps;\n",
              "\n",
              "  const next = steps.next(outputElement.lastPromiseValue);\n",
              "  return Promise.resolve(next.value.promise).then((value) => {\n",
              "    // Cache the last promise value to make it available to the next\n",
              "    // step of the generator.\n",
              "    outputElement.lastPromiseValue = value;\n",
              "    return next.value.response;\n",
              "  });\n",
              "}\n",
              "\n",
              "/**\n",
              " * Generator function which is called between each async step of the upload\n",
              " * process.\n",
              " * @param {string} inputId Element ID of the input file picker element.\n",
              " * @param {string} outputId Element ID of the output display.\n",
              " * @return {!Iterable<!Object>} Iterable of next steps.\n",
              " */\n",
              "function* uploadFilesStep(inputId, outputId) {\n",
              "  const inputElement = document.getElementById(inputId);\n",
              "  inputElement.disabled = false;\n",
              "\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  outputElement.innerHTML = '';\n",
              "\n",
              "  const pickedPromise = new Promise((resolve) => {\n",
              "    inputElement.addEventListener('change', (e) => {\n",
              "      resolve(e.target.files);\n",
              "    });\n",
              "  });\n",
              "\n",
              "  const cancel = document.createElement('button');\n",
              "  inputElement.parentElement.appendChild(cancel);\n",
              "  cancel.textContent = 'Cancel upload';\n",
              "  const cancelPromise = new Promise((resolve) => {\n",
              "    cancel.onclick = () => {\n",
              "      resolve(null);\n",
              "    };\n",
              "  });\n",
              "\n",
              "  // Wait for the user to pick the files.\n",
              "  const files = yield {\n",
              "    promise: Promise.race([pickedPromise, cancelPromise]),\n",
              "    response: {\n",
              "      action: 'starting',\n",
              "    }\n",
              "  };\n",
              "\n",
              "  cancel.remove();\n",
              "\n",
              "  // Disable the input element since further picks are not allowed.\n",
              "  inputElement.disabled = true;\n",
              "\n",
              "  if (!files) {\n",
              "    return {\n",
              "      response: {\n",
              "        action: 'complete',\n",
              "      }\n",
              "    };\n",
              "  }\n",
              "\n",
              "  for (const file of files) {\n",
              "    const li = document.createElement('li');\n",
              "    li.append(span(file.name, {fontWeight: 'bold'}));\n",
              "    li.append(span(\n",
              "        `(${file.type || 'n/a'}) - ${file.size} bytes, ` +\n",
              "        `last modified: ${\n",
              "            file.lastModifiedDate ? file.lastModifiedDate.toLocaleDateString() :\n",
              "                                    'n/a'} - `));\n",
              "    const percent = span('0% done');\n",
              "    li.appendChild(percent);\n",
              "\n",
              "    outputElement.appendChild(li);\n",
              "\n",
              "    const fileDataPromise = new Promise((resolve) => {\n",
              "      const reader = new FileReader();\n",
              "      reader.onload = (e) => {\n",
              "        resolve(e.target.result);\n",
              "      };\n",
              "      reader.readAsArrayBuffer(file);\n",
              "    });\n",
              "    // Wait for the data to be ready.\n",
              "    let fileData = yield {\n",
              "      promise: fileDataPromise,\n",
              "      response: {\n",
              "        action: 'continue',\n",
              "      }\n",
              "    };\n",
              "\n",
              "    // Use a chunked sending to avoid message size limits. See b/62115660.\n",
              "    let position = 0;\n",
              "    do {\n",
              "      const length = Math.min(fileData.byteLength - position, MAX_PAYLOAD_SIZE);\n",
              "      const chunk = new Uint8Array(fileData, position, length);\n",
              "      position += length;\n",
              "\n",
              "      const base64 = btoa(String.fromCharCode.apply(null, chunk));\n",
              "      yield {\n",
              "        response: {\n",
              "          action: 'append',\n",
              "          file: file.name,\n",
              "          data: base64,\n",
              "        },\n",
              "      };\n",
              "\n",
              "      let percentDone = fileData.byteLength === 0 ?\n",
              "          100 :\n",
              "          Math.round((position / fileData.byteLength) * 100);\n",
              "      percent.textContent = `${percentDone}% done`;\n",
              "\n",
              "    } while (position < fileData.byteLength);\n",
              "  }\n",
              "\n",
              "  // All done.\n",
              "  yield {\n",
              "    response: {\n",
              "      action: 'complete',\n",
              "    }\n",
              "  };\n",
              "}\n",
              "\n",
              "scope.google = scope.google || {};\n",
              "scope.google.colab = scope.google.colab || {};\n",
              "scope.google.colab._files = {\n",
              "  _uploadFiles,\n",
              "  _uploadFilesContinue,\n",
              "};\n",
              "})(self);\n",
              "</script> "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving mmm_data.csv to mmm_data.csv\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Change python dataframe to R dataframe\n",
        "import rpy2.robjects as ro\n",
        "from rpy2.robjects.packages import importr\n",
        "from rpy2.robjects import pandas2ri\n",
        "from rpy2.robjects.conversion import localconverter\n",
        "from rpy2.robjects import globalenv\n",
        "\n",
        "# Convert the python dataframe to an R dataframe\n",
        "with localconverter(ro.default_converter + pandas2ri.converter):\n",
        "  Final_dataset_weekly=ro.conversion.py2rpy(Final_dataset_weekly)\n",
        "\n",
        "# Inspect dataframe\n",
        "type(Final_dataset_weekly)\n",
        "# Create a variable name in R's global environment\n",
        "globalenv['Final_dataset_weekly'] = Final_dataset_weekly\n",
        "\n",
        "# Print statistics\n",
        "%R print(summary(Final_dataset_weekly))"
      ],
      "metadata": {
        "id": "1u2NMItQRqzf",
        "outputId": "e40c94e2-0445-4dd4-a859-b4b4ad67ecc7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        }
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "      date        adj_ad_awareness   adj_sales        adj_channel_1    \n",
            " Min.   :  1.00   Min.   : 1.679   Min.   :  495858   Min.   :     15  \n",
            " 1st Qu.: 67.25   1st Qu.: 4.409   1st Qu.: 1253421   1st Qu.: 162261  \n",
            " Median :133.50   Median : 5.396   Median : 2138031   Median : 444077  \n",
            " Mean   :133.50   Mean   : 5.442   Mean   : 2749033   Mean   : 695560  \n",
            " 3rd Qu.:199.75   3rd Qu.: 6.318   3rd Qu.: 3555635   3rd Qu.: 940215  \n",
            " Max.   :266.00   Max.   :11.191   Max.   :19402328   Max.   :3505168  \n",
            " adj_channel_2    ln_ad_awareness    ln_sales      ln_channel_1  \n",
            " Min.   : 20278   Min.   :0.520   Min.   :13.11   Min.   : 2.70  \n",
            " 1st Qu.: 52949   1st Qu.:1.482   1st Qu.:14.04   1st Qu.:12.00  \n",
            " Median :109578   Median :1.685   Median :14.57   Median :13.01  \n",
            " Mean   :141353   Mean   :1.653   Mean   :14.58   Mean   :12.28  \n",
            " 3rd Qu.:198755   3rd Qu.:1.840   3rd Qu.:15.09   3rd Qu.:13.76  \n",
            " Max.   :614497   Max.   :2.420   Max.   :16.78   Max.   :15.07  \n",
            "  ln_channel_2   public_holidays   events_ecom     sunshine_hours \n",
            " Min.   : 9.92   Min.   :0.0000   Min.   :0.0000   Min.   : 0.00  \n",
            " 1st Qu.:10.87   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:15.22  \n",
            " Median :11.61   Median :0.0000   Median :0.0000   Median :28.75  \n",
            " Mean   :11.57   Mean   :0.1541   Mean   :0.1429   Mean   :31.35  \n",
            " 3rd Qu.:12.20   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:48.32  \n",
            " Max.   :13.33   Max.   :1.0000   Max.   :1.0000   Max.   :70.32  \n",
            " special_event   \n",
            " Min.   :0.0000  \n",
            " 1st Qu.:0.0000  \n",
            " Median :0.0000  \n",
            " Mean   :0.2218  \n",
            " 3rd Qu.:0.0000  \n",
            " Max.   :1.0000  \n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<rpy2.robjects.vectors.StrMatrix object at 0x7fc11d964340> [RTYPES.STRSXP]\n",
              "R classes: ('table',)\n",
              "['Min.   :..., '1st Qu.:..., 'Median :..., 'Mean   :..., ..., 'Median :..., 'Mean   :..., '3rd Qu.:..., 'Max.   :...]"
            ],
            "text/html": [
              "\n",
              "        <span>StrMatrix with 78 elements.</span>\n",
              "        <table>\n",
              "        <tbody>\n",
              "          <tr>\n",
              "          \n",
              "            <td>\n",
              "            'Min.   :...\n",
              "            </td>\n",
              "          \n",
              "            <td>\n",
              "            '1st Qu.:...\n",
              "            </td>\n",
              "          \n",
              "            <td>\n",
              "            'Median :...\n",
              "            </td>\n",
              "          \n",
              "            <td>\n",
              "            ...\n",
              "            </td>\n",
              "          \n",
              "            <td>\n",
              "            'Mean   :...\n",
              "            </td>\n",
              "          \n",
              "            <td>\n",
              "            '3rd Qu.:...\n",
              "            </td>\n",
              "          \n",
              "            <td>\n",
              "            'Max.   :...\n",
              "            </td>\n",
              "          \n",
              "          </tr>\n",
              "        </tbody>\n",
              "        </table>\n",
              "        "
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9CXVris8VfIX"
      },
      "source": [
        "**2. DATA**\n",
        "\n",
        "We use a fictive dataset inspired by a real data case. The sample data contains five years. We concentrate on only the last 3 years with 173 weeks for further modeling since a new ad spend strategy has been implemented after the first two years (see more in **3. Modeling approach**).\n",
        "\n",
        "**Media Variables**\n",
        "\n",
        "- Media Spending (channel_1 + channel_2): spending of separate media channels\n",
        "\n",
        "**Brand Equity Variable**\n",
        "- Ad Awareness (ad_awareness): measures the awareness of an ad in % from ranging from 1-100\n",
        "    \n",
        "  **Please note:** other brand mindset metrics can serve as an alternative to ad_awareness which is included in this model. For reasons of simplicity this code is written solely including the ad_awareness variable. You are free to use this code as template for running the model for your own brand equity metrics.\n",
        "\n",
        "**Control Variables**\n",
        "- Special event dummy (special_event): Dummy for particular retail event\n",
        "- Public Holidays (public_holidays): Dummy coded for official public holidays\n",
        "- Retail Events (events_ecom): Dummy coded for, e.g., Black Friday\n",
        "- Weather (sunshine_hours): Different average sunshine hours for different months capturing seasonality\n",
        "\n",
        "Next objects for the variables in the dataset are created: Typically, a log-transformation for monetary in- & output variables is used to linearize multiplicative models. Thereby, changes in ad spend and sales can be directly interepreted as elasticities."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "RVm2_EAN9HUZ"
      },
      "outputs": [],
      "source": [
        "%%R\n",
        "sales <- Final_dataset_weekly$`adj_sales`\n",
        "ln_sales <- Final_dataset_weekly$ln_sales\n",
        "ad_awareness <- Final_dataset_weekly$`adj_ad_awareness`\n",
        "ln_ad_awareness <- Final_dataset_weekly$ln_ad_awareness\n",
        "channel_1 <- Final_dataset_weekly$adj_channel_1\n",
        "ln_channel_1 <- Final_dataset_weekly$ln_channel_1\n",
        "channel_2 <- Final_dataset_weekly$adj_channel_2\n",
        "ln_channel_2 <- Final_dataset_weekly$ln_channel_2\n",
        "special_event <- Final_dataset_weekly$special_event\n",
        "sunshine_hours <- Final_dataset_weekly$sunshine_hours\n",
        "events_ecom <- Final_dataset_weekly$events_ecom\n",
        "public_holidays <- Final_dataset_weekly$public_holidays"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n6oUJJQWV3fA"
      },
      "source": [
        "**Data preparation**\n",
        "\n",
        "Since marketing comes with a certain inertia, it may take some time until ad spend ultimately affects sales. Thus, lags are created for sales and ad spend variables: The media effect on sales may lag behind the original exposure and extend several weeks; modeling a carry-over effect by including an optimal lag length can account for this inertia. In this data case the optimal lag length is 3 weeks. This is calculated through the **AIC (Akaike information criterion)** which serves as a criterion for model selection and estimates the true lag order - also other methods to define an optimal lag could be used, e.g. variable self-selection in LASSO regressions. Thus we capture that advertising may affect sales not only in the current but also in later periods. Of course, adding more lags is also possible. However, this comes at the expense of lower degrees of freedom for the estimation. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "j7vSxgzCDsEO",
        "outputId": "78d06291-e3b7-4ae5-f711-a447338f2b2a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "$selection\n",
            "AIC(n)  HQ(n)  SC(n) FPE(n) \n",
            "     3      3      1      3 \n",
            "\n",
            "$criteria\n",
            "                 1           2           3           4           5\n",
            "AIC(n) -2.90343670 -2.91361411 -2.92062449 -2.91499921 -2.91734272\n",
            "HQ(n)  -2.89245722 -2.89714490 -2.89866554 -2.88755052 -2.88440429\n",
            "SC(n)  -2.87612236 -2.87264261 -2.86599583 -2.84671338 -2.83539972\n",
            "FPE(n)  0.05483446  0.05427926  0.05390015  0.05420433  0.05407763\n",
            "\n"
          ]
        }
      ],
      "source": [
        "%%R\n",
        "library(vars)\n",
        "VARselect(ln_channel_1, lag.max = 5, type = c(\"trend\")) #3\n",
        "VARselect(ln_channel_2, lag.max = 5, type = c(\"trend\")) #3"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "CfAlw8YrCOgD"
      },
      "outputs": [],
      "source": [
        "#Then create single channels' lags\n",
        "%%R\n",
        "library(dplyr)\n",
        "Final_dataset_weekly <- Final_dataset_weekly %>%                            # Add lagged column\n",
        "  dplyr::mutate(lag1_ln_channel_1 = dplyr::lag(ln_channel_1, n = 1, default = 0)) %>% \n",
        "  as.data.frame()\n",
        "library(dplyr)\n",
        "Final_dataset_weekly <- Final_dataset_weekly %>%                            # Add lagged column\n",
        "  dplyr::mutate(lag2_ln_channel_1 = dplyr::lag(ln_channel_1, n = 2, default = 0)) %>% \n",
        "  as.data.frame()\n",
        "library(dplyr)\n",
        "Final_dataset_weekly <- Final_dataset_weekly %>%                            # Add lagged column\n",
        "  dplyr::mutate(lag3_ln_channel_1 = dplyr::lag(ln_channel_1, n = 3, default = 0)) %>% \n",
        "  as.data.frame()\n",
        "\n",
        "library(dplyr)\n",
        "Final_dataset_weekly <- Final_dataset_weekly %>%                            # Add lagged column\n",
        "  dplyr::mutate(lag1_ln_channel_2 = dplyr::lag(ln_channel_2, n = 1, default = 0)) %>% \n",
        "  as.data.frame()\n",
        "library(dplyr)\n",
        "Final_dataset_weekly <- Final_dataset_weekly %>%                            # Add lagged column\n",
        "  dplyr::mutate(lag2_ln_channel_2 = dplyr::lag(ln_channel_2, n = 2, default = 0)) %>% \n",
        "  as.data.frame()\n",
        "library(dplyr)\n",
        "Final_dataset_weekly <- Final_dataset_weekly %>%                            # Add lagged column\n",
        "  dplyr::mutate(lag3_ln_channel_2 = dplyr::lag(ln_channel_2, n = 3, default = 0)) %>% \n",
        "  as.data.frame()\n",
        "\n",
        "#Integrate the lag variables into the dataframe\n",
        "lag1_ln_channel_1 <- Final_dataset_weekly$lag1_ln_channel_1\n",
        "lag2_ln_channel_1 <- Final_dataset_weekly$lag2_ln_channel_1\n",
        "lag3_ln_channel_1 <- Final_dataset_weekly$lag3_ln_channel_1\n",
        "lag1_ln_channel_2 <- Final_dataset_weekly$lag1_ln_channel_2\n",
        "lag2_ln_channel_2 <- Final_dataset_weekly$lag2_ln_channel_2\n",
        "lag3_ln_channel_2 <- Final_dataset_weekly$lag3_ln_channel_2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Oi7OmdejWgx5"
      },
      "source": [
        "**3. MODELING APPROACH**\n",
        "\n",
        "Since different media channels are intertwined and work interactively (synergetic effect), we recommend applying a multiplicative model structure (Tellis, 2016).\n",
        "It is also useful when the amplitude of both the seasonal and irregular variations increase as the level of the trend rises. \n",
        "\n",
        "An additional requirement is that the share of ad spend of each included channel is substantial: In this case, the data is shortened since no substantial ad spend for one particular channel has been reached. Please note depending on the dataset and marekting strategy individual assessment for appropriate thresholds is needed. \n",
        "The single channels' ad spend should not be too heavily correlated with other included channels either to be able to disentangle their effect sizes. Otherwise, we advise combining the ad spend of the correlated channels."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4A3Oaeza-BjB",
        "outputId": "0ecfc5fb-ddb2-4cb0-8a0f-2dcf3606aad7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "      date     adj_ad_awareness   adj_sales        adj_channel_1    \n",
            " Min.   : 94   Min.   : 1.726   Min.   : 1163035   Min.   :     15  \n",
            " 1st Qu.:137   1st Qu.: 4.398   1st Qu.: 2009185   1st Qu.:  44205  \n",
            " Median :180   Median : 5.463   Median : 2889856   Median : 372593  \n",
            " Mean   :180   Mean   : 5.575   Mean   : 3466210   Mean   : 734789  \n",
            " 3rd Qu.:223   3rd Qu.: 6.514   3rd Qu.: 3990831   3rd Qu.:1060389  \n",
            " Max.   :266   Max.   :11.191   Max.   :19402328   Max.   :3505168  \n",
            " adj_channel_2    ln_ad_awareness    ln_sales      ln_channel_1  \n",
            " Min.   : 36789   Min.   :0.550   Min.   :13.97   Min.   : 2.70  \n",
            " 1st Qu.: 98200   1st Qu.:1.480   1st Qu.:14.51   1st Qu.:10.70  \n",
            " Median :173144   Median :1.700   Median :14.88   Median :12.83  \n",
            " Mean   :186054   Mean   :1.674   Mean   :14.90   Mean   :12.06  \n",
            " 3rd Qu.:232587   3rd Qu.:1.870   3rd Qu.:15.20   3rd Qu.:13.87  \n",
            " Max.   :614497   Max.   :2.420   Max.   :16.78   Max.   :15.07  \n",
            "  ln_channel_2   public_holidays   events_ecom     sunshine_hours \n",
            " Min.   :10.51   Min.   :0.0000   Min.   :0.0000   Min.   : 0.00  \n",
            " 1st Qu.:11.49   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:13.37  \n",
            " Median :12.06   Median :0.0000   Median :0.0000   Median :30.32  \n",
            " Mean   :11.96   Mean   :0.1618   Mean   :0.1445   Mean   :32.15  \n",
            " 3rd Qu.:12.36   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:50.04  \n",
            " Max.   :13.33   Max.   :1.0000   Max.   :1.0000   Max.   :70.32  \n",
            " special_event   lag1_ln_channel_1 lag2_ln_channel_1 lag3_ln_channel_1\n",
            " Min.   :0.000   Min.   : 2.70     Min.   : 2.70     Min.   : 2.70    \n",
            " 1st Qu.:0.000   1st Qu.:10.74     1st Qu.:10.83     1st Qu.:10.85    \n",
            " Median :0.000   Median :12.89     Median :12.93     Median :12.93    \n",
            " Mean   :0.341   Mean   :12.08     Mean   :12.10     Mean   :12.12    \n",
            " 3rd Qu.:1.000   3rd Qu.:13.87     3rd Qu.:13.88     3rd Qu.:13.88    \n",
            " Max.   :1.000   Max.   :15.07     Max.   :15.07     Max.   :15.07    \n",
            " lag1_ln_channel_2 lag2_ln_channel_2 lag3_ln_channel_2\n",
            " Min.   :10.51     Min.   :10.51     Min.   :10.51    \n",
            " 1st Qu.:11.49     1st Qu.:11.49     1st Qu.:11.49    \n",
            " Median :12.05     Median :12.05     Median :12.05    \n",
            " Mean   :11.96     Mean   :11.96     Mean   :11.96    \n",
            " 3rd Qu.:12.35     3rd Qu.:12.35     3rd Qu.:12.35    \n",
            " Max.   :13.33     Max.   :13.33     Max.   :13.33    \n"
          ]
        }
      ],
      "source": [
        "%%R\n",
        "Final_dataset_weekly <- Final_dataset_weekly[-c(1:93),]\n",
        "#inspect shorter dataset\n",
        "summary(Final_dataset_weekly)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mTC5FgyIW0dP"
      },
      "source": [
        "**Marketing Mix Models**\n",
        "\n",
        "The model's main purpose is to capture the direct short-term and indirect long-term effect of ad spend on sales. By integrating ad awareness as appropriate measure for brand equity in this case, long-term effects can be assessed. For other cases, other brand equity metrics appear more suitable; this can be tested with correlation analysis for potential brand equity metrics first. \n",
        "Thus, this core question is addressed: What impact does my ad spend have ultimately, and how does it impact sales?\n",
        "\n",
        "See the full model conceptualized in the following; it builds on work from Bruce et al. (2012):\n",
        "\n",
        "![Bild_code_Jupyter.PNG](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DUNtu4W8IUuL"
      },
      "source": [
        "To define this model, a simple multiplicative regression, that is sliced into two separate models is applied: one model measuring the direct effect of ad spend on brand equity **(Model 2)**, i.e., the indirect effect on sales, and one measuring the direct effect of ad spend and brand equity on sales **(Model 3)**. These two models are compared against a simple benchmark model, which only captures the direct effect of ad spend on sales **(Model 1)**, resembling short-term oriented MMMs:\n",
        "\n",
        "\n",
        "*   **Model 1:** Sales measured by current ad spend, previous ad spend and covariates\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        "![image.png](data:image/png;base64,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)![image.png]()\n",
        "\n",
        "*   **Model 2:** Brand Equity measured by current ad spend, previous ad spend and covariates\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        "*   **Model 3:** Sales measured by current ad spend, previous ad spend, ad awareness and covariates (extended version of Model 1)\n",
        "![image.png](data:image/png;base64,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)\n",
        "\n",
        "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAhkAAAF9CAYAAACpl3paAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAE/USURBVHhe7d0NfBXVmT/wA4Q3TZQXCS8iCLQEtY1FeauyXfgQtWpBqogU0XarsPwtVk2hS9eKgrVlVxqLsi4Lut22qIjYIrRaJXykrSgCVo1VASuIRV6CCBiUtxD+93dyHnIymTkzN7k3uS+/bzvOmblzZ+ZeJjPPPeeZM81OxCgiIiKiBGtuxkREREQJxSCDiIiIkoJBBhERESUFgwwiIiJKCgYZRERElBQMMoiIiCgpGGQQERFRUjDIICIioqRgkEFERERJ4ezx8/t3/17t2H1Ql/v27qhmFY/Q5YnTl6mKg0d1efKEgWrYkF5q05Y96u6SF/W8vNxWauHs0bo8f9E6tXrtB7o8sqhAXT/6fF0eN2WJHkPJjMtVt/y82HJbY8uv1/O65ueqB2Zcoct3zHpW7Syv3o/xowvVqKJ+akd5hSqe9ZyeBwtnXxXbbmv12LI31YrSTXresCFnx/ZvkC7b+zyzeLgq6N1JbSjbruYseFnPs/d5zoKXYq/t0GXZ54qDR2LreEbPA9ne8tKN6vFlZXpe0Hc0ddJFakBh94R8R/b24v2OFs8bq8eJ+I5mlKxSm7fs1eV4vqMBhd1i38dQXW7od+TdXjzfkRy3ifiO7OO2Kb+jKMet33dkH7eJ+I7s4zae70iO20R8R8n8247nO7KP23i+I/u4zZTvyD5uIZ7vKOwaEc93ZB+3Tfkd2duL5zuS7UFDv6Mo11G/7ygvt6X65Zxr9LwwziBjzOTFatHcMWaKiIiIst372/aq8/p2NlNuzuYSRDBEREREAjVvUTlrMiorq1Tl8SozRURERNnupfXbVNHQPmbKjYmfREREFJnkfEThDDKQvENERERUH84gQ7KDiYiIiAB3rUTF5hIiIiKKTG6LjcKZ+Ln2rx+qr5zHO0yIiIioWk6L5ionJ1odhXMpdEZCREREJNCxV1TOIAO9jxEREREJ6Tk0CmeQYXdvSkRERBQPJn4SERFRZHj2SVQMMoiIiCgyPFwtKnYrTkRERJEdOnRMtW/X1ky5sSaDiIiIIrMfaR/GGWTgGfZERERE9eEMMlav/cCUiIiIiOLD5hIiIiKKbOHsq0wpnDPIGFlUYEpERERESuXltjalcM4g4/rR55sSERERkVKPLXvTlMKxuYSIiIgiW1G6yZTCOYOMcVOWmBIRERFRfFiTQURERJENKOxmSuEYZBAREVFkUycNNaVwzm7F3968W/Xp2dFMERERUbbLadFc5eREq6NwLlXQu5MpJVdJyRzVtk1L3+Hii4fo1z/55BOzdA28PmrklWYqNb28Zo3eT3wGIqJ44Pwm50K/c6B45JGFJ5fDOSeRsM5UP8/Wh1x3wr4v+TegGhOnLzOlcM4gY3npRlNqHJMm/au676c/Ozn88IfT9fw7//1HauTIK5x/ZI0NB2Ym/uGFydbPTdTUSktXmlJdv/zlo6aUebZu3aJu+/6UhAdP2WrJkif199kQFQePmlI4Z5Dx+LIyU2oc1133LVVcPPXkMHPWvWrNmrU6+Pjra6+pmffMMEtWO3T4mFq+4g9mqnHNnv1TtXLlC2Yq2EUXX6z3E58nE0T93ESUOO3atVO/X7HcTNWGizDOjxdceKGZk1l+97vfqgUL/sdMNT5cY3AOzxTfvnFC7JjZaqaSLy0SP+c+OE9dcsml+kDDHxQRUTYZO/Y69dRTS3xrc1etWqWDkGuuGWPmECXX1EkXmVI4Z5DRNT/XlJreqKtG6zH+oIS3rRBlDKgO6tqlkx5QFmiDO+/cfvp9GG684XrfoAV/yKhOwvuxHMaYlj9wzJNf89598EIVH5axczJkGvsm+4Ox7Ctek20jJ8VbTRj0frTLeklVo/25Jc/FK5Gfm4gS5/Irqv/W1q17VY9taCpBEBLkj398Tv/N23//mOfl/fv3O/cIv3PF3TPuOnmuEHgN5xq8hjLOQ2+VVdeQY904B8s6MOCcYu8bptFcDiNGDNPLiKj7APZ3IMsd2H/AvOqGfbC3i8+DaWwH+48yBpQxD59P3uO3T3JNwBivyf4Hfd84z8v6ZJ3YlnyPNte/tWwXcB5H2e86EMWAwu6mFM4ZZDww4wpTanrnnnOuHr9V5u7OdP36dfrAmzRpsv7DGzhwoJ6PeXKwSr4HvuiLvjq4VqCBg+G8cwt0rQlqT7As1oNp5IUA5vXu3edkecINN+pyPJ5+eqnepzFjrtXr+OSTvboaCwfPo488oqb98N/0PqIa9JprRtc6SAHvx/JFRUX6/XDrlFv0QSvwHnw+HKSyHNa55f339XchQQ001ucmovh9/euX69qK556t3TwsTSUShHjhfPDN0aPU/n379d8sBpQxz3uBwd85/t4HDhykl+vYoaO+sHvhXOFdFueK//zP2SfPFbb7//M/1NKlT+nlcB76cmGhvuBh3a/F9h3naryGZnGck7Fvck7GOQbnI5CcPYhnH3CRxTpx3sP5D9tbsGC+XrYhsJ39+6u/12uvHatrmr7z7RvUpZeOUL169dLze/fpo7fzf//3v+ZdNab98Ad6P7A/cl7Gd2IHWfg3wnl+b+z6gPVhwOfFtsaNG2uWqoZl5d8a68Oy8m+NdXbt1lXPA5zHUR4y+Kt6Ol4byrabUgS4hTXIsWPHTxw6fCzpQ+zD4jbaE6tWrfZ9HQNewzKxA+7kPO80ypj3u2XLT87DIO+NHQi15q9b91qd+bF/HD3vV79eVGvZh+Y9fCL2D3NyH2Vb9jJ+g2wbn1HmYRoDti/zsM+YFzuRnPhox+6T8/2+G3m//TnxngsuvFDPf+fdTXoeXsf6vJ8Fr2M5+7tL9OfmwIFDwwf77y12kdV/z/br+PuUed5zhfyd47xgn1P8zhX4u8e0fZ7CIOu0zxUyD9u2l8W0dz6mMdjbxyDrkO3L4Lcfsqx9DoxnH3D+8p5XUcY873r9Bu85T7btvZ7Id2rvu2zH/v6wPSyH+fbnx/UA87C/Mg/vs6dlwLFg7zu2g2m/f2u8H8vLPCxn7099hmv+9QkTJYRz1mTMKKlpmkgniPptTz75hB5Pm/ZveiwQUSM6tts6EXHH/lF0VGy7+eaJ6u13NupEzkSI/SPr7YvT8k7TY0S1HTp00GUIijRjB1Otz4n33HXX3bosTUp4feeuPXU+S69evU2pRmN9biKqH9RW4Jez/UvX1VSChEnAecE+p9jnCllGkkq/853v6rHwTgNqWmMXQ31usGEa5xDvnS4419nbByTCxy5Wdc5F3c+MVg0fdR/QpLBly/t1zqsoY15DTJ58iylVQ80P2N8ZtoOaBz/Yvv35q69Hk/X+SlMIkk5x/vXqefbZplRN7jy67bY76nxOvB95jU3FGWRs3rLXlFJH//4XmFJ0kkm7svQFXaVkD/Laxnff1WP8A/fpU90k0BROb3e6Kbn5JXlJoPLpp7XbGhFAoXoSORuoPkU7nVdTf24icvM2mYQ1lYhBgwabUo2CggJTqobgBRdn+wIFmMYPGhvOFR1iF1TvuRQDYJ+iwmfAuQnvRfPxxIk3mVfcou5DRUWFHp/3pS/pse2rF0VPXoyH9zsMctllXzelGnL+l/0WCDoQXOLzoUkdTVC27dv/ocdRg7SGysttZUrh0uLuEnjn3Xf0+KwePfS4PpCH4B0kkTETIbhAwtCZ3Trrtj7kbJSuWqkGXDjALEFE6QS1FpJLJXeVeGtuE01+odtwkfc7n2J+FLhoIgn03HMK9LkJ78UPvgvjuA23ofsgP8pSGf6tkeg5aNCFOrcCwQUCwqDakcaycHb1jRhROIOMyROqkyZTwQMlP9fjESNG6HE88IcIqJ4LGqQ5ANH8++/XPUjxR4FsXDtZsim98frrplRj+0fVyTjdu5+lx+hXBEHUQ/MejgVpm/TnRL8jflVn6fK5ibKZ3WQSdleJ8LsjZdOm2o/qxjkSF2dpNrZ5f4hhWTSBeM+h9hAGSYtIdv/dsuXqox279XvQNOBtgggSdR/y8vL0+O2//U2PbWtffcWUmob8cLZt++ADPUaSJmp5kPSJ5NFVq1brz4Tmb3xPw4YP18sJOefLNcCGmg8EdE3FGWQMG9LLlJoWqtHwB4CMWb98gjDfGDlKj6UqTeAPCk0HiBTljwt3e2Bb3ovqI48s0ONz+p2jx00NeSTSbgfY/7lzH9B/fEVFl+h50hR09dXX1Pre/G51TZfPTZTNpMnk8ccWhTaVfPObV+vxvffOrBU8oIx5IMvIOdLb4aHfuQKBDQIP7+2WOB/hXIra0zA41+Diic9jNy/Mn/+wKblF3QfkOeAHFO7i8J4vkdfRlPDD2f53wf7h/IvgCefrnTt26vlFIy6plRPnt+9yzsc1wLtOfE/x1BBFMWfBS6YUzhlk7Civ3S6UbEjQtNvWkD+ACAy3KaFd8Lbb7zBLxgcHJBI8UZWGoELW/09DL9J/qEi2kQMd28C2EEEiuMFyOGCxD1iHJGtKbgj2sal+5eNWKWzf/iyopZDPIvuI1+Qz4/Oj2QQnKls6fW6ibIbzGX5k4G/Y1VSCCxV+mOG8YJ8D5Fxh/2jDOnFxw987/u7l79/vXHH3PbP0uQLNHPiVjGVxPsD5CLUst3wvvMtqvB/7INuSc7231gTOPfc8PUYAgmUhnn1YuPBRPU/Ol9XbKohdjJs25xCBlvy7yL7DffdV32aK2gx897gFVs7JGPvtO875v/p1deDpt077pgd8b+jqAct4g7SoNpTtMKUIzF0mvnCbyiGf21cSPcgtQX5D7MCvc5uSDPK6TKOMefYy9oDtxL7gk+tG2XvLJgbc9oNbfmL/wHq5WCRc67YkDLjdCPO9++Ad5HYl+/1+7/Fbzp4vtyphkPfje5F9xGfx3rqLAbemyjIY47Yr7DvGmOe93SlRn5sDBw4NH/zOaXKbJ/5W7fn4W8V8+1yBAecF73nP71yBAeuQv2+MsRz2wfu3LucKWRYDzinebWO+33kC75dzkGwL68N8nH+wj/ay8j1gsOdH2QcM9jkPA96Hz4ay3/L24P03CPqevcvZ8+3vAO/Dcjg3Y0AZA/YP+2m/F9PefztsH/NlHfby3n9rv3Xi+JFzvPf8HnWI5xZW56Pex0xerBbNZVe1qQY5ErGDtsme20JERPWD2gPUwMQu8Gn7TKtnX9ysrv76uWbKLW3uLiEiIqKmN6ooeiKpM8hYPK92t6VEREREUbEmg4iIiCIbN2WJKYVz5mT8aunr6rqRXzZTRERElO0m3LZULZ0/zky5OWsyVpTW7rCFiIiIKCo2lxAREVFkJTOid2XvDDKGDan9pDciIiLKbt3yq7trj8KZk1FZWaUqj1eZKSIiIsp27CeDiIiIkuLxZTXPgQnjDDImTl9mSkRERETxcQYZFQePmhIRERGRUn17dzSlcGwuISIioshmFVc/3TUKZ+Ln25t3qz49o0csRERElNlyWjRXOTnR6iicSxX07mRKRERERErdMetZUwrnDDJWr91qSkRERERK7Sw/aErhnM0lYyYvVovmjjFTDVNZeUzt3/+pqqj4TB2vOq5OxIbWrZgSkumOHK1SVbFYtkXz5qpzfnvVtu0pKienpXmViJIF59zPP/tMHTr0uaqKnW+PVVYqFXy6p0zRrFnsHJujmsfOuaeempuUc248zy5JepBx8GCFKi//WB0+cky9+uZutb5st9r36VH1yYEjat/+w4qHfOZqFhvat2ujOpzeWrU/rZX6yrmd1MUXdFEtW7ZUXbucofLyTqtekIgSBufcTw/sU8ePx37MeU7vmG4WuwhRZvL798V0ixYtVN5p7RJ2zn1p/TZVNLSPmXJzBhn/MvW36r/vG2Wm4vPZZwfVrt171NZ/HFC//t1G9e77+8wrlO3O6dNe3fjNfqp7l1x1VvcuOtomoobBOffA/k9UVVWVHohsqNlAwNGufccGn3PjSfx0Bhn17VZ89+5ytbt8n/qfxX9T68rKzVyi2gYV5qubx56rzux6hsrPZ5IxUX198snH6vNYkMHggsIg0MjNO021jwUb9fX+tr3qvL6dzZRbQoMMrOqDbdvVO5t3q/9Y+Fd16PBx8wqRv7ZtWqipN/VXX+7XRZ3dszurconigHPunvJd6siRwzrA4N8PhcExg1qN1q3bqE75Xep1zMSTk+Gs75hRssqUokGAsWPXPnXPQ+sZYFAkOE7u/a8N6h879urjh4iiQ4Bx+PAh5lpQZDhOcLwgIRjHT7I5g4zNW/aaUrjy8j2x5T9Wt9+3xswhiu4HP3tFvbVxl25qI6Jw+/btVUePHjFTRPFBsIEaMDS1JVNC7iFFwtFHOz9W9/33ejOHKH5zHn1dbd/xsT6eiCgY/kYOVnyq7yAhqi80sX12sCLuc+7ieWNNKZwzyBg/utCU3HbsLFePLHmHTSTUIDh+/nfpu/p4IqJg+/d9wiYSajBpOsHxlCzOIGNUUT9TClYRi6Y/2lXBu0goIXAcbd7yib7Xn4jqwjkXFwaiRDl+vDKuc+78RetMKZwzyKg4GN7et3v3x/rXJ1GiPPns39WOnXvMFBHZPv10v0IPnkSJhA7colq99gNTCucMMiZOf8aU/KHb2iNHj7GjLUooHE/Hjh3TxxcR1cDfRBXzMCgJkN+TjHNugxI/cQvMG+8mry2HsheaTXB8EVEN/E0wD4OSQW5rjWJkUYEphWtQkPHxxwfUmtc+MlNEiYNn3KDXWCKqgQeesVdPSpaod5lcP/p8UwrnDDIWzr7KlPwdrazUDzsjSjQcV0ePsrmEyIYnWBMly/HKxB9fziAjL7e1Kflrrqr001SJEg3HVU4LM0FEWiUe106UJFETisdNWWJK4ZxBxmPL3jQlf61bNdePaydKNBxXbVozyiCq5cQJ3r5KSYHjKhnHljPIWFG6yZSC8XCnZOBxReSPiZ+UDMk6rhqU+ElERETZZWbxcFMK5wwyBhR2MyUiIsomBQUFenjkkUfMnPi89tpr+v2ZQD4Lhn/84x963k033aSn77nnHj0dr0suuUT94Q9/MFPppaB3J1MK5wwypk4aakpERETRIDAZP368mSIbghQEJx9++KGZk35Wr91qSuHYXEJERBSnRx99VG3atKneNRnpbP6i6E9cdwYZd8x61pSIiCibeZsMUN0v0xgELrr333+/mapudrEvxKjlsN/nvUhjGvPRHCFNEhiwfdkm1iHLybKA5geZh8FLahFcy4C9XWzTT1Bzib1fMmDfAeOioiJdhuLiYv26iLp/6cQZZOwsj+8Z80RElPlwofRW9wddjG24ANsBCDzxxBMngwTbSy+9pAfo0aOHuvDCC3UZsA68T2A5bB8XbZu9T94LvMCFXPIsAPsi2wV8zqhNPwh+7P0SeL+9DT9R9y8VdM3PNaVwbC4hIqK4DB06VDcVYPjWt76l5+FijIshAolp06bpeSBNCriIygVY3osBcFGXX/u2kpISvczKlSvNnBryfuwLYPuyvGxf9gmmT5+ux7IMBtl3NH0A9kECDKxDlkOQE4UEUI8//rh+X2lpqZ6G8vJyHSjZ82RfIMr+pYoHZlxhSuFCEj8vMiUiIqJqt9xyiykpNXLkSFNye/31102p5s4VuznAfh1wYb/yyivNVG1y8YWzzjpLj+3l+/fvr8cCgYbUvEgTBQYJetasWaPHsg9Y180336zLMHv2bFNyk+AAwQTW71cz4Sfq/qUjZ5AxoLC7KREREVXLz883pcTZvn27KVVz1R50757Ya5Nc4BvKzsdIpETtX6LMKFllSuGcQcamLXtMiYiIqOEQPMgvfnvABboxSFOGd2gouzlImlrsppGokrV/ibR5y15TCucMMu4uedGUiIiIounatasp1ZAmDPwql06ocGGWX/5+ORmJgiYVqRl5+OGH9RjkbhUJcOx9tDshk3wJl127dpmSOtnU8vzzz+uxTZp3bFH3Lx0x8ZOIiJIGF0ncsYE8BUnSlLwDuWsD8+27R5Lh9ttv12MkdmLbGKQZQu5usfcRSZze5Vy6dOliSjU5J/adNHYQIuR7QE5GlP1LFeNHF5pSOAYZRESUUEjAlIu1DXdJ2EmbgOnGuHsC+4SmCC80Rdi1C9gX7777vc8LAQruDLHhffJ516+v6cDKuxxE3b9UMKqonymFa3bC8WzXysoqVXm8ykzV9eG2LeqaKXWrg4gS4el5l6kePXubKSLCOZcomaKcc8v3fqZ6dDvdTLmxJoOIiIgiK571nCmFcwYZcxbU9HpGREREFA9nkLGhbIcpEREREcWHzSVEREQU2cLZV5lSOGeQMbIo/Z8AR0RERImTl9valMI5g4zrR59vSkRERERKPbbsTVMKx+YSIiIiimxFafRuzp1BxrgpS0wpfV3wpW7qrRduPTk8OPMb5pVo5H3//r1/NnMyx1+WTqzXd0JE1BjQE6b0fokB3WwDuiW35yej223ZNsZUfxlfk/Gday8wpWr9z6vbpz4REaUeb/Agz/dAd9y2RD+VFUFM1Me0Z6MBhd1MKVzGBxkSVJS9W91vfLvT2jDXhIgoDcizO9A1N7rXRpffds0CuufGfHkgGTWOqZPqdhkfxNmt+Nubd6s+PTuaqbpSvVtxBBPTb/maLn+7+Gk16wcjVM8z2+mA4/rbntLzbWg2GP7VXmaq+j2/KrlGl594pkz99L/+pMt+Hpt7rSo8p+YBOfDlSx8ypdr7MvvhP58sg9/+oJlHti2C1of9nHvPlTqAEvaygOaeb11V81Ab7MPkCYP0e158Zav6/t2/N6+kDnYrTlRbJnUrjmDBW1sgjzT3ew0QbMjj1G2u98lrNjxh1X54GWpIVq5cqcve1wDPMpHnq6DJxn5gmv1aJohyzs1p0Vzl5ESro3AuVdC7kymlpyuG99Xj/Z8eVn/92w615cN9etobDIA3wADvRT6IX4AByHfwYwcYgPf+/pc3mKnqAMJv21gfgg8vLGsHGIB8C+ENMAD74H0PEVFjwGPd/YKIhuRARF0nnmjqDSIQNEi+h4s3wAA8NTXVnpKabBOnLzOlcM4gY3npRlNKT3Lhf/3tnXr8f0/9VY/Bm8gpAca2j/brWgAM0sQSpseZ7fQYNQLyXuGXMOq3DdSwSDMOahgAtSfe5X4w8WI9tvmtDwGEBCSXW8GWLId9JSJqCtOnT9djae7AIE8rRa0AnjqKeZKDIc0lyNEoLS3V80DeD2HrBAQiCArAXg4QPCAXA00veE1ge9JMIwEGnpaK98lTU7HO+gZH6aji4FFTCucMMh5fVmZK6Ucu2CDBBWozcEGGiwZUH7xgLzvj56tMKTbfp0nFz4GKw3qMQEXu1pCLuV8TS9A2Bvc/SwcGUsOA2gesD4METBLQ2BCMiGdf3GxK1ez1zV+0To8BzSMIOoiIGpN9sUYCp9whIs0ga9as0eN4RF3n66+/rscIXvBodSHBhj3Py37c+vjx4/X6Qd6bao9jTxUZm/gpTSWA5gS5WKPGADD2a3qoj2/8y29MqZoEGxjsACZIPBd7vyaOd/++x5Qyz4EDB9RvfvNrM0WUfXD8l70ZvfOjdOdtjkiERK1Tai6EBBsScGSLmcXDTSmcM8jo2zs46TPV+eVIeHlvb20IqbnAYDezeHMh4Jwv1M51kcBhV3mFHgskZ9rrlSGbDB40QE2aeJP685+Dk26JMhWO+2lTi9XgwQPUQw/NNXMzhzQ7eIeGSMY6xYUXXlhrndKcA0gYzRbx5Gs6g4xZxSNMKb3YeRC488J7kZYmE7m91e4iFXegCCR0hkFtiNRayHbRBCKBxul5dWseJOcC7I6w/vin93STjtRs2AGKdJwVZZ9s9vq82/WrFUk127Z9oMdjr42WhEuUKVCLN2nizXoMP5w2VY/THZoV5OL88MMP6zEgqRI1AvXpWCvqOvv376/HqNlA/oXwLtelS90fqXYHYJJ/gTtSZLvbt2/X42ywoSz6Z83I5hLJt8DFFRdZr5c3VFed4SIrzRmSCIlmFAkaotSGYP0SUPjlUEjSqQ3bleUk4RTrkH19zuRV2PsiAcHPF8bfXinr89tuuqg+4WZXBjdlNxzvEmRnmttvv12PkTApF25p0qjvnRpR1omaCEkGtXM3XNvGHSsIQpCvIQEF5nnfO3LkSD3OBnMWvGxK4ZxBxoySmgTFdIGaBcm78LvAg52MKbkbSIT03nGB5oooUHNhJ18KzPPrfwK1KzZs104Axf75bRu1MH5BUxisz7t/mE63xM9sa5um7IWmkeXLnzFTmQcXbG9+A6AJor4JlFHXidqKadOmmaka9nJ2MGJDzYXffNyBgvdQXc7OuMZMXqwWzR1jpupK9c64UglqTKZbnWfVJ1jINuiMC78UbD17nq02bnrPTBFlHgQXqMWQZhIbLoREyRSlM67/d+dy9cs5V5spt4y9u4QyE6qPf3LvLDNFlFlwfAcFGESpYuHs0aYUzhlkTJ4w0JSIUsd9993LZhPKOAgskNwZFGB87WuZ9yRoynzOIGPYkPRKDkxluINF7m5hU0nDjR0b3IxHlI4eejA4DwPNhEueqp3LRdRU5iyo7jU1CmeQscPTbwNRYxs16ipTqg3VypnYbwBlJwQXqKHzc/rpp6v/vH+OHhOlgg1l0X8oO4OM4lnPmRJR01iwMPjphqhaztRb/Ch7SB5GkClTvh8YbBOlOiZ+UkrDr7cnlyw1U3WhsyKidFXd/0tNh1teCC5+fNcMM0WUGsaPrtuTdRAGGZTycKINSnpDt8tsNqF0dd9P7g3sMh95GK6aPKKmMqqonymFcwYZi+eNNSWipuVKesOJms0mlG7QuVxQgMw8DMoUrMmgtICTbdCvOqlyJkoXCIrx4LMgyczDeO2113Qnd9KFtkxjkGdypKrG2Fd8L1h/fZ6hEgQPT8M60T15smAb9e2SPV7jpiwxpXDOIMN+cBhRU7vhhhtV4fn+j85HlTMfCU/pICwPA8d5MvMw5AFiV18drcdGSn0ILu6//34zlVqcQcaKUnZhS6lliSMJFL8M2WxCqS4sD+P+OSVmKvFQE4AHiAGe9UF1Pfroo7r79kTWZGQzNpdQWsFJGG3VfthsQqkuLA9jwcJHkpqHsWLFCj0eOnSoHvuR5gi/JgO7KUEej45Bmi7kdXuwmzXwPszDcnbTBwa/i7q9vniaGuQ9eDy7vQ7ZhjRfYPCu1/6MQj4r3me/F4P9yHhhv+73uYS9nGtZ73L2d4p9k8BRnkDrt0+JVDLjclMK5wwyhg0525SIUsett97mbDbJ5KdXUvoKy8O488d3Jb3r8DVr1ujxV7/6VT32wiPMbU888YTvhQ/z5RHnCFjw9FIsJxc7m3edgOXGjx9vpqphnbiAC1zs7fVhe973hMHj3O11YBu4KNtNC1gvthUF3udtlsA2EDAJXORt2KZfU4Z3OfB+3wgm/JbDd2pvs7F1y88zpXDOIGPyhEGmRJRaXM0m6NiIzSaUSqLkYSB4TjYJDPr376/HXggY0FSAQR5pjgufX5IlHquO5dC8gNexHOCx55hvP3bd7/0lJSUntyVeeeUVPbabdfBYdlmuR48eel5UWN77XnwHsu/yGf2CoyB+n+/111/XYztIkm1geS87QJD14fsA+R5BAg77O5DH1EtuDR4/LzVT8u+X7KawePI12VxCaQnNJkEnZZzI0RsoUapoyjwM4Xeh97J/RdvlsrIyU6qGi9mFF15oppSuyZCLIODXt6vWARd8+0IoF3shF20sd/PNNU2gs2fPNqVorrvuOlOqXhfY+z5wYHwPAcV+4rMC1iHrFBIkYTnZBpaXwEDk5+ebUnWtBL6vwsLCWt8hSPCDmhAsg0FqReIJjBItnnxNZ5ARz20qRI0NuRlBzSZoMmGzCaUC5GA0ZR6GKC8vN6WGkwutTXIZ/JpHvLwX52Tp2rWrKSVG9+7dTalh8P1JzYWQYCOe3JMogWNTY00GpbX77/+5KdXleh4EUWMoe/NNXYsRpDHyMIT96zlIfQMRJBrKL2tpBrGbE6gu1ORIzYVde4HmHG/ipt20ZA9+wV5j6Nu7oymFY5BBaQ0naFezyXV8JDw1ERx/EyfdFJiHgeO2MfIwRJQLkrTzg91cgqp8l507d+qx3Qwid7LUh+SM4IJr5zlMnz7dlFKTJNQir0LyLlDb4E38tO9QEQgahHyfkmvxi1/8Qo9BaozsZNXGDjZmFY8wpXDOIGNm8XBTIkpd+DWIdm0/aDIJagsnSibUYKAmww+a+XDcNjZpppCcBy/URsjFTxIQ7TyEINIsgaDA+36It4YE+QxygbXzESRxNVXZ+SPIScE++zUf2cvJZ8MgLrvsMj2+5ZZb9Nj+XqXGSF6zyb+fHZg1NWeQUdC7kykRpS5p1w4y9tprTImocYTlYSxc8Gij5GF4SSLk9u3b9djL28SBAMOu0QiC2gtvciPumpBAISioccFdK/J+kQ5NMHaNBOAzeL8bwHLezwd2MwiCLb+7UzBPEkshyr9RIt0x61lTCtfsRIwp11H60vtq6MCeZqquD7dtUddMed5MESXW0/MuUz169jZT4ZCDEdS1OG4R5BMtqTGg9uLSS0cENpMgYbm+zSQ45zYEqu7xyxo1Grj1kcgryjl3wm1L1dL548yUm7MmY/6i9aZElPpwG2BQswmCj6Cqa6JESbU8DC/8QsavZ1S/N2VnTpQ9mPhJGSO02YRJoJRk6NEz1fIwvKQtvyGJmZTdJk+I3r+IM8jIy21lSkTpAXebBD0iG72AspMuShbkYAQ11zVlHoYX2vLR7t/Y7fiUOYYN6WVK4ZxBxsLZo02JKH0g9yKo2QQXAjabUKLhmHL1h4GmvKCO44jSzaYte0wpHJtLKOPg12LQk1qBzSaUSFHyMJB4TJQp7i550ZTCOYOMGSWrTIkovaDJxNVsEnR7IVG8cFdTqudhEDUVZ5CxecteUyJKP65bVpGbwWYTaigEq0HPyEmlPAyiptLg5pJmZkyUSIk4rnByf9LxSPhp035gSkTxC8vDQJCbjDwMR9dGWQv9f6CnyygPDMNzQaT3zGSQLsO9zx9JdfEcV4vnjTWlcM4gY/xod3/1R45Wqfbt2pgposTBcXX4yHEzVX9oMgl6ABW6G2ezCdVHlDyMoOa6BmnWLPZ//rSz4WIe5cmvjUW6BLefN5IOcFwl49hyBhmjivqZkr9mzVuoDqe3NlNEiYPj6kSzFmaqYZY89bQp1YVfosjRIIpHU+VhtMzJMSWqL/vpp8lgd3iWbrUZLSIeX/MXrTOlcM4go+LgEVPyd+oprVX709iXBiUejquqKjPRQGg2CcrPwC/RSRNrHlZEFKYp8zByclqaUnqQpoNLLrlE9zAqzRQYpGnDnud3UUZ/HvYy9sO/UC4uLjZTStdoyNNJ7eWljP1wNZfIE05l8OtLBOuwl7Gfhirkaay//e1v9ThdNI9Yk7F6bfQfZs4gY+J0/z8kkZt7qhpY2NlMESUOjqtOHRN3osYthEHt42g2CepEiciGY6Up8jBEm7ZtTSm94Fc9nkpq++53v6sv0jYEDHZ357iA209zBTyVNZ6OxOzHrMsD4vxgX+QJpwLbtreFAMP7JFi8xxtoyKPqvetLdaeckmtKidOgxM+2bU9Rg89nkEGJN6gwX7Vrd5qZSowlriTQqcVsNiEnqfVq9DwMC8656ZqTUVJSopsoMAZcrNGsgHn2k0blia2occBFGg9zk+YNWQ4Xf9SE4JHpsj7A63h6q5e8337Eus2uHcE6sKw88VW2hUECDLxmL4P9tJNO8/PzTUmlzTNicFydcuqpZsptZFH0pNkGBRmoumvVMked06e9mUPUcDieWrdqmfCqYfQCGtRJF5tNKAzyMIICUSQXN0Z/GPibaN4iMblKjQ25ENClSxc9BnmOCvIYEEzY1q+vfkAnLuzSNGEneJaVlZmSm99j1r1eeeUVPcaj7e3HrEtwgnkyH1ArI7Uw9jLCLu/atcuUUhuOq6jn3OtHR6+tcwYZC2eHR+VdunRS14/qa6aIGg7HU7t27cxUYuHXpqvZJKitnbJbWB4GHsyXrDwMr9NPb6+aN2/Q78NG5w0gEmHnzp2m5Na1a1dTajipuRASbEjAka5wPOXlJef4dR6pebnhd47k5uap3j3a6eptoobCcXRW1zx1xhkdzJzEczWbuH6tUnaKkocR9KycZMA5t1mz9AoyGkKaVLxDUNNHMtm1Gxjs4Mluckk7zZqp006LHmSMm7LElMI5j9THlkXrEbFb13x189hzVds26VmNR6kBx893x5yjevZI3C8PP7ggoEbDD5pN+KRWEgg4x157TZPmYfhp176DbkPP5I65Bg6sfpw48h0kr8G+M0RyIOzml/qSu0Ek/wIwlm1hu37bXrly5clAY/v27XoMdn5GIvYvWXD84Dhq376jmZN4ziBjRWm0+4hPPTVXdevSUf3bxAvMHKL4Tb2pv+rcuYM+npINuRlBzSaoFmezCUnAGRRgNFYehh/8jZyam5d2zSbxQA6HXMClWUJuV7VzJ2zI2cAdIPFCrYhsC+vAtiT/A/OxL/b+yDIYJBl05MiRegzl5eWmVF37kapw/KBmLJnn3IQdoZ0756svn9NF/fxH1REhUTxw3JzzhU6qe7fGi/rRn0EQNJtQdnvoQXceBjp5a6w8DD8dOpyhWrduk9G1GagpQHOJDYmc9m2luIgj6Ggov21hGvMFyn7bwh0pdjAhd8h415dKcNy0atVatY8dR/GaWTzclMI1i20o8Aid/fCf1e03XWSmwmFVH2zbrt7auEvNefR1dehww7uFpsyGJhLUYHzh7A7qnILeuuquMeGXalDX4qgGdz37hDIXgovrxo4xU7VVJ3o+2iTNJF445+4p36WOHDmsqqqqGv3vh/yh3ww08+D2WrmrJlXgmEENRsuWrVTnLt3qdczktGiucnKi1VE4g4zKyipVeTz+bhfLy/eoj3Z+rB5Z8o5aV1ZTbURkQ5IncjDy89urs85Mbh5GEFSFDx40IDDZ8/kXSgOffUKZCccCjomgZpI777xL/fiuGWYqNezbt1cdrPg0o2s10gXyMaSpBcmhqQZBxSmn5qqOHTuZOfF7af02VTS0j5lyS0qDXn5+J9X3C2epW288X/3kjsHsR4NqwfGA4+J7EwpVv749mizAALn9MAiS/ih7ILBwdbiF2otbv++fNNyUkLjXIXbRaNGiRUbnaaSD559/Xo/tTsJSAY4L9IWB46QhAQbMX1Tdh0kUzpqMW2f8Xt1/59fNVP1UxKLr3bs/VkeOHlNr/rpLvfHOHrXv06PqkwNH1L79hxXj7syFSjg8TRUPO8OzSNBV+IAvdVItW+aoTmd0jB3oqRN8IgcjqGtxdEke9OwTyiw/uXeWuu8+/9tVcVfSq+s2NGkeRhQ453766X5Vdfx4nZoNTLNJJXMF/fu2aJETO27bqdy8xPSiPOG2pWrp/HFmys0ZZIyZvFgtmuvfLhmvyspj6tChz9X2HXtjERU2fFy1ac1bXjPdkaNV6ljlCdW2TWuVl3eq7io8FR/yFNZs8uqrG5L6TApqeggygxJ+UykPIyqccz///DP1+WcHVVXsNH+8spLNKdkgFmS0aI7eO3N0N/ToKjzR59xp9/1RPTTrG2bKrdGCDKJUh06XLru0pttiG37Fbtz0npmiTJOOeRhETSWexE/nUlMnRb+zhCjdIcEz6JcqLkLspCszRcnDYIBBVD9JubuEKF2x2ST7uG5jTpc8DKLGNGvui+qnP4zW6ZmzJmNDWU03qUTZABeToCe1wtiAvhMoPSEPIyjAkDuPGGAQ1bZ5y15TCucMMuYseNmUiLIHqsddzSZBFyVKL/i3nDa1uptqP+gynH2kEDVMtMwNoizjumUV1etlb0Z7eCClprA8DNy2HPQQPaJsN350oSmFY5BB5ANV5K4uxSdO4rNN0hke3Y67ifwgD+P+OanVkRJRKhlV1M+UwjmDjMXzxpoSUfZBk0lQdTlqMthskp7w78Y8DKL621FeYUrheHcJkQOq07t09n9KIS5EuPMAv3wpPSA4vPTSEYHNJEj6ZTMJkVs8PX6GJH6+ZEpE2an6l61/foa061N6wL8XmrmYh0HUeJxBxoayHaZElL1w8QnqGwPt+kHPPKHUgjyMoIRd/PsyD4Mo8Zj4SRTBEkcSKG6DDOq8i1JDWB7G/ff/nHkYRBEtnB39GT7OIGNkUYEpEWU35F0EddLFZpPUhtoL1GIEYX8YRPHJy21tSuGY+EkUh8GDBwRWueOW16BOvKhpIABEomfQvxlyMFw9vBJRXU+ueEt9e0x/M+XG5hKiOLiaTfCYcDabpBY0ZbnyMFCLQUTxWVG6yZTCOYOMcVOWmBIRAZpNgu5AwK9mPqk1dSAHIygpF/kXCxc8yjwMoiRjTUaWOO/cfqptm5Ynh5fXrDGvJEai1jlq5JW19nPr1i3mFX/J+CxhUL0edLfJ8uXP6IGaVpQ8DD5Nl6h+hg2J3jcQg4wsgAvxTTffrA4dPqaHVatWqxEjhoVewOOB9V508cVmqn5u+/4UPZb9vO+nP1PnnpOaycf4FRwEzSbUdML6w0BNFPvDIKq/yRMGmVI4Z5BRMuNyU6J0VVIyR11yyaWquLimGh/BwKRJ/6rWr1+vAw0EIahBQG0H4GIvNQl4P2oKUBYoS4CC9yxZ8qSeh+WwvF0bIYGDbEfmYeynV69epqT0PiPYAPv9GLAdL+9+g+y7DMIu1wd+BbuaTa7jI+GbDII85mEQpQZnkNEtP8+UKF1t++ADNWz4cDNVY+6D89TYsdeZKaUm3HCjevudjTpgWLDgf/TF/Z13N6k7//1HZonqCzYGBC0IUGDLlvfVwIEDdVmsXPmCfj9qTLAuBAi3ff9WHdhgfs+z/avasE9Y3hsQALaH92L41a8XqUcfecS8Ug37vXXr1pPL4HXs6+zZP9U1IpiH7du1JQ2Fi1VQl+JoMgl6ABclD/IwgpqrmIdBlBgTpy8zpXDOIGN56UZTokzhV8sAEiiseekv+mIMvXr11gHF9o+2nxyvffUVHZBgOQk4sJwN86Brt656DAg8rrvuW7r8zW9ercd+JEhAYIB9lNoVBERSm/HtGyfoeTbsD7Yhnw3BD/YVARYCJcy7/Y5iHcgkCi5WeJhWkLHXXmNK1BjC8jDQPTzzMIgaruLgUVMK5wwyHl9WZkqUrlBrsPrFF81ULHBc8YeTv+rjgYs1LuRYV/UFf+vJi3gySFMJggUEMwiIkJ+BeajJ8CM1JTJgHbIeye+wA6tEQCdO6HbcD5pNmJ/ROKLkYbAPE6LGx8TPDIeLLH7hey+upaWlplTbxUP/STdZAGoO8N7uZ3ZXQwZ/tdZ7kDuBgAPzo0DtxpNPPqHLv/vdb/XYC7UW9n5i+4AaEQQ1CBRgkc9tifZ+A2ou0ISCmhsEKfge8H6sJ9HwzIugZhPcQhmUH0CJk+g8DO9dThhwHDUmbA/bbUxRtil5WJS9ZhZH/3HpDDL69u5oSpTO8EseF1f7hIm7TfyaDlBLgRoBLINf/qg1QKIoBtQqSGImLuoIQKLeUTL3wYdO5lvYNSs25ITYORnYPvI60ByDJhpp9kAZ+yJBCNj7jQFlzMN2cScN5uH9mAZMJ0poswmTQJMqWXkYksuDQe7IasxAA39b2DZRqino3cmUwrFbcWp0uPMDiZkIKjIJ7igJutihup7dVycekmuR+xLUTFLfrt5Rk4GmQNSACW9toATpCFiRJP2NK69Qffr00cE3IDBBoIBf/XYekczH+xDISHK1BDKA4B41iJiu/pGw5eTt3L1796nzt4NtSA0fto+aQ8lHAglW8Bmkxg/bxuez143gHK/L8qi1QEAPst+Yd/c9M3Uel7wP8B1487MoM73x9g415IIeZsqNzSXUKOzqZ5z4fv+HZ80rmQOJhUHNJvi1zWaTxKrOebm50fIwkN+EGkEkMEvTIWo27ORn1PThAo2LNe5sEpgn86XZEHD3F+ZjHRMn3nRyGW+TIO7OkpoVBDJ+t3AjuJg+/d/1xV4CHSwPCEIwSAAhd45h/+07v2wISKR/HSwvAZD4xQMlJ9+HfcN6KDvMWfCyKYVzBhkzSlaZElHDSMKpDJn4iwdV8q7aCjabJJbrWTHJ7A9DmghRA4CAwU5+RjMi2Ldpo9kOF3gE2FKLIOSOKwQnRUVFuux3izeCBrkrC39Ldg2LQA0H9k3+tiRfCvMh6M4xrFv2Q8aAQAqBCPZbaizs5iLJg8Lr2Bb2i8jLGWRs3rLXlIgoCvxyDvr1jAsiajSo4cLyMPAgu/rkYbjYfc7gFz76bsGF2HVLNqB5ATUTCK7lIp+q7NvOAc029o8DCbAAwRPmYRnUcqC2krJDXm4rUwrH5hKiBEOzSRA8QI3NJg2DPIyw/jCCmq3qC7/g8atdAgqMETig6SKsVg45DWjGAG9NRlSodZC7stCM4c0PiSLozjGs2+/OL9SsSLMNPj9qLOxka+wDamgQbCDQeP/96twNynwLZ482pXDOIGPyhNo9OVL6kWpa75DNpOvzIDiR4juyT6jxwC9oJBwGQX8OVD/Iv3AleiYyD0OaCjDglzoSH2tyL6rHUfqJQe0F3o/14GIcdPu4C+6Kkv1BoFCfTuXsO7DQ/IF9Qc0Emjmk2cO+8wvbQOAgnx/L2wEVXkdCK17HeKEjuKbsxbtLMhyCjJn33F0rG11+BdXnRJUJEGTgZBrUhozgAifhhmbLX3ZpUWDX4sjdCHr2CfmrTvS8KbCZBB2jLXnq6YQ3kwTBxZV3VFA2+sWjL6vpt3zNTLk5azJ2lFeYEmUSVJvav6ZwspRBfr0jEJF5EpTg4owy2pjt+WDfPYLARub5zfdbN/gta8Oy2AdZRmokUMZYyP5hkEQ1u0YHbetCai1k8LLfh/XGAxe8IKjuD0paJH8PPejOw0BfJY0RYMgxgzsqGGBQNtpQtsOUwjmDjOJZz5kSZRK0s0omOy7OqAZFAheqg3GvP06iqD7FrzTMR1ku1ijj9lO8JvNxsUe1qqwDVacSrADm44SMGpWgdWMdcvsfBu86BKqM8Tr2GWW0dWObaF/G8ghE0E4uy8htd1iffE47wMLnxftleTtYAeyzvC/o1sEg1Rc+/ypkuf2SokFwMW/eg2aqrmTkYQRBYIHjwe8ODyKqjYmfWQCJZ/JrHAMuyNJUgrK0q+KCLB3v4LY3NBngoosTqmSVo00XJ1kMSBjD80vQ9IBse8ByeO/OHTv1tLRZd+9+lh7jfX7rxjoQcMg+gjzp1SbZ+UhYA7zXzohHAIEeQQFt0PD00qf0WKZlXxGU4PNKezm+B3wfNgRj8v0E3TrogueaBD2UC00p6Hac3FDjg2aSxuoPg4jcxo8uNKVwDDKyAC7quJhjQGDgvY1OfsnLgEAAORwoS+KX1GQkQtC6pbMhGSQoSDQJeITUqshgQzCGeZIwF09NhsDtlEGmTS1ms4kDAgvckRMUYCC4SFZ/GETkb1RR9KZjZ5CxeN5YU6JMgV/j+LUvF0v79jXJP8AvfMk/QECAIAWd9gBqGwDL4Fc/OuFBbQW6CQcEDKgd8N5vL4LWba8Dy9Q3sLFvu5O8jmvGXKvHMi2vS62K3LaH78Sbd4Fp7A+CDQQadj5HVKjGD+qki80mbq48DHyvaCZprERPIqpWcfCIKYVjTUYWQk4F8hlwUbVvX0OzAGo1cPFFkwLmYUAugtQqICjBPDR3oOYBzRVoQsAymI+mB1mHn6B12+uw1x0vBANSQ4LPg1oKwD5Js4dNvgvMx9jb3Tluy8P+4HV8T/W9IwdV+q5mk6ALaTbDd3Lfff79YSCwQODGAIOo8U2cHv185byFdd7/rVU3f2uAmaJsh6DEdesnuaFZpF/BF81UbbhYvrpuQ6MlL6Y6fFeDBw0IbCa588671I/vmmGmiKgxTbhtqVo6f5yZcnPWZKxey7ZiokRBABHUN4bkHlBNE5IrD4MBBlF6cNZkjJm8WC2ay4c6ESXS4MEDArsWr++jyTMJgq2gZ7wgUEOND5tJiJpO+d7PVI9u0f4GnTUZw4aw6pYo0RYuCO5+2XWrZjbALb1BAQYCi8bqcIuIgnXLzzOlcM4gY/KEQaZERImCBFBXswkCjWyEPAzc0hsEt6qi63AialqPLYv+kEfeXULUBHDBDEryxF0VQc88yVRheRjo1IzPeiFKDStKq+/ai8IZZIybssSUiCiRpOo/CJ40mk3wLJegwArB2P1zSswUEaUT1mQQNRFU/eMXup9sajZhHgZReunbu6MphWOQQdSE8As9qNkEF9+gu1AyBT4f8zCI0sus4hGmFM55C+vbm3erPj2jRyxEFD80E1x2afVTcb0QgGzc9J6ZyiyorUGzUFAzCWp5gp5iS0RNJ6dFc5WTE62OwrlUQe9OpkREyYJf6kF9Y+COi0ztpIt5GETp6Y5ZtR+/4OIMMlav3WpKRJRM+MUe1GyCfIVMazbBZ2IeBlF62ll+0JTCOYOM+YvWmxIRJRMuqEFPaoWxYzOn510ETKjFCMI8DKLMwcRPohSBJhNXs0nQL/90gjyMiZOCezVFXxjsD4MotU2ddJEphXMGGV3zc02JiBoDmk2CmgmQm5HuzSaowQj6DOgJFbUYRJTaBhR2N6VwzrtLKiurVOXxKjNFRI0BPX5eF9A8ggvxq69uMFPpBTUxQUmsCKxeeGGV/nxElNre37ZXnde3s5lyY3MJUYpBk0lQTgJqAdKx2SRKHgYDDKL0cHfJi6YUzhlkzChZZUpE1JiWPPW0KdWFizVyNNIF8zCIspczyNi8Za8pEVFjqr6N078jKlys8TCxdIHu0ZmHQZSd2FxClKLQ42VQEwI6sUK346kOTTvIMfGDQGrhguBEVyJKTYvnjTWlcM7Ez9/+8R11xfC+ZoqIGhuaRfoVfNFM1YaL86vrNgR24tXUUHtx6aUjAptJUFMT9IA4IkpdCetWfFRRP1MioqaAACKok65UbjaJkofBAIMoPc1ftM6UwjmDjIqDR0yJiJoKLsiuZpOg5oimxDwMosy1em30xHNnkDFxeuqdvIiy0ZIlS02pLlzQU+luE+ZhEJFg4idRGkCzSdBtnmiSSJUntYb1h4E8DPaHQZTeRhYVmFI4BhlEaQK5GUEXaNQcNHWzCYIdPMjNlYcR9GwWIkof14+O/kPBeXfJvv2HVNu2Lc0UETU11BQMHjzATNWGJohNm99vsqYIdIUeFOggOEK34WwmIUp/Cbu7JC+3tSkRUSrAxdrVbIL8jKbAPAyi7DFuyhJTCucMMh5blt5PfCTKRLgzI6hvDFzoccdJY8L2mIdBRH6cQcaK0k2mRESpAjUCCxY+YqbqGnvtNaaUfNW1JzczD4OIfDHxkygN4SmtQZ1ZNWaziev2Wewj+8Mgyjwzi4ebUjhnkDGgsJspEVGquX9OSWCzCZ5rEtQZVqKE5WGgtoV5GESZp6B3J1MK5wwypk4aakpElGpCm03GjjGlxENwEZaHkarPVCGihlleutGUwrG5hCiNoUkiKOcBzRjJ6KQL60UzCfMwiLLT48vKTCmcM8iYOH2ZKRFRqnLVGqBJI6jZBHeF+L3mamZBYIHAJSjAYB4GEdmcQUbFwaOmRESpCs0mQU9qBW+ziQQKl11apN4sqxtQ/OnPq3WHX37BxkMPBudhINBZ8tTTzMMgynBd83NNKRybS4gyAJonXM0mqNEA1F4MHjTg5PT+/fv02PbSX/6iAwwEGrIc6DyM+/zzMCTQYYBBlPkemHGFKYVzdiu+9q8fqq+cxztMiNIBaigK+vYJbMrALa+468SGeWhusfUr+GKt21KxDJpAEJwErfvOO+9SP75rhpkiokwWT7fiziCjsrJKVR6vMlNElOpQ24BniESF2o8nrcfII4jo0vkMMxWNdx1ElNlmzX1R/fSHl5gpN2cosqFsuykRUTrABR/Jl1F94OlIa9sH/h1rBUEehrcmhIgy2+Yte00pnDPImLPgZVMionSB5MuovEEFkj6jYh4GEYVh4idRBkHCZjxdiqN5xM6zeKss+v3vN974ncBkUyLKXONHF5pSOAYZRBkCd4JceumIwFtMg9i1GUGJnX6wvXi3RUTpb1RRP1MK5wwyFs8ba0pElKpQe4FkT1cnWS77D+w3JaXedHTE5Ue2S0TZY0d5hSmFY00GUZpD8ma8wYHtzTff0GMEK0FPVHVBjQb61KjPe4ko/RTPes6UwoUkfr5kSkSUqpAXsXHTe85eP10O7K+u/fDeaRIPNLm4HphGRNnJGWRsKNthSkSU6vBgMgQb6DwrHh9+uE2P/boRD4M7SxDkvPDCKt7KSkR1sLmEKINIvxWvvroh8qPWJY/jrbei31liBxfoiKvw/PPNK0SU6eLJ13QGGfHcpkJEqQMX/ahNKJLPESWvA8EFakwYXBBRFOxWnCjDoaZi2tTiOs8tEQgcXl23QT+zJAiWQb8Y35syJXINCRFlpidXvKW+Paa/mXJjcwlRhkOAIE0ofjUPCELefvttM1Wb1FwgCEGtCAMMIlpRusmUwjmDjHFTlpgSEaU7BBgINBBweIMFPN7dhuACT1ZlcEFEDcGaDKIsg7tPkK+BIEK8um6tHtvBBR7dzuCCiLyGDYl+XnDmZIyZvFgtmhv9sdFElF5w2+q8eQ+qVatWqX/5l++qG268kYEFETnltGiucnKi1VE4g4wPdxxQ+R1PNVNEmemTA8fUP3YdVuV7D6vPD59QR45Wqsrj5sUssX3bRtW9Z/TnEWSCnBZKtWrZQrVt01x169RGndm5jepwekvzKhEFSViQwbtLKJO99d5B9fcPP1PHYsd5VdWJ2IC5zWJD4J8EZRL8MzdrFhtV/3u3zGmmWjRvps7pk6vO7Z2r5xFRXf/vzuXql3OuNlNuzlBkeelGUyLKHH//x+fq6ZW71KYPDqpDh4/HgmkJMIABRtZAPBn798YIA46DI0er1N9iwSeODxwnRFRXxcGjphTOGWQ8vix6D4BE6WBt2X71xruf6ovJ0dhA5IUaXBwff337gHr5jX1mLhHVB+8uoaxw+Mhx9fyaPeofOw+ro8cYXFC4yuMn1Ic7D+njBscPEVWbWTzclMI5g4y+vTuaElF6+9OGT9Qnnx7T+RdEUaEZbe/+Y/r4IaJqBb07mVI4Jn5SxkOVN36R1uRdEMWneeznWI+ubdVFX2lv5hBlrzfe3qGGXNDDTLmxuYQyGpL3dpQfYYBBDYLjZ/uuw0wGJYqZs+BlUwrnDDJmlKwyJaL09Ma7B5iDQQmBHI03N35qpogoCmeQsXnLXlMiSj/oB6PqhL5PkSghjlWeUO9sOWimiLJTXm4rUwrH5hLKWO99cFDnFRElCjpte/d9BhmU3RbOHm1K4ZxBxuQJA02JKL2gq/DK2AWBKNGOx44rHF9EFM4ZZAwb0suUiNILnkXCZE9KBtwGjeOLKFvFk6/pDDI2bdljSkTpBQ87wy9OokRrFvvfro8ZZFD2iidf0xlk3F3yoikRpZfPDlXpiwFR4jVTn8eOLyIKx8RPykhHjx1XKrifOaIGOKGOVbKbccpe40cXmlI4BhmUkfQ1gBUZlCSMMSibjSrqZ0rhnEHG4nljTYmIiIgIj3o/YkrhWJNBREREkU2c/owphXMGGfMXrTMlIiIiovg4g4zVaz8wJSIiIqL4sLmEiIiIIiuZcbkphXMGGcOGnG1KREREREp1y88zpXDOIGPyhEGmRERERKTUY8veNKVwbC4hIiKiyFaUbjKlcM4gY9yUJaZEREREFB/WZBAREVFkAwq7mVI4BhlEREQU2dRJQ00pnDPImFk83JSIiIiI4uMMMgp6dzIlIiIiIqXumPWsKYVzBhmr1241JSIiIiKldpYfNKVwziBj/qL1pkREREQUHyZ+EhERUWRTJ11kSuGcQUbX/FxTIiIiIsItrN1NKZwzyHhgxhWmRERERKTUpi17TCkcm0uIiIgosrtLXjSlcM4gY0bJKlMiIiIiio8zyNi8Za8pEREREcWHzSVEREQU2eJ5Y00pnDPIGD+60JSIKBU9cO+N6qZrep4cfvS9r5lX4vPcsvkNej8RkR9nkDGqqJ8pEVGqQYDxtzf+ZKaqle/apoMFIqJkmb9onSmFcwYZFQePmBIRpZL33l1/MsCY/pOl6tGnt6nZD/9FTwNqJoiIkmH12g9MKZwzyJg4/RlTIqJU1a5DZz3u1LmH+tJX/lmX95Zv12OxaMGPazWrYECgEmbP7g/rvM/LbxkGOUQETPwkSkMSWMD0W/5JN53AHXf9WtdqTJj0Ez0NuOC/+PxvzFSN2T8eowOEIAhCsG4vBBHyPoz9lln6m58x0CDKUCOLCkwpHIMMojSEWot/veMhM6V004nUInhrKHDBB79mlf2f7Daluv533g/0GNvB+zAMv+wGPe/5Zxbo8db33tBjkGXG3PAjPf3nlY/rMRFllutHn29K4ZqdiDHlOvbtP6Tatm1ppojSx+N/2GFKmQ93hCDh04YL/eWjJ5upGghCbAg8vnjOQF3rgGAkv0tP9bP/+nNgDYWQ5RDQoEbEhkAjG4y/spspEWWXnBbNVU5OtDoK51J5ua1NiYhSFS72uLDbNRRSewF2PkaiSFCDAEVqLoRsS5pwiCizjJuyxJTCOYOMx5a9aUpElEokcLAv5GhCQc2EQG0EahokHwPBgDcYiUKaWbyDQI2JzLPXjSacKMmlRJS5nEHGitJNpkREqaTvuYP0GBfydS8t12V49S81d4Qh6Ni3d6eZqg4GYMMrz+qxC96LJhH4/dKa3A80zSC4QZADEuxIJ154nx1o2NsnouzDxE+iNDRo6KiTQcD/PHDrySYKu9YC2nfsqscgy9hNKa4g4JvfmqrHdlKpNJNcdtWkWmPpBAyDncuB/SSizDKzeLgphXMGGQMKmdhElKqQiyF3e9hwN4jUWiBnwr4LBdD8Ie/b/E5wz30IEOzmF4FmEdRYAMaYloBHYNpuUiGizFHQu5MphXPeXVJZWaUqj1eZKaL0kU13l1DT4N0llK2efXGzuvrr55opNzaXEBERUWSPLyszpXDOIGPi9GWmRERERBQfZ5BRcfCoKREREREp1TU/15TCsbmEiIiIIntgxhWmFM4ZZEyddJEpEREREcXHGWQMKOxuSkRERERKzShZZUrhnEHGhrLtpkRERESk1OYte00pnDPImLPgZVMiIiIiig8TP4mIiCiyyRMGmlI4Z5CRl9vKlIiIiIiUGjaklymFcwYZC2ePNiUiIiIipXaUV5hSODaXEBERUWTFs54zpXAhiZ8vmRIRERFRfJxBxoYyPsmSiIiI6ofNJURERBTZ4nljTSmcM8gYP7rQlIiIiIji4wwyRhX1MyUiIiIipR5b9qYphWNzCREREUW2onSTKYVzBhnjpiwxJSIiIqL4sCaDiIiIIhs25GxTCscgg4iIiCKbPGGQKYVzBhklMy43JSIiIqL4OIOMbvl5pkRERESk1MTpy0wpnDPIWF660ZSIiIiIlKo4eNSUwjmDjMeXlZkSERERUXyY+ElERESRzSwebkrhnEFG394dTYmIiIhIqYLenUwpnDPImFU8wpSIiIiIlFq9dqsphWNzCWWknBamQJRoJ3h8UXabv2i9KYVzBhl3zHrWlIjSS+tWObH/NqueIEqkZs1Uq5aMMoiicAYZO8sPmhJRejmlDQKM2E9OogQ7Eftf61YMYCl75eW2MqVwbC6hjJTfsY2+GBAlQ+eOrU2JKPssnD3alMI5g4zJEwaaElF6OatLG9UyhzE0JV6L2GF19pmnmCkicnGehYcN6WVKROmlw+ktYxcDVmlT4uW0aKaPL6JsNaNklSmFcwYZm7bsMSWi9HNOn1yVw9oMSqDmscC1oBef6UTZbfOWvaYUznkGvrvkRVMiSj/n9s7VVdtEiYJbV7/8xVwzRURheAqmjHZ+v9N09TZRQ+E4+nLBaWaKKHuNH11oSuEYZFBG+8JZp6ge3dqq5jzSqQFw/HTt1EYV9DzVzCHKXqOK+plSuGYnYky5jsrKKlV5vMpMEaWv59fsUXv3HzNTRNE1iwUYp53SQl35z53NHKLsdujQMdW+XVsz5cbfd5QV/nlAB9WxHe8IoPigBgMBxoghZ5g5RDRx+jOmFM4ZZMxftM6UiNJbm9Yt1GUXd1Jnn9mWORoUCY6THl3b6hoMHD9EFD9nkLF67QemRJQZLvpKe3XBeaerVi2b6dsRibxwXOD4OP+c0/TxQkT158zJGDN5sVo0d4yZIsos72w5qN75e4Wqiv0FHKus/jNohoeq4U+C8UeWwD/0Cd0sguACcSf6weBtqkTB4snJcAYZv1r6urpu5JfNFFFm+uTAMfXR7sNq++5D6sjRE+roseOq8rh5kTIW+rxoGfvPKW2bqy5ntNFd0bMnT6JwOS2aR+7okHeXEBERUWRPrnhLfXtMfzPlFi0UISIiIopZUbrJlMI5g4xxU5aYEhEREVF8WJNBREREkQ0o7GZK4RhkEBERUWRTJw01pXDOxM+3N+9WfXp2NFNERESU7eK5u8S5VEHvTqZEREREpNQds541pXDOIGP12q2mRERERKTUzvKDphTOGWTMX7TelIiIiIjiw8RPIiIiimzqpItMKZwzyOiaz/77iYiIqMaAwu6mFI7dihMREVFk72/bq87r29lMubG5hIiIiCK7u+RFUwrnDDJmlKwyJSIiIqL4OIOMzVv2mhIRERFRfNhcQkRERJEtnjfWlMI5g4zxowtNiYiIiCg+ziBjVFE/UyIiIiJSas6Cl0wpnPMW1gMVh9VN05aZKaUWzr5K5eW2VstLN6rHl5XpeX17d1Szikfo8sTpy1TFwaO6jM46cC/tpi17Tmai5uW2iq1jtC7PX7ROrV77gS6PLCpQ148+X5fHTVmix1Ay43LVLT+v1vbQd8cDM67QZfSfLt2botYFQdGO8gpVPOs5PQ+kWuexZW+qFaWbdHnYkLPV5AmDdNne55nFw/XzWjaUbY99iS/refY+IxFW8lRknysOHomt4xk9D/y+IzwWV55a19DvyLu9eL6jyRMGxj57r4R8R+hyXnqEbcrvCAf7hrIduhzPd2Qft4n4juzjNp7vSI7bRHxHQcdtlO8o7G87nu/IPm7j+Y7s4zZTviP7uIV4viM5bhPxHdnHbVN+R/b24vmOZHvQ0O/Ie9zG8x2FXSMa4zuyt5eI7yjKddT7HXXrnKsenPkN86qbM8ggIiIiqi8mfhIREVFSMMggIiKipGCQQUREREnBIIOIiIiSgkEGERERJQWDDCIiIkoKBhlERESUFAwyiIiIKCkYZBAREVFSMMggIiKipGCQQUREREmg1P8HqPE4lBcp+/sAAAAASUVORK5CYII=)\n",
        "\n",
        "where \n",
        "\n",
        "*   t := time periods\n",
        "*   i := lags\n",
        "*   c := channels\n",
        "*   k := covariates"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DtAWlqAOGwqM"
      },
      "source": [
        "**3.1 MODEL 1**\n",
        "\n",
        "Model 1: Sales as measured by current ad spend, previous ad spend and covariates"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rA1PkbheCpgm",
        "outputId": "110cb423-770a-4876-b1c4-aa4559d4900b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Call:\n",
            "lm(formula = ln_sales ~ ln_channel_1 + lag1_ln_channel_1 + lag2_ln_channel_1 + \n",
            "    lag3_ln_channel_1 + ln_channel_2 + lag1_ln_channel_2 + lag2_ln_channel_2 + \n",
            "    lag3_ln_channel_2 + special_event + sunshine_hours + events_ecom + \n",
            "    public_holidays, data = Final_dataset_weekly)\n",
            "\n",
            "Residuals:\n",
            "     Min       1Q   Median       3Q      Max \n",
            "-0.39769 -0.11400 -0.00731  0.08739  0.67568 \n",
            "\n",
            "Coefficients:\n",
            "                    Estimate Std. Error t value Pr(>|t|)    \n",
            "(Intercept)        7.4844643  0.3784523  19.777  < 2e-16 ***\n",
            "ln_channel_1       0.0119480  0.0087318   1.368   0.1731    \n",
            "lag1_ln_channel_1 -0.0101459  0.0105496  -0.962   0.3376    \n",
            "lag2_ln_channel_1 -0.0074902  0.0105333  -0.711   0.4781    \n",
            "lag3_ln_channel_1  0.0064990  0.0088144   0.737   0.4620    \n",
            "ln_channel_2       0.7897532  0.0666845  11.843  < 2e-16 ***\n",
            "lag1_ln_channel_2 -0.0639320  0.0905859  -0.706   0.4814    \n",
            "lag2_ln_channel_2  0.0387727  0.0924753   0.419   0.6756    \n",
            "lag3_ln_channel_2 -0.1455872  0.0628502  -2.316   0.0218 *  \n",
            "special_event      0.2496683  0.0351074   7.112 3.61e-11 ***\n",
            "sunshine_hours    -0.0040514  0.0008458  -4.790 3.78e-06 ***\n",
            "events_ecom        0.2801483  0.0446896   6.269 3.24e-09 ***\n",
            "public_holidays    0.0287047  0.0437460   0.656   0.5127    \n",
            "---\n",
            "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
            "\n",
            "Residual standard error: 0.1812 on 160 degrees of freedom\n",
            "Multiple R-squared:  0.8891,\tAdjusted R-squared:  0.8807 \n",
            "F-statistic: 106.8 on 12 and 160 DF,  p-value: < 2.2e-16\n",
            "\n"
          ]
        }
      ],
      "source": [
        "%%R\n",
        "modFit.1 <- lm(ln_sales ~ ln_channel_1+lag1_ln_channel_1+lag2_ln_channel_1+lag3_ln_channel_1+ln_channel_2+lag1_ln_channel_2+lag2_ln_channel_2+lag3_ln_channel_2+special_event+sunshine_hours+events_ecom+public_holidays, data = Final_dataset_weekly)\n",
        "summary(modFit.1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7WuSKrFEXLxa"
      },
      "source": [
        "**3.2  MODEL 2**\n",
        "\n",
        "Model 2: Brand Equity as measured by current ad spend, previous ad spend and covariates."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iTp2K2hdW_99",
        "outputId": "b0f7c40f-a3d4-47c0-a6d1-6d6365ab6617"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Call:\n",
            "lm(formula = ln_ad_awareness ~ ln_channel_1 + lag1_ln_channel_1 + \n",
            "    lag2_ln_channel_1 + lag3_ln_channel_1 + ln_channel_2 + lag1_ln_channel_2 + \n",
            "    lag2_ln_channel_2 + lag3_ln_channel_2 + sunshine_hours + \n",
            "    events_ecom + public_holidays + special_event, data = Final_dataset_weekly)\n",
            "\n",
            "Residuals:\n",
            "    Min      1Q  Median      3Q     Max \n",
            "-1.0710 -0.1201  0.0137  0.1676  0.6101 \n",
            "\n",
            "Coefficients:\n",
            "                   Estimate Std. Error t value Pr(>|t|)   \n",
            "(Intercept)       -0.957179   0.494540  -1.935  0.05469 . \n",
            "ln_channel_1       0.032081   0.011410   2.812  0.00555 **\n",
            "lag1_ln_channel_1  0.008620   0.013786   0.625  0.53269   \n",
            "lag2_ln_channel_1 -0.013104   0.013764  -0.952  0.34251   \n",
            "lag3_ln_channel_1  0.004607   0.011518   0.400  0.68971   \n",
            "ln_channel_2       0.109748   0.087139   1.259  0.20970   \n",
            "lag1_ln_channel_2  0.019368   0.118372   0.164  0.87023   \n",
            "lag2_ln_channel_2  0.004313   0.120841   0.036  0.97157   \n",
            "lag3_ln_channel_2  0.061554   0.082129   0.749  0.45467   \n",
            "sunshine_hours    -0.002769   0.001105  -2.506  0.01323 * \n",
            "events_ecom        0.140278   0.058398   2.402  0.01745 * \n",
            "public_holidays   -0.027602   0.057165  -0.483  0.62986   \n",
            "special_event     -0.048676   0.045876  -1.061  0.29028   \n",
            "---\n",
            "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
            "\n",
            "Residual standard error: 0.2368 on 160 degrees of freedom\n",
            "Multiple R-squared:  0.4358,\tAdjusted R-squared:  0.3934 \n",
            "F-statistic:  10.3 on 12 and 160 DF,  p-value: 7.33e-15\n",
            "\n"
          ]
        }
      ],
      "source": [
        "%%R\n",
        "modFit.2 <- lm(ln_ad_awareness ~ ln_channel_1+lag1_ln_channel_1+lag2_ln_channel_1+lag3_ln_channel_1+ln_channel_2+lag1_ln_channel_2+lag2_ln_channel_2+lag3_ln_channel_2+sunshine_hours+events_ecom+public_holidays+special_event, data = Final_dataset_weekly)\n",
        "summary(modFit.2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "52KxE3c4XDrm"
      },
      "source": [
        "**3.3 MODEL 3**\n",
        "\n",
        "Model 3: Sales measured by current ad spend, previous ad spend, ad awareness and covariates (extended version of Model 1)\n",
        "This is close as it gets to the full model: We model the base model with the component of ad awareness, in which sales is still the dependent variable. Thus one can capture the two paths that ad spend can take: either the direct way to sales or the indirect one via ad awareness to sales (Bruce et al., 2012)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Pz_YnykMW-w_",
        "outputId": "38142354-a348-4503-df23-23c532c23e22"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Call:\n",
            "lm(formula = ln_sales ~ ln_channel_1 + lag1_ln_channel_1 + lag2_ln_channel_1 + \n",
            "    lag3_ln_channel_1 + ln_channel_2 + lag1_ln_channel_2 + lag2_ln_channel_2 + \n",
            "    lag3_ln_channel_2 + ln_ad_awareness + sunshine_hours + events_ecom + \n",
            "    public_holidays + special_event, data = Final_dataset_weekly)\n",
            "\n",
            "Residuals:\n",
            "     Min       1Q   Median       3Q      Max \n",
            "-0.46817 -0.10487 -0.00893  0.09031  0.66072 \n",
            "\n",
            "Coefficients:\n",
            "                    Estimate Std. Error t value Pr(>|t|)    \n",
            "(Intercept)        7.6400143  0.3752995  20.357  < 2e-16 ***\n",
            "ln_channel_1       0.0067345  0.0087683   0.768  0.44360    \n",
            "lag1_ln_channel_1 -0.0115467  0.0103540  -1.115  0.26645    \n",
            "lag2_ln_channel_1 -0.0053606  0.0103546  -0.518  0.60539    \n",
            "lag3_ln_channel_1  0.0057504  0.0086447   0.665  0.50689    \n",
            "ln_channel_2       0.7719182  0.0656914  11.751  < 2e-16 ***\n",
            "lag1_ln_channel_2 -0.0670795  0.0888052  -0.755  0.45115    \n",
            "lag2_ln_channel_2  0.0380718  0.0906502   0.420  0.67506    \n",
            "lag3_ln_channel_2 -0.1555903  0.0617176  -2.521  0.01269 *  \n",
            "ln_ad_awareness    0.1625088  0.0593050   2.740  0.00684 ** \n",
            "sunshine_hours    -0.0036014  0.0008452  -4.261 3.48e-05 ***\n",
            "events_ecom        0.2573519  0.0445904   5.771 4.00e-08 ***\n",
            "public_holidays    0.0331902  0.0429137   0.773  0.44042    \n",
            "special_event      0.2575786  0.0345352   7.458 5.35e-12 ***\n",
            "---\n",
            "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
            "\n",
            "Residual standard error: 0.1777 on 159 degrees of freedom\n",
            "Multiple R-squared:  0.8941,\tAdjusted R-squared:  0.8854 \n",
            "F-statistic: 103.2 on 13 and 159 DF,  p-value: < 2.2e-16\n",
            "\n"
          ]
        }
      ],
      "source": [
        "%%R\n",
        "modFit.3 <- lm(ln_sales ~ ln_channel_1+lag1_ln_channel_1+lag2_ln_channel_1+lag3_ln_channel_1+ln_channel_2+lag1_ln_channel_2+lag2_ln_channel_2+lag3_ln_channel_2+ln_ad_awareness+sunshine_hours+events_ecom+public_holidays+special_event, data = Final_dataset_weekly)\n",
        "summary(modFit.3)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IXpxmAqpXldq"
      },
      "source": [
        "**4. COMPARISON OF MODELS**\n",
        "\n",
        "The absolute value of the t-statistic is computed for each model parameter of the regression models to determine the variable importances and thus weigh relative shares of importance of each model parameter.\n",
        "To compare the models we recommend, calculating the variable importance, e.g. with the varImp-function of the \"caret\"-package."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GSTSFCByCtcl",
        "outputId": "c809c2c3-ec7a-4112-ff52-46e89d4eec94"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                     Overall\n",
            "ln_channel_1       1.3683332\n",
            "lag1_ln_channel_1  0.9617336\n",
            "lag2_ln_channel_1  0.7110930\n",
            "lag3_ln_channel_1  0.7373192\n",
            "ln_channel_2      11.8431312\n",
            "lag1_ln_channel_2  0.7057608\n",
            "lag2_ln_channel_2  0.4192764\n",
            "lag3_ln_channel_2  2.3164153\n",
            "special_event      7.1115577\n",
            "sunshine_hours     4.7899231\n",
            "events_ecom        6.2687561\n",
            "public_holidays    0.6561670\n"
          ]
        }
      ],
      "source": [
        "#show variable importances\n",
        "%%R\n",
        "varImp(modFit.1)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "%%R \n",
        "varImp(modFit.2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_wu5oSbGf5JM",
        "outputId": "eefa459b-c87a-4509-c3a6-401e7bcb5b2a"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                     Overall\n",
            "ln_channel_1      2.81161989\n",
            "lag1_ln_channel_1 0.62525434\n",
            "lag2_ln_channel_1 0.95205003\n",
            "lag3_ln_channel_1 0.39997106\n",
            "ln_channel_2      1.25945591\n",
            "lag1_ln_channel_2 0.16362284\n",
            "lag2_ln_channel_2 0.03569366\n",
            "lag3_ln_channel_2 0.74947964\n",
            "sunshine_hours    2.50555135\n",
            "events_ecom       2.40211573\n",
            "public_holidays   0.48284988\n",
            "special_event     1.06102075\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "%%R\n",
        "varImp(modFit.3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4rQWOfB2f_Km",
        "outputId": "36d4a17f-7f61-4957-d8cd-7877876d4f45"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                     Overall\n",
            "ln_channel_1       0.7680518\n",
            "lag1_ln_channel_1  1.1151896\n",
            "lag2_ln_channel_1  0.5177023\n",
            "lag3_ln_channel_1  0.6651872\n",
            "ln_channel_2      11.7506752\n",
            "lag1_ln_channel_2  0.7553559\n",
            "lag2_ln_channel_2  0.4199853\n",
            "lag3_ln_channel_2  2.5210024\n",
            "ln_ad_awareness    2.7402201\n",
            "sunshine_hours     4.2608083\n",
            "events_ecom        5.7714653\n",
            "public_holidays    0.7734186\n",
            "special_event      7.4584247\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#calculate variable importances for model 1\n",
        "%%R\n",
        "mod1           <- data.frame(varImp(modFit.1))\n",
        "mod1$impProcent <- mod1$Overall/sum(mod1$Overall)*100 \n",
        "mod1"
      ],
      "metadata": {
        "id": "ticvE-MvDCz_",
        "outputId": "ec83d25b-ebd5-416c-a8eb-520915925e50",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                     Overall impProcent\n",
            "ln_channel_1       1.3683332   3.611382\n",
            "lag1_ln_channel_1  0.9617336   2.538261\n",
            "lag2_ln_channel_1  0.7110930   1.876756\n",
            "lag3_ln_channel_1  0.7373192   1.945974\n",
            "ln_channel_2      11.8431312  31.257054\n",
            "lag1_ln_channel_2  0.7057608   1.862683\n",
            "lag2_ln_channel_2  0.4192764   1.106578\n",
            "lag3_ln_channel_2  2.3164153   6.113613\n",
            "special_event      7.1115577  18.769221\n",
            "sunshine_hours     4.7899231  12.641833\n",
            "events_ecom        6.2687561  16.544852\n",
            "public_holidays    0.6561670   1.731793\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "id": "d3t6txhWg2rF",
        "outputId": "8ff7b88d-e805-4ad6-a445-5eb9e79dcd94"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#plot variable importances for model 1\n",
        "%%R\n",
        "mod1$var        <- rownames(mod1) \n",
        "mod1 %>% ggplot(aes(x=impProcent, y=reorder(var, impProcent))) +\n",
        "  geom_bar(stat=\"identity\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#calculate variable importances for model 2\n",
        "%%R\n",
        "mod2           <- data.frame(varImp(modFit.2)) \n",
        "mod2$impProcent <- mod2$Overall/sum(mod2$Overall)*100 \n",
        "mod2"
      ],
      "metadata": {
        "id": "3v8FZxKdDWtY",
        "outputId": "1b753e82-a12f-4ba5-cbbc-2d670aac6807",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                     Overall impProcent\n",
            "ln_channel_1      2.81161989 20.9062810\n",
            "lag1_ln_channel_1 0.62525434  4.6491856\n",
            "lag2_ln_channel_1 0.95205003  7.0791310\n",
            "lag3_ln_channel_1 0.39997106  2.9740533\n",
            "ln_channel_2      1.25945591  9.3649000\n",
            "lag1_ln_channel_2 0.16362284  1.2166456\n",
            "lag2_ln_channel_2 0.03569366  0.2654063\n",
            "lag3_ln_channel_2 0.74947964  5.5728842\n",
            "sunshine_hours    2.50555135 18.6304559\n",
            "events_ecom       2.40211573 17.8613427\n",
            "public_holidays   0.48284988  3.5903129\n",
            "special_event     1.06102075  7.8894014\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "id": "QMCn5k1sseT6",
        "outputId": "34a014ff-e3cd-4f23-fc88-63af7a735042"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#plot variable importances for model 2\n",
        "%%R\n",
        "mod2$var        <- rownames(mod2) \n",
        "mod2 %>% ggplot(aes(x=impProcent, y=reorder(var, impProcent))) +\n",
        "  geom_bar(stat=\"identity\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#calculate variable importances for model 3\n",
        "%%R\n",
        "mod3           <- data.frame(varImp(modFit.3)) \n",
        "mod3$impProcent <- mod3$Overall/sum(mod3$Overall)*100 \n",
        "mod3"
      ],
      "metadata": {
        "id": "HYEpQXuYDik3",
        "outputId": "61c48b19-830a-412e-9c4c-a2597f17a254",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                     Overall impProcent\n",
            "ln_channel_1       0.7680518   1.943575\n",
            "lag1_ln_channel_1  1.1151896   2.822016\n",
            "lag2_ln_channel_1  0.5177023   1.310059\n",
            "lag3_ln_channel_1  0.6651872   1.683273\n",
            "ln_channel_2      11.7506752  29.735381\n",
            "lag1_ln_channel_2  0.7553559   1.911447\n",
            "lag2_ln_channel_2  0.4199853   1.062783\n",
            "lag3_ln_channel_2  2.5210024   6.379460\n",
            "ln_ad_awareness    2.7402201   6.934196\n",
            "sunshine_hours     4.2608083  10.782083\n",
            "events_ecom        5.7714653  14.604839\n",
            "public_holidays    0.7734186   1.957155\n",
            "special_event      7.4584247  18.873732\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "id": "-VvXxwMesiBd",
        "outputId": "5003e4ac-e3a1-4fd9-a865-591088616da5"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#plot variable importances for model 3\n",
        "%%R\n",
        "mod3$var        <- rownames(mod3)\n",
        "mod3 %>% ggplot(aes(x=impProcent, y=reorder(var, impProcent))) +\n",
        "  geom_bar(stat=\"identity\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3FIB_N6Qrdnr"
      },
      "source": [
        "**Model Results**\n",
        "\n",
        "With **Model (1)**, higher weights for channel 2 (31.26%) vs. substantially lower weights for channel 1 (3.61%) are found. This would lead to the first assumption that mainly channel 2 can contribute to sales. \n",
        "\n",
        "In **Model (2)**, ad spend mainly relates with ad awareness with a reverse systematic as compared to Model (1): channel 1 weighs with 20.91% on ad awareness. Nevertheless, also channel 2 weighs on this variable, however with only half of the weight.\n",
        "\n",
        "**Model (3)** extends Model (1) through ad awareness as an additional independent variable on the dependent variable sales.\n",
        "Comparing how the weights for both ad channels change, as the brand mindset metric is incorporated one can see that both channels' weights decrease by nearly two percentage points each. In total, 6.93% of the model’s effects are captured by ad awareness and channel 1, in particular, relates to ad awareness. If one would be solely looking at performance measurements from Model (1), one would ignore this connection.\n",
        "\n",
        "**Model (3)** in this case study is the preferred MMM as it not only offers a better model fit but also somewhat higher diagnosticity: With **Model (3)**, the adjusted R-squared statistic improves from 88.07% **(Model 1)** to 88.54% **(Model 3)**, which suggests superiority of **Model (3)**. \n",
        "\n",
        "\n",
        "\n",
        "**Next steps: Towards a dynamic linear model extension**\n",
        "\n",
        "In this code, a naive multiplicative regression model examines the link between ad spend, ad awareness, and sales. \n",
        "One shortcoming is that this analysis contains separate regression models. That is, one can not capture the dynamics of ad spend directly on sales and indirectly, mediated through brand equity. A better model captures the multiple equations into a single model and accounts for the fact that the two processes exist at a different speed.\n",
        "Dynamic linear models (DLMs) offer the potential to overcome these issues as they act like regression models in which the coefficients are allowed to vary in time, which gives a better model flexibility (Ataman et al., 2010; Hu et al., 2014). Since DLM modeling requires advanced statistical knowledge, these models are not a standard venture for data teams today, and sufficient time for tests and adjustments needs to be planned. Yet, this venture is worth the effort to disentangle spurious from true correlations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3oeXJpP0XtU-"
      },
      "source": [
        "**5. CONCLUSION/SUMMARY**\n",
        "\n",
        "This MMM case with fictive data highlights that ignoring brand equity measures could potentially lead to misinterpretation of certain ad channels because they do not directly contribute to sales. Instead, these channels may serve a different purpose and contribute to brand equity, which is left out in most of today’s MMM models.\n",
        "\n",
        "**MMM-Partnership**\n",
        "\n",
        "WHU together with Meta, established a partnership to enhance MMM techniques. Academic modeling knowledge and research partner data input from third parties are key ingredients in this cooperation; Meta’s marketing science department serves as a sparring partner and regularly exchanges thoughts and experiences. If you want to contribute with your business data and see what the MMM approach suggests for your company you can support this joint initiative by contacting us: christian.schlereth@whu.edu, christina.reh@whu.edu.\n",
        "\n",
        "**Q&A**\n",
        "\n",
        "If you have questions, comments, suggestions, and practical problems (when applying this script to your datasets), feel free to get back to the WHU-team."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zdnjVFdx9nbm"
      },
      "source": [
        "**6. AUTHORS**\n",
        "\n",
        "Christina Reh,\n",
        "WHU – Otto Beisheim School of Management, Marketing and Sales Group, Chair of Digital Marketing, Burgplatz 2, 56179 Vallendar, Germany, christina.reh@whu.edu\n",
        "\n",
        "Konstanze Fichtner,\n",
        "Facebook Germany GmbH, Marketing Science Department, Caffamacherreihe 7, 20355 Hamburg, Germany, kfichtner@fb.com\n",
        "\n",
        "Christian Schlereth,\n",
        "WHU – Otto Beisheim School of Management, Marketing and Sales Group, Chair of Digital Marketing, Burgplatz 2, 56179 Vallendar, Germany, christian.schlereth@whu.edu, \n",
        "\n",
        "Torsten Müller-Klockmann,\n",
        "Facebook Germany GmbH, Marketing Science Department, Caffamacherreihe 7, 20355 Hamburg, Germany, torstenm@fb.com\n",
        "\n",
        "Manuel Weber,\n",
        "WHU – Otto Beisheim School of Management, Marketing and Sales Group, Chair of Digital Marketing, Burgplatz 2, 56179 Vallendar, Germany, manuel.weber@whu.edu "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s5YaRuno96kq"
      },
      "source": [
        "**7. REFERENCES**\n",
        "\n",
        "Ataman, M. B., Van Heerde, H. J., & Mela, C. F. (2010). The long-term effect of marketing strategy on brand sales. *Journal of Marketing Research*, 47(5), 866-882. https://journals.sagepub.com/doi/full/10.1509/jmkr.47.5.866\n",
        "\n",
        "Bruce, N. I., Peters, K., & Naik, P. A. (2012). Discovering how advertising grows sales and builds brands. *Journal of Marketing Research*, 49(6), 793-806. https://journals.sagepub.com/doi/full/10.1509/jmr.11.0060\n",
        "\n",
        "Hu, Y., Du, R. Y., & Damangir, S. (2014). Decomposing the impact of advertising: Augmenting sales with online search data. *Journal of Marketing Research*, 51(3), 300-319. https://journals.sagepub.com/doi/full/10.1509/jmr.12.0215\n",
        "\n",
        "Reh, Christina Antonie and Fichtner, Konstanze and Schlereth, Christian and Mueller-Klockmann, Torsten and Weber, Manuel, Integrating Brand Equity in MMM for a Long-term Ad Effectiveness Measurement (November 23, 2022). Available at SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4103941\n",
        "\n",
        "Tellis, G. J. (2006). Modeling marketing mix. Handbook of marketing research, 506-522. https://methods.sagepub.com/book/the-handbook-of-marketing-research/n24.xml"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "toc_visible": true,
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}