07_11_22_day5_single_cell_and_hypothesis_testing/code/solutions/SOLUTIONS_regressionColabExercises.ipynb

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      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/SaberaTalukder/Chen_Institute_DataSAI_for_Neuroscience/blob/main/07_11_22_day5_single_cell_and_hypothesis_testing/code/solutions/SOLUTIONS_regressionColabExercises.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MozW3XxY8ezr"
      },
      "source": [
        "**Regression Modeling for Single-cell Data**\n",
        "\n",
        "For this set of exercises we will be applying linear and logistic regression techniques to model and predict features of interest across cells, assess the assumptions of these methods, and to implement a partial correlation analysis."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_tty4AYi77ys"
      },
      "source": [
        "#To run a code cell, select the cell and hit Command/Ctrl+Enter or click the run/play symbol\n",
        "#Click Insert --> Code Cell or the '+ Code' option to insert a new code cell"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BAjFr_0y8Sxb"
      },
      "source": [
        "#Click Insert --> Text Cell or the '+ Text' option to insert a cell for text as below"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# This is  used to time the running of the notebook\n",
        "import time\n",
        "start_time = time.time()"
      ],
      "metadata": {
        "id": "Nj7fi7kx05Mu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fk0Xsqkn4k32"
      },
      "source": [
        "Text here for descriptions, explanations, etc"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "qtWUtrIhFfjo"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5oPRpu328neb"
      },
      "source": [
        "##**Import data and install packages**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "vYTZEjs9AqwV"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import scipy.io as sio\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt #Can use other plotting packages like seaborn"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "kNFuUFJ78cN5"
      },
      "outputs": [],
      "source": [
        "# ! allows you to run commands in the command line, as you would in your normal terminal/command line interface"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
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        "id": "yH-EpSmB9Y_x",
        "outputId": "af0d05bf-c3c4-418f-cf57-77eef74e8c8c"
      },
      "outputs": [
        {
          "output_type": "stream",
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          "text": [
            "--2022-07-12 00:09:34--  https://data.caltech.edu/tindfiles/serve/2a3c58f3-dde2-4a46-9497-eaf6a4f9c3fc/\n",
            "Resolving data.caltech.edu (data.caltech.edu)... 34.252.192.177, 34.250.186.131, 34.251.243.51\n",
            "Connecting to data.caltech.edu (data.caltech.edu)|34.252.192.177|:443... connected.\n",
            "HTTP request sent, awaiting response... 302 FOUND\n",
            "Location: https://tind-caltechdata.s3.amazonaws.com:443/569c2bfe8716497eaf26d58a6fa7512a?Signature=J%2FJf8Z%2BDqR3yvnhV6hz2%2FG8F4aM%3D&Expires=1657584875&AWSAccessKeyId=AKIAJSK7IFF5HDDM5UBQ&response-content-type=application/force-download&response-content-disposition=attachment%3Bfilename%3D%22regrMOP.tar.gz%22 [following]\n",
            "--2022-07-12 00:09:35--  https://tind-caltechdata.s3.amazonaws.com/569c2bfe8716497eaf26d58a6fa7512a?Signature=J%2FJf8Z%2BDqR3yvnhV6hz2%2FG8F4aM%3D&Expires=1657584875&AWSAccessKeyId=AKIAJSK7IFF5HDDM5UBQ&response-content-type=application/force-download&response-content-disposition=attachment%3Bfilename%3D%22regrMOP.tar.gz%22\n",
            "Resolving tind-caltechdata.s3.amazonaws.com (tind-caltechdata.s3.amazonaws.com)... 52.218.60.2\n",
            "Connecting to tind-caltechdata.s3.amazonaws.com (tind-caltechdata.s3.amazonaws.com)|52.218.60.2|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 28310869 (27M) [application/force-download]\n",
            "Saving to: ‘regrMOP.tar.gz’\n",
            "\n",
            "regrMOP.tar.gz      100%[===================>]  27.00M  17.1MB/s    in 1.6s    \n",
            "\n",
            "2022-07-12 00:09:37 (17.1 MB/s) - ‘regrMOP.tar.gz’ saved [28310869/28310869]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "#Download count matrix of cell by gene counts\n",
        "#Cells are 10x sequenced mouse primary cortex cells (...)\n",
        "\n",
        "!wget --content-disposition https://data.caltech.edu/tindfiles/serve/2a3c58f3-dde2-4a46-9497-eaf6a4f9c3fc/"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "xrGNmEHwAKAF"
      },
      "outputs": [],
      "source": [
        "#Gunzip the files we downloaded\n",
        "!tar -xf *.gz"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PPv4FIlm8rtQ"
      },
      "source": [
        "## **Read in data for analysis**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bldcPDtroHZ_"
      },
      "source": [
        "**The dataset**\n",
        "\n",
        "We will be working with 10x Genomics sequencing data from the mouse primary cortex, produced by the BRAIN Initiative Cell Census Network (BICCN) [(Yao et al. 2021)](https://www.nature.com/articles/s41586-021-03500-8). They assayed 94,162 cells by 10x sequencing (as well as SMART-seq), though we will work with only a subsetted sample today.  The cell type labels include GABAergic and Glutamatergic cells as well as Non-Neuronal cells, and were sampled from both sexes.\n",
        "\n",
        "<center><img src=\"https://drive.google.com/uc?export=view&id=1TKA0m3BEox8aBpoSNFMnIb3yftCfWyM4\" alt=\"EMFigure\" width=\"350\" height=\"350\"><center>\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2qq9TO5V97Vr"
      },
      "source": [
        "**The Count matrix**\n",
        "\n",
        "Count matrix has 14,690 cells with counts for 2000 genes. Though greater numbers of genes were measured, the dataset is subsetted to 2000 genes for ease of analysis. This matrix includes cells from both male and female mice.\n",
        "\n",
        "The 2000 genes were selected by filtering for genes expressed in greater than 1% of cells, and subsetting to the 2000 most variable of those genes.\n",
        "\n",
        "\n",
        " \n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tZ1h_dME8vJb",
        "outputId": "0ac64860-a852-4396-9798-87bcb6fa1dc4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(14690, 2000)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "#Get gene count matrix\n",
        "count_mat = sio.mmread('mop_count_mat.mtx')\n",
        "count_mat.shape"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Here we will conduct standard normalizations on the data\n",
        "#This normalizes read counts across cells to the same total reads, \n",
        "#stabilizes variance across genes, and makes the data continuous (more on this later)\n",
        "\n",
        "row_sums = np.sum(count_mat,axis=1)\n",
        "avg = np.mean(row_sums)\n",
        "coeffs = avg/row_sums\n",
        "\n",
        "for i in range(len(coeffs)):\n",
        "  count_mat[i,:] = count_mat[i,:]*coeffs[i]\n",
        "  \n",
        "count_mat = np.log1p(count_mat)"
      ],
      "metadata": {
        "id": "yphcm0MbSZ87"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "iaNMMX9rYXxs"
      },
      "execution_count": 6,
      "outputs": []
    },
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      "execution_count": 7,
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        "id": "NFissu8VB92P",
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        {
          "output_type": "execute_result",
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              "                                barcode      cell_type     sex\n",
              "0  AAACCCAAGAGGCTGT-9L8TX_190430_01_A08  Glutamatergic  Female\n",
              "1  AAACCCAAGATTGGGC-9L8TX_190430_01_A08  Glutamatergic  Female\n",
              "2  AAACCCAAGGAGAATG-9L8TX_190430_01_A08      GABAergic  Female\n",
              "3  AAACCCAAGTTGCGAG-9L8TX_190430_01_A08   Non-Neuronal  Female\n",
              "4  AAACCCAGTAACATCC-9L8TX_190430_01_A08  Glutamatergic  Female"
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              "      <th>0</th>\n",
              "      <td>AAACCCAAGAGGCTGT-9L8TX_190430_01_A08</td>\n",
              "      <td>Glutamatergic</td>\n",
              "      <td>Female</td>\n",
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              "      <th>1</th>\n",
              "      <td>AAACCCAAGATTGGGC-9L8TX_190430_01_A08</td>\n",
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              "      <th>2</th>\n",
              "      <td>AAACCCAAGGAGAATG-9L8TX_190430_01_A08</td>\n",
              "      <td>GABAergic</td>\n",
              "      <td>Female</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>AAACCCAAGTTGCGAG-9L8TX_190430_01_A08</td>\n",
              "      <td>Non-Neuronal</td>\n",
              "      <td>Female</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>AAACCCAGTAACATCC-9L8TX_190430_01_A08</td>\n",
              "      <td>Glutamatergic</td>\n",
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          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "#Get metadata dataframe for the 14k cells (rows of the matrix)\n",
        "meta = pd.read_csv('cell_metadata.csv')\n",
        "meta.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
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            "text/plain": [
              "  gene_name\n",
              "0    Malat1\n",
              "1   mt-Atp6\n",
              "2      Plp1\n",
              "3   Camk2n1\n",
              "4      Nrgn"
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              "      <th>0</th>\n",
              "      <td>Malat1</td>\n",
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              "      <th>1</th>\n",
              "      <td>mt-Atp6</td>\n",
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              "      <th>2</th>\n",
              "      <td>Plp1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Camk2n1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Nrgn</td>\n",
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              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-d53af782-31a4-48aa-bc39-524a10ac56d0 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-d53af782-31a4-48aa-bc39-524a10ac56d0');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "\n",
        "#Get metadata dataframe for the 2k genes (columns of the matrix)\n",
        "\n",
        "meta_gene = pd.read_csv('gene_metadata.csv')\n",
        "meta_gene.head()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xzz-5cVyCsS4",
        "outputId": "8088b481-3026-40ea-9284-963a0fc3f713"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    Glutamatergic\n",
              "1    Glutamatergic\n",
              "2        GABAergic\n",
              "3     Non-Neuronal\n",
              "4    Glutamatergic\n",
              "Name: cell_type, dtype: object"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "#Access the list in each column by meta['name_of_col']\n",
        "cell_types = meta['cell_type']\n",
        "cell_types[0:5]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "plqTILR-DdnC",
        "outputId": "26111d48-bd56-477d-86b1-b89665157a3c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array(['GABAergic', 'Glutamatergic', 'Low Quality', 'Non-Neuronal'],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "#See all the cell type categories\n",
        "np.unique(meta['cell_type']) #Cell populations are marked by the genes they express (as comparec to other cell populations)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-kcBQFk_p3bC",
        "outputId": "6a4dcb53-e050-4e1d-9f95-9ecdcfbb2f39"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1414, 2000)"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "#Filter the count matrix for a particular cell type (across all genes)\n",
        "\n",
        "#Remember! Cells are ROWS and Genes are COLUMNS\n",
        "\n",
        "indices = meta['cell_type'].isin(['GABAergic']) #Get indices for where the cell_type is Dlk1_1 only\n",
        "\n",
        "count_sub = count_mat[indices,:] #Filter rows (cells) of matrix\n",
        "count_sub.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xRCYW1VVErG1",
        "outputId": "87fa0d2a-6cbd-4fbc-8cf8-e313b27eda0b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array(['Female', 'Male'], dtype=object)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "#The sexes\n",
        "np.unique(meta['sex'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vOCNwfTzRn6M"
      },
      "source": [
        "## **Fitting Regression Models to the Data**\n",
        "Here we will explore how to use (1) linear and (2) logistic regression to model gene count relationships, and investigate the assumptions these models will make.\n",
        "\n",
        "Given the multiple categories of metadata we have for these cells, we will also utilize (3) partial correlations to remove the influence of possibly confounding variables from our calculations of correlation between genes and their expression profiles."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5CsRl1eaXI91"
      },
      "source": [
        "***Linear Regression***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_0S8CxwBQoCO"
      },
      "source": [
        "How to use linear regression functions from sklearn:\n",
        "https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html \n",
        "```\n",
        ">>> import numpy as np\n",
        ">>> from sklearn.linear_model import LinearRegression\n",
        ">>> X = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])\n",
        ">>> # y = 1 * x_0 + 2 * x_1 + 3\n",
        ">>> y = np.dot(X, np.array([1, 2])) + 3\n",
        ">>> reg = LinearRegression().fit(X, y)\n",
        ">>> reg.score(X, y)\n",
        "1.0\n",
        ">>> reg.coef_\n",
        "array([1., 2.])\n",
        ">>> reg.intercept_\n",
        "3.0...\n",
        "```\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rsc39i5zRr0Q"
      },
      "source": [
        "### **a) Find x ~ y and y ~ x regression model coefficients for a pair of genes and plot x versus y in each case.** \n",
        "\n",
        "By regressing y (gene 2) on x (gene 1) written as y ~ x, or vice versa, we are modeling how gene 2's expression changes as a function of gene 1. Specifically, the $\\beta$ parameter from the fit $y = \\alpha + \\beta x$ represents the change in the value of dependent variable (y here) corresponding to unit change in the value of independent variable (x here). \n",
        "\n",
        "**Using the given gene pair (below), report the intercept and coefficient values for each of the two models.**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 331
        },
        "id": "bAaRsWVlwvDV",
        "outputId": "cc40bba6-ec35-4ebe-a381-fabaf66a85b2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "coefficient:  0.7876742294913899 \n",
            " intercept:  0.12122307991512149\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#Set genes\n",
        "gene1 = 'Slc6a1' # Slc6a1\n",
        "gene2 = 'Gad1' # \n",
        "\n",
        "#Do regression x ~ y and y ~ x\n",
        "from sklearn.linear_model import LinearRegression\n",
        "\n",
        "g1_indices = meta_gene['gene_name'].tolist().index(gene1) \n",
        "g2_indices = meta_gene['gene_name'].tolist().index(gene2)\n",
        "\n",
        "x = count_mat[:,g1_indices] \n",
        "y = count_mat[:,g2_indices]\n",
        "\n",
        "reg = LinearRegression().fit(x.reshape(-1, 1), y.reshape(-1, 1))\n",
        "\n",
        "print(\"coefficient: \", reg.coef_[0,0], \"\\n intercept: \",reg.intercept_[0])\n",
        "\n",
        "plt.plot(x,reg.coef_[0,0]*x+reg.intercept_[0],label=\"regression line\")\n",
        "plt.plot(x,y,'.',label=\"data points\")\n",
        "plt.xlabel(\"Slc6a1\")\n",
        "plt.ylabel(\"Gad1\")\n",
        "plt.title(\"regressing y (gene 2) on x (gene 1) \")\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 331
        },
        "id": "V66ZJeKiwFEj",
        "outputId": "3fc37fcf-3ec0-4ed0-eac5-ae9dbafb6f8a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "coefficient:  0.887295703931101 \n",
            " intercept:  0.1068091692535198\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "reg = LinearRegression().fit(y.reshape(-1, 1), x.reshape(-1, 1))\n",
        "\n",
        "print(\"coefficient: \", reg.coef_[0,0], \"\\n intercept: \",reg.intercept_[0])\n",
        "\n",
        "plt.plot(y,reg.coef_[0,0]*y+reg.intercept_[0],label=\"regression line\")\n",
        "plt.plot(y,x,'.',label=\"data points\")\n",
        "plt.xlabel(\"Slc6a1\")\n",
        "plt.ylabel(\"Gad1\")\n",
        "plt.title(\"regressing x (gene 1) on y (gene 2) \")\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5S1p_kUJSMuH"
      },
      "source": [
        "### **b) Calculate the $R^2$ and the Pearson correlation coefficient for the gene pair, given each regression model** \n",
        "\n",
        "The  $R^2$ coefficient of determination is defined as 1 - (sum of squares of the residuals)/(sum of total squares). Here the numerator represents deviation from the model predictions, and the denominator represents the variance of the given dataset (observations). $R^2 = 1 - \\frac{SS_{res}}{SS_{tot}} = 1 - \\frac{\\sum_i (y_i - y_{pred})^2}{\\sum_i (y_i - \\bar{y})^2} $ (where $\\bar{y}$ is the mean). This measures the proportion of the variation in y that is predictable from x.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RMCHl3ZFR54F"
      },
      "source": [
        "Pearson correlation (Pearson's r) is defined as $\\frac{\\sum_i (x_i - \\bar{x})(y_i - \\bar{y})}{\\sqrt{\\sum_i (x_i - \\bar{x})^2 \\sum_i (y_i - \\bar{y})^2}}$. This represents the covariance of two variables divided by the product of their standard deviations i.e. a normalized representation of covariance to measure the linear correlation between the variables.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bOf45te0TlDj"
      },
      "source": [
        "**Report the $R^2$ for each model and the Pearson correlation calculations (you will only need to calculate one Pearson correlation value). Calculate these values directly using the formulas given. Additionally, print the 'score' for each regression model and check that this matches your $R^2$ calculation.**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5orzxAEESLyV",
        "outputId": "686013a1-1856-41d4-f42a-e991604f8aac"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Pearson correlation:  0.8360023683728122\n",
            "regressing y (gene 2) on x (gene 1): \n",
            " y =  0.7876742294913899 x +  0.12122307991512149 with R^2 score  0.6988999599249512\n",
            "Calculated R^2:  0.6988999599249512\n"
          ]
        }
      ],
      "source": [
        "#Report values\n",
        "p = np.sum((x-np.mean(x))*(y-np.mean(y)))/np.sqrt(np.sum((x-np.mean(x))**2)*np.sum((y-np.mean(y))**2))\n",
        "print(\"Pearson correlation: \",p)\n",
        "reg = LinearRegression().fit(x.reshape(-1, 1), y.reshape(-1, 1))\n",
        "print(\"regressing y (gene 2) on x (gene 1): \\n y = \", reg.coef_[0,0], \"x + \", reg.intercept_[0], \"with R^2 score \", reg.score(x.reshape(-1, 1), y.reshape(-1, 1)))\n",
        "R2=1-np.sum((y-reg.coef_[0,0]*x-reg.intercept_[0])**2)/np.sum((y-np.mean(y))**2)\n",
        "print(\"Calculated R^2: \", R2)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dB_tWBmZSn_S",
        "outputId": "05beae92-0615-4596-e54f-8d06d0996e4a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "regressing x (gene 1) on y (gene 2): \n",
            "y x =  0.887295703931101 y +  0.1068091692535198 with R^2 score  0.6988999599249512\n",
            "Calculated R^2:  0.6988999599249512\n"
          ]
        }
      ],
      "source": [
        "#Report values\n",
        "reg = LinearRegression().fit(y.reshape(-1, 1), x.reshape(-1, 1))\n",
        "print(\"regressing x (gene 1) on y (gene 2): \\ny x = \", reg.coef_[0,0], \"y + \", reg.intercept_[0], \"with R^2 score \", reg.score(y.reshape(-1, 1), x.reshape(-1, 1)))\n",
        "\n",
        "R2=1-np.sum((x-reg.coef_[0,0]*y-reg.intercept_[0])**2)/np.sum((x-np.mean(x))**2)\n",
        "print(\"Calculated R^2: \", R2)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cQpdWwmKlrcM"
      },
      "source": [
        "**Note that $R^2$ for each model is the same.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_K5_xbs1Rlfo"
      },
      "source": [
        "### **c) Plot model residuals to check homoscedascity assumption for the gene pair**\n",
        "\n",
        "OLS (ordinary least squares) assumes that the error term (“noise” in the relationship between the independent and the dependent variable) is the same across all values of the independent variable i.e. all variables are treated the same or given the same 'weight'. If this is true for our dataset, we would expect a random distribution of residuals (deviations from the prediction) about the zero line.\n",
        "\n",
        "**Plot the residuals (predicted - observed) values for each model. The plots will have the residuals on the y-axis versus the independent (input) variable values. Do you think the homoscedascity assumption is met?**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "6klRDuJh7Ipg",
        "outputId": "4c86f606-79fd-4b18-a953-e5dd726809d4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f250032ff90>"
            ]
          },
          "metadata": {},
          "execution_count": 144
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#Example plot\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt \n",
        "\n",
        "xs = np.random.randint(100, size=10)\n",
        "ys = xs*3 + 2\n",
        "plt.scatter(xs,ys)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "Gk9wztnr6Bh1",
        "outputId": "9a64b746-3f8e-4eb9-d183-026aacf75fb4"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#Plot residuals for the predicted y's (for both model) and describe if you believe the assumption holds\n",
        "\n",
        "reg = LinearRegression().fit(x.reshape(-1, 1), y.reshape(-1, 1))\n",
        "\n",
        "plt.plot(x,(reg.coef_[0,0]*x+reg.intercept_[0])-y,'.')\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"residuals\")\n",
        "plt.title(\"regressing y (gene 2) on x (gene 1) \")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "MzOMCDtBoQ7y",
        "outputId": "ca07dfed-add7-4454-b3d6-4cb899e1b77c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "reg = LinearRegression().fit(y.reshape(-1, 1), x.reshape(-1, 1))\n",
        "\n",
        "plt.plot(y,(reg.coef_[0,0]*y+reg.intercept_[0])-x,'.')\n",
        "plt.xlabel(\"y\")\n",
        "plt.ylabel(\"residuals\")\n",
        "plt.title(\"regressing x (gene 1) on y (gene 2) \")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A2vF36K4-OmD"
      },
      "source": [
        "**The assumption doesn't seem to hold.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F79PCQO2XQGa"
      },
      "source": [
        "***Logistic Regression***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_YpRMAuhVBX3"
      },
      "source": [
        "How to use logistic regression functions from sklearn: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html \n",
        "\n",
        "\n",
        "```\n",
        ">>> from sklearn.datasets import load_iris\n",
        ">>> from sklearn.linear_model import LogisticRegression\n",
        ">>> X, y = load_iris(return_X_y=True)\n",
        ">>> clf = LogisticRegression(random_state=0).fit(X, y)\n",
        "# .coef_ and .intercept_ the same as LinearRegression\n",
        "```\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iHCx7Bx1S4X-"
      },
      "source": [
        "### **d) Set up logistic regression model for cell type classification of GABAergic cells and report genes with largest coefficients.** \n",
        "\n",
        "With logistic regression we can model a categorical variable (e.g. cell type) as a continuous value (i.e. the probability of being in the category). Here we will model the contribution of each gene to the probability of a cell being in the GABAergic cell type or not. \n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "drvWgEnNclnC"
      },
      "source": [
        "\n",
        "In order to determine which genes contribute to designating that a cell is in that cell type or not, we will subset the count matrix (X) for only female cells, and then perform logistic regression. Y will be binary, 0 or 1, representing whether a cell is GABAergic or not.\n",
        "\n",
        "Thus the logistic regression model models the probability that Y = 1, that Y is of the GABAergic cell type, not from the remaining cells.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fNnIAEswcnyM"
      },
      "source": [
        "**Fit separate, logistic regression models for each of the 2000 genes, and report the top 10 genes with the highest beta coefficients i.e. the genes where changes in their expression highly contribute to the probability of the cell being in the desired category**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "yry8RWdG8q_J"
      },
      "outputs": [],
      "source": [
        "#Set up model and extract beta\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "Y=meta['cell_type'].isin(['GABAergic']) & meta['sex'].isin(['Female'])\n",
        "coefficients=np.zeros(count_mat.shape[1])\n",
        "\n",
        "#Determine top ten genes which identify the female only cell type (Rank the model coefficients)\n",
        "for i in range(count_mat.shape[1]):\n",
        "  lr=LogisticRegression(random_state=0).fit(count_mat[:,i].reshape(-1,1), Y)\n",
        "  coefficients[i]=lr.coef_[0]\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2Hv2dzMwvaoi",
        "outputId": "48e5de3f-14f6-40fd-eda6-051dad3f3363"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "['Atp1a3', 'Atp1b1', 'Zwint', 'Tcf4', 'Ttc3', 'Slc25a4', 'Hsp90ab1', 'Cox6c', 'Impact', 'Atp6v0c']\n"
          ]
        }
      ],
      "source": [
        "idx=np.flip(np.argsort(coefficients)[-10:])\n",
        "top_genes=meta_gene.iloc[idx]\n",
        "print(top_genes[\"gene_name\"].tolist())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5baFDcEWXdz5"
      },
      "source": [
        "***Partial Correlations***"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dc2eAWytRfO-"
      },
      "source": [
        "Partial correlation is a measure of association between two variables, after controlling for the effect of a third random variable. As a general example, one may want to measure correlation between age and memory performance, but may want to remove the effect of education level from this correlation.\n",
        "\n",
        "Partial correlation can be framed as correlation of the residuals from two regression problems: (1) X ~ Z and (2) Y ~ Z. The partial correlation between X and Y is then the pearson correlation of the residuals of (1) and (2).\n",
        "\n",
        "Below we will go through the steps of calculating the partial correlation for the gene pair in parts a-d."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QTrI3Q8YThtj"
      },
      "source": [
        "### **e) Find linear regression fits of each gene's expression profile for the gene pair given below, against the sex of cells. Report the coefficient and intercept for each model.**\n",
        "\n",
        "Fit linear regression models of (1) gene 1 expression against sex (binary 0 or 1 for Male or Female) and (2) gene 2 expression against sex (binary 0 or 1 for Male or Female). This is done across all cells (the count matrix with both sexes and all cell types). Convert the 'M' and 'F' to binary values, (0 or 1), for the regression models.\n",
        "\n",
        "**Print the coefficient and intercept for each model as well as the original pearson correlation of the genes, Atp5g3 and mt-Atp8 (which we will use for comparison). You can use [scipy.stats.pearsonr](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html)**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TF6Q3qD99ydp",
        "outputId": "3b92b206-0aba-4215-ac13-79c261802728"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "coefficient:  [0.89944113] \n",
            " intercept:  [1.69204968]\n",
            "coefficient:  [0.26339151] \n",
            " intercept:  [1.23680049]\n"
          ]
        }
      ],
      "source": [
        "#Set up regression models\n",
        "from scipy import stats\n",
        "\n",
        "#Example of scipy.stats.pearsonr\n",
        "#r = stats.pearsonr([1, 2, 3, 4, 5], [10, 9, 2.5, 6, 4])[0]\n",
        "#print(r)\n",
        "\n",
        "gene1 = 'mt-Atp8'\n",
        "gene2 = 'Atp5g3'\n",
        "\n",
        "g1_indices = meta_gene['gene_name'].tolist().index(gene1) \n",
        "g2_indices = meta_gene['gene_name'].tolist().index(gene2)\n",
        "\n",
        "\n",
        "g1 = count_mat[:,g1_indices] \n",
        "g2 = count_mat[:,g2_indices]\n",
        "\n",
        "x = meta['sex']=='Female'\n",
        "x = np.reshape(x.tolist(),(-1, 1))\n",
        "\n",
        "reg1 = LinearRegression().fit(x, g1.reshape(-1, 1))\n",
        "print(\"coefficient: \", reg1.coef_[0], \"\\n intercept: \",reg1.intercept_)\n",
        "\n",
        "reg2 = LinearRegression().fit(x, g2.reshape(-1, 1))\n",
        "print(\"coefficient: \", reg2.coef_[0], \"\\n intercept: \",reg2.intercept_)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XTjolzJ1UoR2"
      },
      "source": [
        "### **f) Report the residuals from each regression fit.**\n",
        "Residuals are defined as predicted - observed values, for each model.\n",
        "\n",
        "**Report the first 5 residual values for each model.**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "FgwkxqywUtJG"
      },
      "outputs": [],
      "source": [
        "#Get residuals\n",
        "residual1=x*reg1.coef_[0,0]+reg1.intercept_[0]-g1.reshape(-1, 1)\n",
        "residual2=x*reg2.coef_[0,0]+reg2.intercept_[0]-g2.reshape(-1, 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "639xg27RHFtE",
        "outputId": "f8915989-9bfe-4446-a930-e17f00e7a887"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.38029055]\n",
            " [0.1532959 ]\n",
            " [0.83074896]\n",
            " [2.59149081]\n",
            " [0.54414858]]\n",
            "[[-0.59300836]\n",
            " [-1.20361361]\n",
            " [-0.26054985]\n",
            " [ 1.500192  ]\n",
            " [-0.49118007]]\n"
          ]
        }
      ],
      "source": [
        "print(residual1[0:5])\n",
        "print(residual2[0:5])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T3gBo2a3Ut07"
      },
      "source": [
        "### **g) Now find and report the partial correlation between the genes in pair. This is the Pearson correlation coefficient, as defined in b, between the residuals.**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bhN_g33uU06j",
        "outputId": "142f23aa-1055-486d-ad41-d9455df29083"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-0.4125381409253329\n"
          ]
        }
      ],
      "source": [
        "#Get correlation\n",
        "p = np.sum((residual1-np.mean(residual1))*(residual2-np.mean(residual2)))/np.sqrt(np.sum((residual1-np.mean(residual1))**2)*np.sum((residual2-np.mean(residual2))**2))\n",
        "print(p)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "oOkTOI_RYIhD"
      },
      "execution_count": null,
      "outputs": []
    }
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