Exercise11.ipynb

{
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        "<a href=\"https://colab.research.google.com/github/choiitea/Choi_DSPN_S24/blob/main/Exercise11.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S5Fpqv6H_cZA"
      },
      "source": [
        "# Exercise 11: The beauty of kNN\n",
        "\n",
        "In this exercise, you'll gain practice working with kNN. We'll use the [diamonds](https://ggplot2.tidyverse.org/reference/diamonds.html) dataset, which comes as part of `ggplot2`. This dataset provides information on the quality and price of 50,000 diamonds\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "is-1Gkl6_cZC"
      },
      "source": [
        "## 1. Data, Plotting, and Train/Test Sets (2 pts)\n",
        "-----\n",
        "* Load the the `class` and `tidyverse` packages.\n",
        "* Assign the `diamonds` data set to a simpler name. Then, create a new variable `price_bin` that splits the `price` variable into a binary variable, where 1 indicates that the diamond costs greater than the mean price, and 0 indicates that the diamond costs less than the mean price. Set `price_bin` to be a factor. (*Hint: use the if_else() function*)\n",
        "* Select just the `carat`, `depth`, `table`, `x`, `y`, and your new `price_bin` variables\n",
        "* Print the first few lines of the data set\n",
        "* Print the dimensions of the data set\n"
      ]
    },
    {
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        "outputId": "235ea5eb-83a1-4c99-8089-d582c6f93e1d"
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      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Loading required package: tidyverse\n",
            "\n",
            "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n",
            "\u001b[32m✔\u001b[39m \u001b[34mdplyr    \u001b[39m 1.1.4     \u001b[32m✔\u001b[39m \u001b[34mreadr    \u001b[39m 2.1.5\n",
            "\u001b[32m✔\u001b[39m \u001b[34mforcats  \u001b[39m 1.0.0     \u001b[32m✔\u001b[39m \u001b[34mstringr  \u001b[39m 1.5.1\n",
            "\u001b[32m✔\u001b[39m \u001b[34mggplot2  \u001b[39m 3.4.4     \u001b[32m✔\u001b[39m \u001b[34mtibble   \u001b[39m 3.2.1\n",
            "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.3     \u001b[32m✔\u001b[39m \u001b[34mtidyr    \u001b[39m 1.3.1\n",
            "\u001b[32m✔\u001b[39m \u001b[34mpurrr    \u001b[39m 1.0.2     \n",
            "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n",
            "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n",
            "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m    masks \u001b[34mstats\u001b[39m::lag()\n",
            "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m<http://conflicted.r-lib.org/>\u001b[39m\u001b[23m) to force all conflicts to become errors\n",
            "Loading required package: class\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A tibble: 6 × 10</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>carat</th><th scope=col>cut</th><th scope=col>color</th><th scope=col>clarity</th><th scope=col>depth</th><th scope=col>table</th><th scope=col>price</th><th scope=col>x</th><th scope=col>y</th><th scope=col>z</th></tr>\n",
              "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;ord&gt;</th><th scope=col>&lt;ord&gt;</th><th scope=col>&lt;ord&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td>0.23</td><td>Ideal    </td><td>E</td><td>SI2 </td><td>61.5</td><td>55</td><td>326</td><td>3.95</td><td>3.98</td><td>2.43</td></tr>\n",
              "\t<tr><td>0.21</td><td>Premium  </td><td>E</td><td>SI1 </td><td>59.8</td><td>61</td><td>326</td><td>3.89</td><td>3.84</td><td>2.31</td></tr>\n",
              "\t<tr><td>0.23</td><td>Good     </td><td>E</td><td>VS1 </td><td>56.9</td><td>65</td><td>327</td><td>4.05</td><td>4.07</td><td>2.31</td></tr>\n",
              "\t<tr><td>0.29</td><td>Premium  </td><td>I</td><td>VS2 </td><td>62.4</td><td>58</td><td>334</td><td>4.20</td><td>4.23</td><td>2.63</td></tr>\n",
              "\t<tr><td>0.31</td><td>Good     </td><td>J</td><td>SI2 </td><td>63.3</td><td>58</td><td>335</td><td>4.34</td><td>4.35</td><td>2.75</td></tr>\n",
              "\t<tr><td>0.24</td><td>Very Good</td><td>J</td><td>VVS2</td><td>62.8</td><td>57</td><td>336</td><td>3.94</td><td>3.96</td><td>2.48</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA tibble: 6 × 10\n\n| carat &lt;dbl&gt; | cut &lt;ord&gt; | color &lt;ord&gt; | clarity &lt;ord&gt; | depth &lt;dbl&gt; | table &lt;dbl&gt; | price &lt;int&gt; | x &lt;dbl&gt; | y &lt;dbl&gt; | z &lt;dbl&gt; |\n|---|---|---|---|---|---|---|---|---|---|\n| 0.23 | Ideal     | E | SI2  | 61.5 | 55 | 326 | 3.95 | 3.98 | 2.43 |\n| 0.21 | Premium   | E | SI1  | 59.8 | 61 | 326 | 3.89 | 3.84 | 2.31 |\n| 0.23 | Good      | E | VS1  | 56.9 | 65 | 327 | 4.05 | 4.07 | 2.31 |\n| 0.29 | Premium   | I | VS2  | 62.4 | 58 | 334 | 4.20 | 4.23 | 2.63 |\n| 0.31 | Good      | J | SI2  | 63.3 | 58 | 335 | 4.34 | 4.35 | 2.75 |\n| 0.24 | Very Good | J | VVS2 | 62.8 | 57 | 336 | 3.94 | 3.96 | 2.48 |\n\n",
            "text/latex": "A tibble: 6 × 10\n\\begin{tabular}{llllllllll}\n carat & cut & color & clarity & depth & table & price & x & y & z\\\\\n <dbl> & <ord> & <ord> & <ord> & <dbl> & <dbl> & <int> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t 0.23 & Ideal     & E & SI2  & 61.5 & 55 & 326 & 3.95 & 3.98 & 2.43\\\\\n\t 0.21 & Premium   & E & SI1  & 59.8 & 61 & 326 & 3.89 & 3.84 & 2.31\\\\\n\t 0.23 & Good      & E & VS1  & 56.9 & 65 & 327 & 4.05 & 4.07 & 2.31\\\\\n\t 0.29 & Premium   & I & VS2  & 62.4 & 58 & 334 & 4.20 & 4.23 & 2.63\\\\\n\t 0.31 & Good      & J & SI2  & 63.3 & 58 & 335 & 4.34 & 4.35 & 2.75\\\\\n\t 0.24 & Very Good & J & VVS2 & 62.8 & 57 & 336 & 3.94 & 3.96 & 2.48\\\\\n\\end{tabular}\n",
            "text/plain": [
              "  carat cut       color clarity depth table price x    y    z   \n",
              "1 0.23  Ideal     E     SI2     61.5  55    326   3.95 3.98 2.43\n",
              "2 0.21  Premium   E     SI1     59.8  61    326   3.89 3.84 2.31\n",
              "3 0.23  Good      E     VS1     56.9  65    327   4.05 4.07 2.31\n",
              "4 0.29  Premium   I     VS2     62.4  58    334   4.20 4.23 2.63\n",
              "5 0.31  Good      J     SI2     63.3  58    335   4.34 4.35 2.75\n",
              "6 0.24  Very Good J     VVS2    62.8  57    336   3.94 3.96 2.48"
            ]
          },
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        {
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          "name": "stdout",
          "text": [
            "\u001b[90m# A tibble: 6 × 6\u001b[39m\n",
            "  carat depth table     x     y price_bin\n",
            "  \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[90m<fct>\u001b[39m\u001b[23m    \n",
            "\u001b[90m1\u001b[39m  0.23  61.5    55  3.95  3.98 0        \n",
            "\u001b[90m2\u001b[39m  0.21  59.8    61  3.89  3.84 0        \n",
            "\u001b[90m3\u001b[39m  0.23  56.9    65  4.05  4.07 0        \n",
            "\u001b[90m4\u001b[39m  0.29  62.4    58  4.2   4.23 0        \n",
            "\u001b[90m5\u001b[39m  0.31  63.3    58  4.34  4.35 0        \n",
            "\u001b[90m6\u001b[39m  0.24  62.8    57  3.94  3.96 0        \n",
            "[1] 53940     6\n"
          ]
        }
      ],
      "source": [
        "# INSERT CODE HERE\n",
        "require(tidyverse)\n",
        "require(class)\n",
        "\n",
        "data <- diamonds\n",
        "head(data)\n",
        "\n",
        "data <- data %>%\n",
        "  mutate(price_bin = if_else(price > mean(price), 1, 0))\n",
        "\n",
        "data$price_bin <- as.factor(data$price_bin)\n",
        "\n",
        "data_selected <- data %>%\n",
        "  select(carat, depth, table, x, y, price_bin)\n",
        "\n",
        "print(head(data_selected))\n",
        "\n",
        "print(dim(data_selected))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OE--UOxM_cZD"
      },
      "source": [
        "### Plot\n",
        "Create a scatterplot of the link between `carat` and `depth`, and use the `color` aesthetics mapping to differentiate between diamonds that cost above versus below the mean price."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "SZQl5C9H_cZD",
        "vscode": {
          "languageId": "r"
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "outputId": "db2432cc-8bc9-4a20-caa9-a5d9d2f8f18f"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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oJdtJMkx0vPyRVHna9Ya4t97y7Vwjs5zGkCAAAQdXArNspJmze6Ut0xDof4yXuh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5DVlcEP8IAlp9JdHc5XX3QrPP8LeocGJUGNds1m17tv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c5/u78wAA4CwodgBu7dSpUyKRqKKi4tGjR8v3\nazSaQ4cOzc7OhoeHWywWiqLEYrHjp9evXzebzTab7b++5k/naZqmKMpqtTr7aAAA3B0uxQK4\nNT8/v9bWVqlUmpqampycHB8f7+Hh0dfXd//+faFQ+OTJE4FAwOVyg4KCmpqaYmJi/Pz87t27\n19PTk5iY2NPT8/z58x8egEdR1ObNm1eeDwwMpCjq0qVL0dHRmZmZTBw3AACZ8Bw7AKBmZmZq\namra2trev3/PYrFCQ0NlMplSqbQ/l4SiqFevXimVSo1Gw+Vy09PTr1y50t7enpuba7PZurq6\nCgsLh4eHP3z44HjBlee9vb1lMtm7d+9CQ0MHBgaYOWYAABKh2AEAAAAQAvfYAQAAABACxQ4A\nAACAECh2AAAAAIRAsQMAAAAgBIodAAAAACFQ7AAAAAAIgWIHAAAAQAgUOwAAAABCoNgBAAAA\nEALFDgAAAIAQKHYAAAAAhPgLafJ4A8r9TTAAAAAASUVORK5CYII="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ],
      "source": [
        "# INSERT CODE HERE\n",
        "ggplot(data_selected, aes(x = carat, y = depth, color = price_bin)) +\n",
        "  geom_point() +\n",
        "  labs(title = \"Scatterplot of Carat vs. Depth\",\n",
        "       x = \"Carat\",\n",
        "       y = \"Depth\",\n",
        "       color = \"Price Category\") +\n",
        "  theme_minimal()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j-K6NEON_cZD"
      },
      "source": [
        "Based on the above scatterplot, how do you think kNN will perform using only these two variables to predict diabetes diagnosis? Which variable, carat or depth, gives us the most information about which price class the diamond will belong to?\n",
        "> Diabetes diagnosis? It will perform very poorly... because carats and depth has nothing to do with diabetes - I'm confused, is this a typo...? With respect to price class the diamond belongs to, the carat of the diamond seems to provide us with the most information - we see a clear divide in price category by carat. When the carat is greater 1 (roughly), it belongs in price cateogry 1.\n",
        ">\n",
        ">\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wT7O-CHO_cZE"
      },
      "source": [
        "### Test vs Train\n",
        "\n",
        "Before we run KNN on these data, we need to set aside a portion of the observations as our test set. Below, randomly divide the data such that 30% are allotted to the `test` set and the rest are allotted to the `train` set. Print the first few lines of each set, and print the dimensions of each set to double check your division of the data."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "Oj3YcEP0_cZE",
        "vscode": {
          "languageId": "r"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "outputId": "95bc30a5-2383-4872-92de-f0b55f0928ca"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "16182"
            ],
            "text/markdown": "16182",
            "text/latex": "16182",
            "text/plain": [
              "[1] 16182"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A tibble: 6 × 7</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>carat</th><th scope=col>depth</th><th scope=col>table</th><th scope=col>x</th><th scope=col>y</th><th scope=col>price_bin</th><th scope=col>is.test</th></tr>\n",
              "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;lgl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td>0.23</td><td>61.5</td><td>55</td><td>3.95</td><td>3.98</td><td>0</td><td>FALSE</td></tr>\n",
              "\t<tr><td>0.21</td><td>59.8</td><td>61</td><td>3.89</td><td>3.84</td><td>0</td><td> TRUE</td></tr>\n",
              "\t<tr><td>0.23</td><td>56.9</td><td>65</td><td>4.05</td><td>4.07</td><td>0</td><td>FALSE</td></tr>\n",
              "\t<tr><td>0.29</td><td>62.4</td><td>58</td><td>4.20</td><td>4.23</td><td>0</td><td>FALSE</td></tr>\n",
              "\t<tr><td>0.31</td><td>63.3</td><td>58</td><td>4.34</td><td>4.35</td><td>0</td><td>FALSE</td></tr>\n",
              "\t<tr><td>0.24</td><td>62.8</td><td>57</td><td>3.94</td><td>3.96</td><td>0</td><td>FALSE</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA tibble: 6 × 7\n\n| carat &lt;dbl&gt; | depth &lt;dbl&gt; | table &lt;dbl&gt; | x &lt;dbl&gt; | y &lt;dbl&gt; | price_bin &lt;fct&gt; | is.test &lt;lgl&gt; |\n|---|---|---|---|---|---|---|\n| 0.23 | 61.5 | 55 | 3.95 | 3.98 | 0 | FALSE |\n| 0.21 | 59.8 | 61 | 3.89 | 3.84 | 0 |  TRUE |\n| 0.23 | 56.9 | 65 | 4.05 | 4.07 | 0 | FALSE |\n| 0.29 | 62.4 | 58 | 4.20 | 4.23 | 0 | FALSE |\n| 0.31 | 63.3 | 58 | 4.34 | 4.35 | 0 | FALSE |\n| 0.24 | 62.8 | 57 | 3.94 | 3.96 | 0 | FALSE |\n\n",
            "text/latex": "A tibble: 6 × 7\n\\begin{tabular}{lllllll}\n carat & depth & table & x & y & price\\_bin & is.test\\\\\n <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <fct> & <lgl>\\\\\n\\hline\n\t 0.23 & 61.5 & 55 & 3.95 & 3.98 & 0 & FALSE\\\\\n\t 0.21 & 59.8 & 61 & 3.89 & 3.84 & 0 &  TRUE\\\\\n\t 0.23 & 56.9 & 65 & 4.05 & 4.07 & 0 & FALSE\\\\\n\t 0.29 & 62.4 & 58 & 4.20 & 4.23 & 0 & FALSE\\\\\n\t 0.31 & 63.3 & 58 & 4.34 & 4.35 & 0 & FALSE\\\\\n\t 0.24 & 62.8 & 57 & 3.94 & 3.96 & 0 & FALSE\\\\\n\\end{tabular}\n",
            "text/plain": [
              "  carat depth table x    y    price_bin is.test\n",
              "1 0.23  61.5  55    3.95 3.98 0         FALSE  \n",
              "2 0.21  59.8  61    3.89 3.84 0          TRUE  \n",
              "3 0.23  56.9  65    4.05 4.07 0         FALSE  \n",
              "4 0.29  62.4  58    4.20 4.23 0         FALSE  \n",
              "5 0.31  63.3  58    4.34 4.35 0         FALSE  \n",
              "6 0.24  62.8  57    3.94 3.96 0         FALSE  "
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "set.seed(2023)\n",
        "\n",
        "# INSERT CODE HERE\n",
        "nrow(data_selected) * .3\n",
        "#pull random sample of 30% row indices which are 16182\n",
        "test.inds <- sample(1:nrow(data_selected),16182)\n",
        "\n",
        "# TRUE/FALSE indicator for whether each observation is a test item or not.\n",
        "data_selected$is.test <- 1:nrow(data_selected) %in% test.inds\n",
        "head(data_selected)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lFtmRUBN_cZF"
      },
      "source": [
        "## 2: KNN (3 points)\n",
        "----\n",
        "Now, use the `knn()` function from the `class` library to predict `price_bin` from the `carat` and `depth`. Set `k = 3`.\n",
        "\n",
        "*Hint: Review the format required for the arguments of knn()*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "9pcL8AM9_cZG",
        "scrolled": true,
        "vscode": {
          "languageId": "r"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "a8e685ef-b648-4ec1-97d5-5952b5c43a4a"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>1</li><li>1</li><li>1</li><li>0</li><li>0</li><li>1</li><li>1</li><li>0</li><li>0</li><li>0</li></ol>\n",
              "\n",
              "<details>\n",
              "\t<summary style=display:list-item;cursor:pointer>\n",
              "\t\t<strong>Levels</strong>:\n",
              "\t</summary>\n",
              "\t<style>\n",
              "\t.list-inline {list-style: none; margin:0; padding: 0}\n",
              "\t.list-inline>li {display: inline-block}\n",
              "\t.list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "\t</style>\n",
              "\t<ol class=list-inline><li>'0'</li><li>'1'</li></ol>\n",
              "</details>"
            ],
            "text/markdown": "1. 1\n2. 1\n3. 1\n4. 0\n5. 0\n6. 1\n7. 1\n8. 0\n9. 0\n10. 0\n\n\n\n**Levels**: 1. '0'\n2. '1'\n\n\n",
            "text/latex": "\\begin{enumerate*}\n\\item 1\n\\item 1\n\\item 1\n\\item 0\n\\item 0\n\\item 1\n\\item 1\n\\item 0\n\\item 0\n\\item 0\n\\end{enumerate*}\n\n\\emph{Levels}: \\begin{enumerate*}\n\\item '0'\n\\item '1'\n\\end{enumerate*}\n",
            "text/plain": [
              " [1] 1 1 1 0 0 1 1 0 0 0\n",
              "Levels: 0 1"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "set.seed(2023)\n",
        "# INSERT CODE HERE\n",
        "\n",
        "library(class)\n",
        "# training data pulls the \"not test\" rows\n",
        "train.preds <- cbind(data_selected$depth[-test.inds], data_selected$carat[-test.inds])\n",
        "train.price_bin <- data_selected$price_bin[-test.inds]\n",
        "\n",
        "# testing data pulls the test rows\n",
        "test.preds <- cbind(data_selected$depth[test.inds], data_selected$carat[test.inds])\n",
        "\n",
        "# run kNN\n",
        "test.price_bin.knn <- knn(train.preds, test.preds, train.price_bin, k = 3)\n",
        "\n",
        "# print first 10 test price_bin predictions\n",
        "test.price_bin.knn[1:10]\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RXnTKbdi_cZG"
      },
      "source": [
        "Now, output a confusion matrix and calculate the test error to evaluate model performance."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "qhwTYq9B_cZH",
        "vscode": {
          "languageId": "r"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        },
        "outputId": "9c7f3070-c4b6-40e9-fe27-b8175985db83"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "         actual\n",
              "predicted    0    1\n",
              "        0 9707  316\n",
              "        1  539 5620"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"---\"\n",
            "[1] \"Accuracy: 0.947163515016685\"\n"
          ]
        }
      ],
      "source": [
        "# INSERT CODE HERE\n",
        "# new variable for each observation's predicted price bin.\n",
        "data_selected$price_bin_pred <- data_selected$price_bin\n",
        "\n",
        "# add the KNN predictions for test obs to dataset.\n",
        "data_selected$price_bin_pred[test.inds] <- test.price_bin.knn\n",
        "\n",
        "# in which cases does the observed Species equal the predicted?\n",
        "data_selected$KNN_correct <- data_selected$price_bin == data_selected$price_bin_pred\n",
        "\n",
        "confusion_df <- data.frame(predicted = test.price_bin.knn,actual = data_selected$price_bin[test.inds])\n",
        "table(confusion_df)\n",
        "print(\"---\")\n",
        "print(paste(\"Accuracy:\",mean(confusion_df$predicted == confusion_df$actual)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mOQSLQ37_cZK"
      },
      "source": [
        "How did your model perform?\n",
        "> * Write your response here\n",
        ">\n",
        "> * Performed with very high accuracy of 94.7%. From the confusion matrix, there doesn't seem to be any particular bias towards one response, meaning that the model is correctly classifying both price bins.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p0lvEh3F_cZL"
      },
      "source": [
        "Let's try to improve our model by adding all of the other variables in our data set as predictors. Rerun your `knn()` below, keeping `k = 3`. Again, output a confusion matrix and error rate for your updated model fit."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "KWsncoDP_cZL",
        "vscode": {
          "languageId": "r"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        },
        "outputId": "3da5037d-2ad7-4a35-9971-07bb39809d08"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "         actual\n",
              "predicted    0    1\n",
              "        0 9728  391\n",
              "        1  518 5545"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"---\"\n",
            "[1] \"Accuracy: 0.943826473859844\"\n"
          ]
        }
      ],
      "source": [
        "set.seed(2023)\n",
        "# INSERT CODE HERE\n",
        "# carat, depth, table, x, y are the variables.\n",
        "# training data pulls the \"not test\" rows\n",
        "train.preds <- cbind(data_selected$depth[-test.inds], data_selected$carat[-test.inds], data_selected$table[-test.inds], data_selected$x[-test.inds], data_selected$y[-test.inds])\n",
        "train.price_bin <- data_selected$price_bin[-test.inds]\n",
        "\n",
        "# testing data pulls the test rows\n",
        "test.preds <- cbind(data_selected$depth[test.inds], data_selected$carat[test.inds], data_selected$table[test.inds], data_selected$x[test.inds], data_selected$y[test.inds])\n",
        "\n",
        "# run kNN\n",
        "test.price_bin.knn <- knn(train.preds, test.preds, train.price_bin, k = 3)\n",
        "\n",
        "# new variable for each observation's predicted price bin.\n",
        "data_selected$price_bin_pred <- data_selected$price_bin\n",
        "\n",
        "# add the KNN predictions for test obs to dataset.\n",
        "data_selected$price_bin_pred[test.inds] <- test.price_bin.knn\n",
        "\n",
        "# in which cases does the observed Species equal the predicted?\n",
        "data_selected$KNN_correct <- data_selected$price_bin == data_selected$price_bin_pred\n",
        "\n",
        "confusion_df <- data.frame(predicted = test.price_bin.knn, actual = data_selected$price_bin[test.inds])\n",
        "table(confusion_df)\n",
        "print(\"---\")\n",
        "print(paste(\"Accuracy:\",mean(confusion_df$predicted == confusion_df$actual)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t2Dyykaf_cZM"
      },
      "source": [
        "Did your model predictions improve?\n",
        "> * Write your response here\n",
        ">\n",
        "> * No the model predictions didn't improve - it actually fell by a small amount (about .3%)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WYHprC4m_cZN"
      },
      "source": [
        "# 3: for loop (3 points)\n",
        "----\n",
        "\n",
        "So adding additional predictors didn't shift our error much. Let's see if adjusting `k` has a larger impact on model accuracy.\n",
        "\n",
        "Using your initial model above with just `carat` and `depth`, run a `for loop` that runs the same model 30 times, for `k = 1:30`.\n",
        "\n",
        "Output a data frame that has `k` and the overall `error` as columns.\n",
        "\n",
        "The structure of the output data frame and `for loop` are provided for you below. Note that your loop will take a minute or two to run because there are so many observations in the dataset. It may be helpful while you are writing and testing your loop to run it on a subset of the data with only a handful of rows."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "D-GAvxGH_cZN",
        "scrolled": false,
        "vscode": {
          "languageId": "r"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "dce801e0-e7a8-401e-9981-f15fd42a7755"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 6 × 2</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>k</th><th scope=col>error</th></tr>\n",
              "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;lgl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>1</th><td>1</td><td>NA</td></tr>\n",
              "\t<tr><th scope=row>2</th><td>2</td><td>NA</td></tr>\n",
              "\t<tr><th scope=row>3</th><td>3</td><td>NA</td></tr>\n",
              "\t<tr><th scope=row>4</th><td>4</td><td>NA</td></tr>\n",
              "\t<tr><th scope=row>5</th><td>5</td><td>NA</td></tr>\n",
              "\t<tr><th scope=row>6</th><td>6</td><td>NA</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA data.frame: 6 × 2\n\n| <!--/--> | k &lt;int&gt; | error &lt;lgl&gt; |\n|---|---|---|\n| 1 | 1 | NA |\n| 2 | 2 | NA |\n| 3 | 3 | NA |\n| 4 | 4 | NA |\n| 5 | 5 | NA |\n| 6 | 6 | NA |\n\n",
            "text/latex": "A data.frame: 6 × 2\n\\begin{tabular}{r|ll}\n  & k & error\\\\\n  & <int> & <lgl>\\\\\n\\hline\n\t1 & 1 & NA\\\\\n\t2 & 2 & NA\\\\\n\t3 & 3 & NA\\\\\n\t4 & 4 & NA\\\\\n\t5 & 5 & NA\\\\\n\t6 & 6 & NA\\\\\n\\end{tabular}\n",
            "text/plain": [
              "  k error\n",
              "1 1 NA   \n",
              "2 2 NA   \n",
              "3 3 NA   \n",
              "4 4 NA   \n",
              "5 5 NA   \n",
              "6 6 NA   "
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "# this is provided\n",
        "# setting up empty table to store for loop output\n",
        "output  <- data.frame(k = seq(1:30),\n",
        "                     error = rep(NA, 30))\n",
        "head(output)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "we6mzfCJ_cZN",
        "vscode": {
          "languageId": "r"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "bf4aff7a-3cbb-4ec7-ab84-852a255a51d2"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 6 × 2</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>k</th><th scope=col>error</th></tr>\n",
              "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>1</th><td>1</td><td>0.05314547</td></tr>\n",
              "\t<tr><th scope=row>2</th><td>2</td><td>0.05363985</td></tr>\n",
              "\t<tr><th scope=row>3</th><td>3</td><td>0.05382524</td></tr>\n",
              "\t<tr><th scope=row>4</th><td>4</td><td>0.05258930</td></tr>\n",
              "\t<tr><th scope=row>5</th><td>5</td><td>0.05246570</td></tr>\n",
              "\t<tr><th scope=row>6</th><td>6</td><td>0.05240391</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA data.frame: 6 × 2\n\n| <!--/--> | k &lt;int&gt; | error &lt;dbl&gt; |\n|---|---|---|\n| 1 | 1 | 0.05314547 |\n| 2 | 2 | 0.05363985 |\n| 3 | 3 | 0.05382524 |\n| 4 | 4 | 0.05258930 |\n| 5 | 5 | 0.05246570 |\n| 6 | 6 | 0.05240391 |\n\n",
            "text/latex": "A data.frame: 6 × 2\n\\begin{tabular}{r|ll}\n  & k & error\\\\\n  & <int> & <dbl>\\\\\n\\hline\n\t1 & 1 & 0.05314547\\\\\n\t2 & 2 & 0.05363985\\\\\n\t3 & 3 & 0.05382524\\\\\n\t4 & 4 & 0.05258930\\\\\n\t5 & 5 & 0.05246570\\\\\n\t6 & 6 & 0.05240391\\\\\n\\end{tabular}\n",
            "text/plain": [
              "  k error     \n",
              "1 1 0.05314547\n",
              "2 2 0.05363985\n",
              "3 3 0.05382524\n",
              "4 4 0.05258930\n",
              "5 5 0.05246570\n",
              "6 6 0.05240391"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "# training data pulls the \"not test\" rows\n",
        "train.preds <- cbind(data_selected$depth[-test.inds], data_selected$carat[-test.inds])\n",
        "train.price_bin <- data_selected$price_bin[-test.inds]\n",
        "\n",
        "# testing data pulls the test rows\n",
        "test.preds <- cbind(data_selected$depth[test.inds], data_selected$carat[test.inds])\n",
        "\n",
        "for (k in seq(1:30)) {\n",
        "    knn_fits  <- knn(train.preds, test.preds, train.price_bin, k = k) # your knn function here\n",
        "\n",
        "    #overall error\n",
        "    conf_df  <- table(predicted = knn_fits, actual = data_selected$price_bin[test.inds]) # data frame of test predictions versus actual test\n",
        "    output$error[k] <- 1 - mean(knn_fits == data_selected$price_bin[test.inds])\n",
        "\n",
        "}\n",
        "head(output)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ofk0jafy_cZN"
      },
      "source": [
        "*Create* a line plot of your `output` object using `ggplot`. Add a (non-linear) `geom_smooth` layer."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "9Oia_P98_cZN",
        "scrolled": false,
        "vscode": {
          "languageId": "r"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 567
        },
        "outputId": "a45b768f-4946-47d1-99a7-a9612dadef59"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\u001b[1m\u001b[22m`geom_smooth()` using method = 'loess' and formula = 'y ~ x'\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 1 × 2</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>k</th><th scope=col>error</th></tr>\n",
              "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>17</th><td>17</td><td>0.0504264</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA data.frame: 1 × 2\n\n| <!--/--> | k &lt;int&gt; | error &lt;dbl&gt; |\n|---|---|---|\n| 17 | 17 | 0.0504264 |\n\n",
            "text/latex": "A data.frame: 1 × 2\n\\begin{tabular}{r|ll}\n  & k & error\\\\\n  & <int> & <dbl>\\\\\n\\hline\n\t17 & 17 & 0.0504264\\\\\n\\end{tabular}\n",
            "text/plain": [
              "   k  error    \n",
              "17 17 0.0504264"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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EGwAwAACBEEOwAAgBBBsAMAAAgRBDsA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cA7l9YotkPxYkF2Ttje6ettXjW/QUJYA+U3pyKrW2Q0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          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ],
      "source": [
        "# INSERT CODE HERE\n",
        "ggplot(output, aes(x = k, y = error)) +\n",
        "  geom_line() + # line plot specified\n",
        "  geom_smooth() +  # Add a non-linear smooth line\n",
        "  labs(title = \"Error Rate for Different k in kNN\",\n",
        "       x = \"k Value\",\n",
        "       y = \"Error Rate\") +\n",
        "  theme_minimal()\n",
        "\n",
        "output[which.min(output$error), ]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EG2gQhU0_cZO"
      },
      "source": [
        "Interpret your plot. What would you select as the best value of `k`? How much does this improve your test error?\n",
        "> * *Write your response here*\n",
        ">\n",
        "> * As k increases, the error rate decreases. But there is a visible minima in the error rate curve, suggesting a point of optimal balance between bias and variance. After reaching the minima, the error rate starts to increase again slightly as k grows further. The best value of k appears to be roughly between 16 and 20 - visually, I'm going with 19. The imporvement in test error is low, around 0.003.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R5GYp8mt_cZO"
      },
      "source": [
        "# 4: Standardizing predictors (2)\n",
        "-----\n",
        "\n",
        "Because knn is based on distances between points, it is very sensitive to the scale of your variables. Looking at our predictor variables, we can see that `carat` and `depth` are orders of magnitude different in terms of scales. Maybe we can improve our fit even more by addressing this!\n",
        "\n",
        "Below, use the `scale()` function to standardize your predictors. (Note that you don't need to standardize `price_bin`.)\n",
        "\n",
        "Then, run your model a final time with your standardized predictors (just `carat` and `depth` still). Set `k` to the optimal value you determined in your plot above. Output the confusion matrix and error rate again."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "DVAfP_iB_cZO",
        "vscode": {
          "languageId": "r"
        },
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        },
        "outputId": "e93133c5-8950-4222-de3f-db408e3c7e85"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "         actual\n",
            "predicted    0    1\n",
            "        0 4363  857\n",
            "        1 2827 3300\n",
            "[1] 0.05054999\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.949450006179706"
            ],
            "text/markdown": "0.949450006179706",
            "text/latex": "0.949450006179706",
            "text/plain": [
              "[1] 0.94945"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "set.seed(2023)\n",
        "#INSERT CODE HERE\n",
        "\n",
        "# standardize the predictors in the training and testing sets\n",
        "train.preds.scaled <- scale(train.preds)\n",
        "test.preds.scaled <- scale(test.preds)\n",
        "\n",
        "# kNN on the standardized predictors\n",
        "test.price_bin.knn.scaled <- knn(train.preds.scaled, test.preds.scaled, train.price_bin, k = 19)\n",
        "\n",
        "# create a confusion matrix from the predictions and the actual test set values\n",
        "conf_matrix_scaled <- table(predicted = test.price_bin.knn.scaled, actual = train.price_bin[test.inds])\n",
        "\n",
        "print(conf_matrix_scaled)\n",
        "\n",
        "# calculate the error from the confusion matrix\n",
        "error_rate_scaled <- 1 - mean(test.price_bin.knn.scaled  == data_selected$price_bin[test.inds])\n",
        "\n",
        "print(error_rate_scaled)\n",
        "mean(test.price_bin.knn.scaled  == data_selected$price_bin[test.inds])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yl3pqjEA_cZO"
      },
      "source": [
        "What impact did rescaling the data have on your error rate?\n",
        "> * *Write response here*\n",
        ">\n",
        "> * scaling the data reduced the error rate slightly. but... there appears to be more incorrect predictions with the scaled data too.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XSFcQXke_cZO"
      },
      "source": [
        "**DUE:** 5pm March 20, 2024\n",
        "\n",
        "**IMPORTANT** Did you collaborate with anyone on this assignment? If so, list their names here.\n",
        "> *Someone's Name*\n",
        ">\n",
        ">\n"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "R",
      "language": "R",
      "name": "ir"
    },
    "language_info": {
      "codemirror_mode": "r",
      "file_extension": ".r",
      "mimetype": "text/x-r-source",
      "name": "R",
      "pygments_lexer": "r",
      "version": "4.2.0"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}