notebooks/Part I/Chapter 2 Data Relationships.ipynb

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   "source": [
    "# Introduction\n",
    "The examples in this chapter from 1-9 aren't really examples at all; we begin with example 2.9.  If you went through Chapter 1, you can continue here.  If not, then you'll need to perform the setup steps below.\n",
    "\n",
    "# Setup\n",
    "First load the IPS (short for Introduction to the Practice of Statistics) package and dependencies. If you're doing this for the first time, there may be a great deal more output as the dependent packages are download and compiled. This typically only happens once."
   ]
  },
  {
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   "id": "75b1d1df-3bd0-473a-8241-0bf8c02a1b4e",
   "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "To load \"ips\":\n",
      "  Load 1 ASDF system:\n",
      "    ips\n",
      "; Loading \"ips\"\n",
      "[package yason.system]."
     ]
    },
    {
     "data": {
      "text/plain": [
       "(:IPS)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "(ql:quickload :ips)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f4354750-45f1-4ed1-a568-b8efcf50c063",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#<PACKAGE \"IPS\">"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(in-package :ips)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3deacaa-fae7-4700-8f19-e0cd9b8e7507",
   "metadata": {},
   "source": [
    "# 2.2 Scatterplots\n",
    "### Example 2.9 Laundry detergents\n",
    "With the setup complete, we can now load the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2076755f-c6fc-4ee7-b148-fe1fdedfcc1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#<DATA-FRAME (53 observations of 3 variables)>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(defdf detergents-1 (read-csv ips:eg02-08))"
   ]
  },
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   "execution_count": 5,
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"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ips:plot\n",
    " (vega:defplot detergents-plot-1\n",
    "   `(:title \"Detergents\"\n",
    "     :data (:values ,detergents-1)\n",
    "     :mark :point\n",
    "     :encoding (:x (:field :price  :type \"quantitative\" :title \"Price per load (cents)\")\n",
    "                :y (:field :rating :type \"quantitative\" )))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0823848e-7762-47db-86a0-868b08e18dc1",
   "metadata": {},
   "source": [
    "The second figure in this example is the plot with the outlier removed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "738f096d-91d8-4a89-a9bc-1fa9b9c32aec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#<DATA-FRAME (52 observations of 3 variables)>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(defdf detergents-2 (filter-rows detergents-1 '(< price 40)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3c5ac9fc-0816-47a4-9f8e-4b22e7515ba3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v4+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
       "data": {
        "values": [
         {
          "price": 12,
          "rating": 32,
          "type": "Liquid"
         },
         {
          "price": 6,
          "rating": 35,
          "type": "Liquid"
         },
         {
          "price": 28,
          "rating": 38,
          "type": "Liquid"
         },
         {
          "price": 28,
          "rating": 40,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 71,
          "type": "Liquid"
         },
         {
          "price": 7,
          "rating": 60,
          "type": "Liquid"
         },
         {
          "price": 29,
          "rating": 37,
          "type": "Liquid"
         },
         {
          "price": 12,
          "rating": 61,
          "type": "Liquid"
         },
         {
          "price": 8,
          "rating": 31,
          "type": "Liquid"
         },
         {
          "price": 11,
          "rating": 51,
          "type": "Liquid"
         },
         {
          "price": 25,
          "rating": 81,
          "type": "Liquid"
         },
         {
          "price": 25,
          "rating": 71,
          "type": "Liquid"
         },
         {
          "price": 19,
          "rating": 68,
          "type": "Liquid"
         },
         {
          "price": 23,
          "rating": 81,
          "type": "Powder"
         },
         {
          "price": 5,
          "rating": 35,
          "type": "Liquid"
         },
         {
          "price": 26,
          "rating": 46,
          "type": "Liquid"
         },
         {
          "price": 26,
          "rating": 47,
          "type": "Powder"
         },
         {
          "price": 13,
          "rating": 61,
          "type": "Powder"
         },
         {
          "price": 25,
          "rating": 43,
          "type": "Powder"
         },
         {
          "price": 8,
          "rating": 42,
          "type": "Liquid"
         },
         {
          "price": 21,
          "rating": 49,
          "type": "Liquid"
         },
         {
          "price": 10,
          "rating": 47,
          "type": "Liquid"
         },
         {
          "price": 11,
          "rating": 42,
          "type": "Liquid"
         },
         {
          "price": 7,
          "rating": 42,
          "type": "Liquid"
         },
         {
          "price": 25,
          "rating": 71,
          "type": "Powder"
         },
         {
          "price": 25,
          "rating": 85,
          "type": "Liquid"
         },
         {
          "price": 20,
          "rating": 74,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 66,
          "type": "Liquid"
         },
         {
          "price": 21,
          "rating": 46,
          "type": "Liquid"
         },
         {
          "price": 22,
          "rating": 64,
          "type": "Liquid"
         },
         {
          "price": 22,
          "rating": 52,
          "type": "Liquid"
         },
         {
          "price": 24,
          "rating": 48,
          "type": "Liquid"
         },
         {
          "price": 26,
          "rating": 53,
          "type": "Liquid"
         },
         {
          "price": 8,
          "rating": 51,
          "type": "Powder"
         },
         {
          "price": 12,
          "rating": 73,
          "type": "Liquid"
         },
         {
          "price": 30,
          "rating": 58,
          "type": "Liquid"
         },
         {
          "price": 11,
          "rating": 70,
          "type": "Liquid"
         },
         {
          "price": 20,
          "rating": 39,
          "type": "Liquid"
         },
         {
          "price": 16,
          "rating": 46,
          "type": "Liquid"
         },
         {
          "price": 12,
          "rating": 44,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 25,
          "type": "Liquid"
         },
         {
          "price": 13,
          "rating": 58,
          "type": "Powder"
         },
         {
          "price": 14,
          "rating": 58,
          "type": "Liquid"
         },
         {
          "price": 13,
          "rating": 65,
          "type": "Liquid"
         },
         {
          "price": 18,
          "rating": 44,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 29,
          "type": "Liquid"
         },
         {
          "price": 8,
          "rating": 41,
          "type": "Liquid"
         },
         {
          "price": 10,
          "rating": 57,
          "type": "Liquid"
         },
         {
          "price": 12,
          "rating": 53,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 60,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 58,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 60,
          "type": "Liquid"
         }
        ]
       },
       "encoding": {
        "x": {
         "field": "price",
         "title": "Price per load (cents)",
         "type": "quantitative"
        },
        "y": {
         "field": "rating",
         "type": "quantitative"
        }
       },
       "mark": "point",
       "title": "Detergents"
      },
      "image/png": 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"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ips:plot\n",
    " (vega:defplot detergents-plot-2\n",
    "   `(:title \"Detergents\"\n",
    "     :data (:values ,detergents-2)\n",
    "     :mark :point\n",
    "     :encoding (:x (:field :price  :type \"quantitative\" :title \"Price per load (cents)\")\n",
    "                :y (:field :rating :type \"quantitative\" )))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9a4587a-3d5f-4a9c-8143-1cca0f61eb01",
   "metadata": {},
   "source": [
    "### Example 2.10 Scatterplot with a straight line"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a559e35e-3c58-4a2a-a3d0-106e1aec6cb0",
   "metadata": {},
   "source": [
    "Here we obtain the slope and intercept of a line that forms a linear regression for our data points.  To plot that line we'll use the 'fit-line' function in the SCTPLT package.  This package contains functions useful for working with scatterplots in Vega."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "297eb9c2-9dda-41f2-80a9-7bb2a4e78b5c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v4+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
       "data": {
        "values": [
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          "rating": 32,
          "type": "Liquid"
         },
         {
          "price": 6,
          "rating": 35,
          "type": "Liquid"
         },
         {
          "price": 28,
          "rating": 38,
          "type": "Liquid"
         },
         {
          "price": 28,
          "rating": 40,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 71,
          "type": "Liquid"
         },
         {
          "price": 7,
          "rating": 60,
          "type": "Liquid"
         },
         {
          "price": 29,
          "rating": 37,
          "type": "Liquid"
         },
         {
          "price": 12,
          "rating": 61,
          "type": "Liquid"
         },
         {
          "price": 8,
          "rating": 31,
          "type": "Liquid"
         },
         {
          "price": 11,
          "rating": 51,
          "type": "Liquid"
         },
         {
          "price": 25,
          "rating": 81,
          "type": "Liquid"
         },
         {
          "price": 25,
          "rating": 71,
          "type": "Liquid"
         },
         {
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          "rating": 68,
          "type": "Liquid"
         },
         {
          "price": 23,
          "rating": 81,
          "type": "Powder"
         },
         {
          "price": 5,
          "rating": 35,
          "type": "Liquid"
         },
         {
          "price": 26,
          "rating": 46,
          "type": "Liquid"
         },
         {
          "price": 26,
          "rating": 47,
          "type": "Powder"
         },
         {
          "price": 13,
          "rating": 61,
          "type": "Powder"
         },
         {
          "price": 25,
          "rating": 43,
          "type": "Powder"
         },
         {
          "price": 8,
          "rating": 42,
          "type": "Liquid"
         },
         {
          "price": 21,
          "rating": 49,
          "type": "Liquid"
         },
         {
          "price": 10,
          "rating": 47,
          "type": "Liquid"
         },
         {
          "price": 11,
          "rating": 42,
          "type": "Liquid"
         },
         {
          "price": 7,
          "rating": 42,
          "type": "Liquid"
         },
         {
          "price": 25,
          "rating": 71,
          "type": "Powder"
         },
         {
          "price": 25,
          "rating": 85,
          "type": "Liquid"
         },
         {
          "price": 20,
          "rating": 74,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 66,
          "type": "Liquid"
         },
         {
          "price": 21,
          "rating": 46,
          "type": "Liquid"
         },
         {
          "price": 22,
          "rating": 64,
          "type": "Liquid"
         },
         {
          "price": 22,
          "rating": 52,
          "type": "Liquid"
         },
         {
          "price": 24,
          "rating": 48,
          "type": "Liquid"
         },
         {
          "price": 26,
          "rating": 53,
          "type": "Liquid"
         },
         {
          "price": 8,
          "rating": 51,
          "type": "Powder"
         },
         {
          "price": 12,
          "rating": 73,
          "type": "Liquid"
         },
         {
          "price": 30,
          "rating": 58,
          "type": "Liquid"
         },
         {
          "price": 11,
          "rating": 70,
          "type": "Liquid"
         },
         {
          "price": 20,
          "rating": 39,
          "type": "Liquid"
         },
         {
          "price": 16,
          "rating": 46,
          "type": "Liquid"
         },
         {
          "price": 12,
          "rating": 44,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 25,
          "type": "Liquid"
         },
         {
          "price": 13,
          "rating": 58,
          "type": "Powder"
         },
         {
          "price": 14,
          "rating": 58,
          "type": "Liquid"
         },
         {
          "price": 13,
          "rating": 65,
          "type": "Liquid"
         },
         {
          "price": 18,
          "rating": 44,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 29,
          "type": "Liquid"
         },
         {
          "price": 8,
          "rating": 41,
          "type": "Liquid"
         },
         {
          "price": 10,
          "rating": 57,
          "type": "Liquid"
         },
         {
          "price": 12,
          "rating": 53,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 60,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 58,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 60,
          "type": "Liquid"
         }
        ]
       },
       "layer": [
        {
         "encoding": {
          "x": {
           "field": "price",
           "title": "Price per load (cents)",
           "type": "quantitative"
          },
          "y": {
           "field": "rating",
           "type": "quantitative"
          }
         },
         "mark": "point"
        },
        {
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         "encoding": {
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          },
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         },
         "mark": {
          "color": "red",
          "interpolate": "basis",
          "type": "line"
         }
        }
       ],
       "title": "Detergents",
       "width": 350
      },
      "image/png": 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"
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ips:plot\n",
    "   (vega:defplot detergents-plot-2\n",
    "     `(:title \"Detergents\"\n",
    "       :width 350\n",
    "       :data (:values ,detergents-2)\n",
    "       :layer #((:mark :point\n",
    "                 :encoding (:x (:field :price  :type \"quantitative\" :title \"Price per load (cents)\")\n",
    "                            :y (:field :rating :type \"quantitative\")))\n",
    "       ,(sctplt:fit-line detergents-2:price detergents-2:rating)))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f8e7470-058b-49c4-9553-f6c36e94dfaa",
   "metadata": {},
   "source": [
    "### Example 2.11: Education spending and population: Benchmarking"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3976bd6-58fe-4eaa-8d5d-6f2b181ca24d",
   "metadata": {},
   "source": [
    "The last example had data points spread out widely from the line, indicating only a weak relationship between price and rating.\n",
    "In this example we see a stronger positive relationship in the spending of states.  We expect that states with higher populations spend more than states with lower populations.  Are some states spending more or less based on their populations?  This type of exercise is known as **benchmarking**, comparing a process or expenditure of an organisation with organisations that share similar characteristics.\n",
    "The figure below shows a scatter plot of state spending vs. population, with a fitted straight line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b3a8b0ac-4441-4c37-950e-f5e2bfd89031",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#<DATA-FRAME (50 observations of 3 variables)>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(defdf edu-spending (read-csv eg02-11))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d577346f-2351-4eef-8783-3533a79b8c78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v4+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
       "data": {
        "values": [
         {
          "population": 0.6,
          "spending": 2.7,
          "state": "Wyoming"
         },
         {
          "population": 5.8000004,
          "spending": 18.9,
          "state": "Wisconsin"
         },
         {
          "population": 1.8,
          "spending": 6,
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"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ips:plot\n",
    " (vega:defplot education-spending\n",
    "   `(:title \"Education Spending\"\n",
    "     :data (:values ,edu-spending)\n",
    "     :layer #((:mark :point\n",
    "               :encoding (:x (:field :population  :type \"quantitative\" :title \"Population (millions)\")\n",
    "                          :y (:field :spending    :type \"quantitative\" :title \"Spending ($ billions)\")))\n",
    "              ,(sctplt:fit-line edu-spending:population edu-spending:spending)))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b13850c2-e562-4965-b2e8-1a1e27f15546",
   "metadata": {},
   "source": [
    "### Example 2.12 Calcium retention\n",
    "This example trys to answer the question of how much calcium our bodies need.  In the study, the researchers measured the amount of calcium retained by the body as a response variable and the amount consumed as an explanatory variable.  The results are plotted below, with a curve fitted to the data for children aged 11 to 15 years.  You can clearly see there is a relationship, however it is not linear across the range of values.  It starts in a relatively linear manner, then begins to reach a plateau. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "bb640c89-3c3e-4d82-8c89-b2ef952ea032",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "T"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(load #P\"IPS:DATA;calcium-retention\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "29fb75bf-b5d0-4af6-af90-148b491ea366",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v4+json": {
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       "data": {
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         {
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       },
       "layer": [
        {
         "encoding": {
          "x": {
           "field": "caintake",
           "scale": {
            "domain": [
             500,
             2000
            ]
           },
           "title": "Calcium intake (mg/d)",
           "type": "quantitative"
          },
          "y": {
           "field": "caretention",
           "title": "Calcium retention (mg/d)",
           "type": "quantitative"
          }
         },
         "mark": "point"
        },
        {
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"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ips:plot\n",
    " (vega:defplot calcium-retention-plot\n",
    "   `(:title \"Calcium Retention\"\n",
    "     :data (:values ,calcium-retention)\n",
    "     :width 350\n",
    "     :layer #((:mark :point\n",
    "               :encoding (:x (:field :caintake  :type \"quantitative\" :title \"Calcium intake (mg/d)\" :scale (domain #(500 2000)))\n",
    "                          :y (:field :caretention :type \"quantitative\" :title \"Calcium retention (mg/d)\")))\n",
    "              ,(sctplt:fit-lowess calcium-retention:caintake calcium-retention:caretention)))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4fdcbcb-c7c7-4579-8b80-cde980f7b3b9",
   "metadata": {},
   "source": [
    "## The log transformation\n",
    "One of the most important transformations is the **log transformation**, that is often used to reduce skewness of a variable.  For more information, see [Log-transformation and its implications for data analysis (2014)](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4120293/).\n",
    "\n",
    "### Example 2.13 Calcium retention with logarithms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d0623c49-50a2-45ee-9a47-5772c5653fd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v4+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
       "data": {
        "values": [
         {
          "caintake": 1834.8001,
          "caretention": 581.7,
          "logret": 6.365955
         },
         {
          "caintake": 1816.3,
          "caretention": 344.6,
          "logret": 5.842384
         },
         {
          "caintake": 1792,
          "caretention": 735.10003,
          "logret": 6.600007
         },
         {
          "caintake": 1777.7,
          "caretention": 640,
          "logret": 6.461468
         },
         {
          "caintake": 1715,
          "caretention": 592.60005,
          "logret": 6.3845193
         },
         {
          "caintake": 1666.9,
          "caretention": 307,
          "logret": 5.7268476
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"
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ips:plot\n",
    " (vega:defplot calcium-retention-linear-fit\n",
    "   `(:title \"Calcium Retention\"\n",
    "     :data (:values ,calcium-retention)\n",
    "     :width 350\n",
    "     :layer #((:mark :point\n",
    "               :encoding (:x (:field :caintake  :type \"quantitative\" :title \"Calcium intake (mg/d)\" :scale (domain #(600 2000)))\n",
    "                          :y (:field :logret :type \"quantitative\" :title \"Log calcium retention (mg/d)\" :scale (domain #(4 7)))))\n",
    "              ,(sctplt:fit-line calcium-retention:caintake calcium-retention:logret)))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b60bf54-e932-4a15-bfc7-6d6acd8778c9",
   "metadata": {},
   "source": [
    "### Example 2.14 Education spending and population with logarithms\n",
    "In this example we will take the log of both variables and fit a line.  Note how we're creating a temporary data frame here rather than modifying the one in the workspace.  This is a common practice when we're experimenting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2c853530-37d7-430b-bf03-32d234ce9b15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v4+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
       "data": {
        "values": [
         {
          "population": -0.51082563,
          "spending": 0.9932518
         },
         {
          "population": 1.7578581,
          "spending": 2.939162
         },
         {
          "population": 0.5877867,
          "spending": 1.7917594
         },
         {
          "population": 1.9740811,
          "spending": 3.054001
         },
         {
          "population": 2.1282318,
          "spending": 3.2148677
         },
         {
          "population": -0.51082563,
          "spending": 0.9162907
         },
         {
          "population": 1.0986123,
          "spending": 2.3025851
         },
         {
          "population": 3.310543,
          "spending": 4.4931206
         },
         {
          "population": 1.8870696,
          "spending": 2.7663192
         },
         {
          "population": -0.105360515,
          "spending": 0.74193734
         },
         {
          "population": 1.5892352,
          "spending": 2.3795462
         },
         {
          "population": 0.095310175,
          "spending": 1.252763
         },
         {
          "population": 2.549445,
          "spending": 3.624341
         },
         {
          "population": 1.3862944,
          "spending": 2.4248028
         },
         {
          "population": 1.3609765,
          "spending": 2.3795462
         },
         {
          "population": 2.4510053,
          "spending": 3.4688562
         },
         {
          "population": -0.22314355,
          "spending": 1.0986123
         },
         {
          "population": 2.3025851,
          "spending": 3.407842
         },
         {
          "population": 2.985682,
          "spending": 4.308111
         },
         {
          "population": 0.74193734,
          "spending": 1.8870696
         },
         {
          "population": 2.1972246,
          "spending": 3.6000484
         },
         {
          "population": 0.26236427,
          "spending": 1.4350846
         },
         {
          "population": 1.0647108,
          "spending": 1.740466
         },
         {
          "population": 0.64185387,
          "spending": 1.8718022
         },
         {
          "population": 0,
          "spending": 0.9932518
         },
         {
          "population": 1.8082888,
          "spending": 2.791165
         },
         {
          "population": 1.0986123,
          "spending": 2.091864
         },
         {
          "population": 1.7047481,
          "spending": 2.8735647
         },
         {
          "population": 2.2925349,
          "spending": 3.1780538
         },
         {
          "population": 1.9169226,
          "spending": 3.054001
         },
         {
          "population": 1.7917594,
          "spending": 2.9231617
         },
         {
          "population": 0.26236427,
          "spending": 1.4350846
         },
         {
          "population": 1.5475625,
          "spending": 2.5726122
         },
         {
          "population": 1.4816046,
          "spending": 2.549445
         },
         {
          "population": 1.0647108,
          "spending": 2.1517622
         },
         {
          "population": 1.1314021,
          "spending": 2.3795462
         },
         {
          "population": 1.8870696,
          "spending": 2.8622007
         },
         {
          "population": 2.5572273,
          "spending": 3.6375862
         },
         {
          "population": 0.53062826,
          "spending": 1.2237755
         },
         {
          "population": 0.33647224,
          "spending": 1.1939224
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O2rFCNfxsk3f69OkB76GSEUvSvDLoqelhhQQuKCyBg4WlEIdHRYlxtdabPJcuooO7wAMWZcA1H2QzsA6/8N9wzVNT5IC7XDtsyYvjQ/MYd5cDXd8qgyKRVwY9NcmrHzESdVPeQU0bI1nPVp2HEyUVvtSbz473bVABwLJnFgH07x84q58NSMOWvGQ2hwc5bMiy60XNyGF07nvk+GloFhsNT//5GYjf6rtjat+KbHi7uoV5Ll0bozDrn42mPCnqeLeZyEvklZVIM3LwYyI890WnCUy9iVr46/3H4XcLH4Nr9+5kXTj74XpYVS+RaWfTRNg2Om3WPxtNeVLUMXk96Y2uUTKb5VBWVfj4qP2d8aIZfWnAz6H97h1Q0jwJVj80FQ52vUEDyk1nClXxs3RUhIiJAfmzZ88G3MBy6yHyyiGpqvDpyatp04ICKBnxW2Yqn2l5Neyflwmb4ttrIN2V2tlVZwpV8bNEXn83abhJYCJv3SYvrnmXrd0JJ05XQIuSH+GuN+ZBu++2w6mEJNj5r8+lj4LM0A1b8voLyncrCJ+DSuQ1E6/A36sqfOKoPv3mCLy3fD28+MI49vF37a+Dlye9ANclt4BHhveWA8iktqr4mWpeIi9tWMkyR08OXM/i07RJI+3qmU8XZ8Etj6Szzwu794btb/wN9h4+yYIVRB9o2b74qx+25NWvd/ngyWz2QoyctamK8Om9pXC0uM699cxBaHzHIDb4sj63QMyWXPa3lWAFZ4jVrKUKfvqxmmperMAD8nlYoJuB+Ng+mc1yIqiC8PFgdz5SdMLAI592u7fDmOd8nlJ7r02BD59/g2njdknxUFpWyUIH3TwWqnOaV060zGsTec0xClRCBfIePhPBgg/Emyrylr4LKQ+OZEPbctPt8Ordk1mgfUJcFLviBp+E2Cgym/fv95tLyVDz6m/QoMCE2ikW5SjnXm2VyKvF6wqpRz68YzRsGfEQnCitgNjGDaG6+iIUnjrLiHxt66bwzOhU98Dy05IK+NlK8Unk/c8sqzq5nkq8jcYRP37BG2reh7athkbz/shaWP3gVFj3036Q1KwxjL0jBbbnH4OSskr4ev+PcP7CJfj9r29y9UyXzGYbE2elKJnNVlAyLqPCjwuuefEst99/z4SUzR+ywWCAAXpNlVedh+jIq2rE8vKAfa93mrEfKuBnW/PiZet6c5mLEMXzyhHOzdqhInw8Muh4STnTnpENIyAuOhKSYuvBiNt7QWVqX2j0aY5G3NIbfwboLcWjifidVnyjCgtOGd7b80wGoYKfkUzY9m02Ckgg8rpJO3faCgXh48dAeEXNgWMl2sBwwykq4hJMXjwVWn/zle/zjRuhtPfNGimNooq83mXmnQwF/AJJgm3yuiNW1lohs9kaTnZ/meVatVebXyrXoH49OFNxHhpdVR/KKs5DTKOrYMzzU6B9fh6ca3MNNFy+zHfLo+7RB+f36JToucYNW/LKaF7xXDglJQVWrlwZ8KZJIq89ouhLh4LmmLPMZw53uaYZ7Dl8kh3v7MvdDjc+N5Wd5WJk0BdPzYVBeDF6iD2hgJ+rmleGvHhVbEFBAUtQhn9v2LAhYBQSkVdOmoMtfKgl8cG4W37HMidvfEwku1BuUIv60ObJKcxULm2eBMueeQXa9enuS0sSYk+w8bM7/CtmNhN57U6V/fLBFD7xXqni0xUsV1DzuGhoEt0QCk+ehYsXLsKFAwfg9689Dc2Ki+Bks0R4fs7/hSYxjT13trCPnK9GMPFz0kfb5JU95+Wm85YtW2qYzUhmzOmrf0aMGOFkXFQnyAi8sX4vXLh4CYpOVUCDBvWg8rzPE6pFk0i4CJeg+6Hv4KHMJ9ln37a/Dl6Z9BzEN24ITRpFwKh+tZN+Bbn7yr7O9lGRmKPIqYcVknjBggUwceJEw7xGZDbLyVSwNAeG7b278Ts4XnIWWsQ3hmtaNGE+yBu3F0BFVTXcVnYQ7vnjZDaYkz37wO5l/4+5OVacOQlD0nrIDdLD2sHCz+kQbGtepy/Cehjviw+ueVGDT5s2DebOnUvklQE1QN1gCB8eBWWt38XcFiurqqFRZAT06JgIg2/qAH//93cQsfkTmP7mDNZLdLwoeOc9LYg+GP2TgVbV/lmKKtJvXpk5aOijkNBMDnRtLGleGdHzfs3G17noCYXHPyVn0GSuD60SmkBCk0io98kmePz1P7BB7Ei9A9b8bir7W0yh6c/skxu1e7XDlrx6InLI3AwLJPLKCaLXwscdMPAYqOjkWdh14DicqTwP589Xw+27NsHvshexAXx811jo/bfX2d+Y6xaf6WPSlN0QkpsV92o7Npu51hUzJuCmE95rRbmK3JsgmZa8Jq+YjLp/j3bw8t8/h+8OFcPdH/8Nfrv576zrr949CQ7fMQyGpnWGqxOawJrcfHYLBro3Yv5b0rzOZ9gxefGVSNSBAwdqpq+V4x87XSXNawet2mW9Ji83m7nvMZ7lVvw2HX725UesM0uGTYH1P+kL0VENWbb6pIQYKDxZBonNYmD2/f1I88pNryF+AeN5KTDBh7rX5JCc26D0j2tf7Os9cydDx/w81u3CVf8D845EwInTlXDuXDXERF0FFy75RtStbQJMHZ0alP7JYKjq/BJ5Lcy6qpNrYWiGRXhazYOFJRAf04glA0ON23rEUGi+/QtW73/m/Rn6ThkDC9/9HAqLy6Cs6jxcvHgREuIas/VwUrMYyCDNKzMNAZWHpd1m6bebNEBmsxzCbv+4iF5UYs8mvPy4RlyMxcWQvhu7XA3/2nYAfjx1Fk6VVcLFSz6NyyOLHvtNH4i+dIbWvBJTLLXmlXivpapEXkswGRZym7w8EB6Perp3xNxApUzjdvo+jwUYbHhkJhR0uwHOVpxnWeqRqJVV5yGiQQPo0CoO0lLawnub9kD5uWq4qUsr+MUNCUReiSkm8noAnkSTrlZ1m7w8yACPeUBIPXKiaUv4xwPPQGH3Xoy0VyfEAAbeo4/z4R9PszunurRNgIgG9dn46tUDuHQJYMBPmkJar5+6OmY3G3MbPzf7hm0ReSUQVXVynQyZB8bjzvLYbnHQZJIvLy4S96UX3oE/3HMLS4q9Ovf7GjdB/n7xR3D6bBW0bxXPPu/eKVG7urV3hxhyj3QyGZfrOCKveJ6L7fDdZysxunb6SmazHbRql7Xy48I3oPCKmXZJmIU+3jDY/ZXsL+HUrj0wY6Yvg8H3nbrDgoefgzYtYrVraXjwPb+mhpvaeDskBtJjuODy9V+z+qR5vZlfww0r7lnVt29fRlo86z169ChkZmZCdnY2bN68mf0dFRUl1zO6dF0aPzPy+stUgNpRzLaHR0H4fLx1P7TI2wpTXvFFBmHOoGdHz2JEv29Id+avLG5oMdMaAIyussHL1dOujaE1r8Qs29a86D01evTogK8083G22l/SvFaR8l/OjLx8DYtaEY97Nu04xLyfkFhjBncHrjVx7doy70uY+pdp7EXHru8FLz38HMveFxsdye5QjouJZJkO8NHfMYUEfj9nD/uem85IdrP+yY1evraq/bOkeZOTkyEtLY3F4WKAgaiFSfPKC49sC4GEj2tdkWiixxRqX27edt3/NYzImMi6g5FBeX95h53vbthWAK0ub07xvtq5HE5VcsjOi1v1bWtefDGueZG0+PDEYvjZpEmTTO+lstNx0rx20KpdNhA5uGcU17K8NtfGeNcUbj7derpAy9J36tejYPFdk5j27NejLfseyYp+zeLVN1Z7TeS1ipQ9y4qcNCzgqrLwiVoWiYgbVZ/sOKgl8MLNq4PPL4Khf5nHkPjkVw9A7rAHGEnxOKhjq3jpNJsq42dBPDwvYlvz+svLq++lW0m2SfPKzb8ZOUS/ZP4mjM29sXMruOZPC6HPyjfYxzunvwD/6PAztmZF4sZGN2QujmJyMCc9NeufkzbdrKNq/wJqXtFsNgLLLNDeCshEXisoGZexIny49j1YWMr+Q2IeL62AUctf1FKPzHtwLvyY0htiG0ey89qKqvNwXfsWzMMKN51kHiv9k2lftq6q/bNkNvvbec7KymJHSG48RF45FEXhQy2LwQSlZVXsPBfXqXjMIz7oUDHx5ceh8z7fOeyauX+GTc06wKWLl6B7x5bsXqoOVzeFjdsOsHZwhxk/c0piVckhNyvu1bZtNrv3avOWiLzmGAUqwSeXH/mIZfXnueiAcdsTD0C3A7tYMQwwOJ7Sm4X04TWu6HQhOliIbWnpOW12l8hrEzBdcSKvBH4qCF/96ATtyAd3kHFjasfeIpbQWtxpPtDtBmi/ewecSkiChlnLYGurLqwMBhegayOSF7P54Tkw95by5w5pB04V8FPxpg9LZrOdiXJSljSvE9T+UwfJUVjRkF3L2iTqKri2TTMWg3tD51bw1od5vg2nG1tA5b3pLEtfcbNE+Of4aRD/i8HMPP7T+9vgdHkVuw3y8ZF9oEZgwuXXcK2ePuh62/lyibzy82vr3mb+ukBpT9zycSbyyk3uzm/zYfmmwyxjAV5D06ZlLGsQA+Pr168P8ScK4ZE1r7IAAwzpe3vaK1DcLEl7af6RkywiaMZ9faFpk0bs8jj9DrPel9lOj4m8dtCqXdax2WyWs8iNWySJvHKT++bqz6Cg+DwLy2vVrDEjL/6NZE6uKtECDKr79mPExaMgXN9Wnb8ARcVlUK9Bfeh5bSJzlWTr4HU7NRdHdg5cWMrMaHyc5Msl8srNr2Py4mv1F9DxS9XRbdKNWySJvHKTu2jlJiitqs92l5Fo+Oj9lFlaTcyLe7ZKW9Pyt6KWHTOke418uXzdK/bMicmM9Ym8cvPrmLz+rn7lzhl4HezixYvZfwkJCY57SOR1DB2ryMkrbjDlL8/W/JQ5cflbeC5czOaHj78jIH0ZmXy5RF65+XVMXqNL10eNGsV6FBcXJx0aSOSVm9y1OTvgy/1lWiRP/NYtkPLgSNZoWZ9bIGZLrtwLJGsTeeUAdExeZoIVF2uB+PhvDAVctGgRTJkyheXdDZTKxEq3ibxWUDIugxtWn+4tg+35hdBxbx48tcSXbuS7Ab+EbhvWyDXuQm0irxyIUuSVe7V5bSKvOUZGJTDwYMl7nwM0aAjtPsiGh997hRX98I506PbXV2wf6zjviXFNIq8cqlLk9ece6VYgPg6LyOt8cnFneNe+Y9B/TRb8Ym0Wa+gvw6dATq/boOPVTR3tDjvvjf+aRF45RB2T1+ioiMgrNyFu1UaHitsWz4Kbv/wXaxLdHXObdWR3KGPG+pEDf+LYJ9mtPhJ55ZCUJq8ba1ujIZDmdTa5uCNc0utmaLd7O2vgjcczIfL2gfDZriNw8mwVNKhfH/pe3wYm3H2jsxe4VIvIKwekY/Lia9FsxjNd2Y0pIq/cJNaqPWAA85rCJ+O+2YBOGG0TY5lzxrcFx1kO3Z6dk+CxEX1cfrG95oi89vDSl3ZMXjKbQ9TJQCDuvHGzYWurbixbPWpbfCIjGkBV9QW46+ZO8JsBP5GTHsnaRF45AINKXv3ZsFnAPpnNNieXEzc5GeDNN+H1k1fB9gOlUHWuGpo0jmRpR/B+ZkyxOeSmDrTmNYFX1R8XT6KKuPskBuuj5p42bRrMnTvX0AuLyGuRvAUFAPff7zOVLxMXvadytn4DG789xRqpvnCR/Z+nHHHii2yxN5aLqUoOywP0uKBtzYukmzx5MvsP/ZfXrVtXo4tWd5tRCy9YsAAmTpxI5JWZZD1xDxzQWsPJPXOpsXYfM36BMbz9UtrROa8FzFX9cQmYn1eWvNx8Tk9P1za78F4sNKP1z4gRIyzAXHeKlFVWQ0yjCJ8WPXIE2vbvz/6u6NMHjr39dt0BgkbKEHAUz+sUO665Z82aBV26dAnYTF03m3mqEcxm8EPxWdi6+wcNrz5F+TDoqXG+f1+ODNKDqarmcCpbbtdTFb+AmpcnFvMHViCzec+ePYCktRptVJfJK947hbc2YihfQlwUtG0RC3FfbYExz00JSFz8UlXhc5uETttTFT8LbT08AAATdElEQVRPyItr5BkzZmhYmq2P6yp5V+fms8vPeV6fNbn5UFRSDm1bNIG519YDwF3ly6lHLm3caLh+VVX4nJLN7Xqq4mdpt1kfjI/r1g0bNrCIIjeeukrel1ZuYQ4Vv+rbFW65rjW7O+rIj6ch9eQ+TePuu/1ueHv0E4CXyqV0TPQLt6rC54bsuNGGqviZktdfML6Yt1cmCJ8DXxfJi+byR18VMAgw7+3VzRrDueoL0Pwf78J9KzPZ55VTn4U3eg5lV9AEOvJRVfjcIJ4bbaiKnyl5jYLx3bi7qq6Sl69zj5ecBTyWra6+AM3iomH4m89Dr898R3JrJ0yHL382iP2tTxLmb8MqIbE1y1gf17hRSBwPiX1UlRxu/DC40Ybtc17xpf6C8dERww2ti++pa5qXX616643J8K+vClj6kdsXz4a+23yRQS89/DyU35xqibhY6O8fbYXdxyq1KePZ/YzMbDcEyk4bRF47aNUuK0VeuVeb165L5BWz9j0yvDdgDqHEYb+EpJ1bGVCf/2kFdE0fzv7WpynxhyRuen32dQFER0czDc0TX8smBzOfNesliLzWsfJXUoq8FIy/3+8huZMpwTA+vBcZH7YJ9eAoLTIIY3HvnvY7S6Tl70YtXl5eDn9I78/qie07ve3RybgC1SHyyiHqmLwUVeT+OSo/IsIzXIzFxYvQVz80FaB/f+3uZCvTzYmK5H3uYd/6GB9+QTqR1wqK7s+vtbdaLyVNXgrG72AdbZOSZ77Nhwv33Qd4yyMSd8MjMyHh7jsdRf9wzTvk5q6svqh5QyEoAaEgzSsnOo7Ji6+lYHz3zGYIEGDgZIpxzfzOR3lszSs+KR1bwtDUzk6adL0OkVcOUsfkJbPZRc2BxG3f3jeTBn7KTqZZ3G3m3lpOc+k6eb9ZHSKvGUKBvyfySuDnivBhDO5ld0c3iUtmqcTEXq7qyvzKd8OwBcfk9bBPWtNhf1TkIXGJvPISGtbkFU3nJUuWwN69e2HcuHGmoX5WYQ1r8npMXCKvVSkzLhe25NW7RyJ5t23bxpDIzMyEqKgoafTClrwicceOZfdNefGoKnxeYOGkTVXxM/VtFoPqt271eQH16tXLVryuGaDhQt7Dx8/ANS2a+Ib71lu++6bwmTULYOZMMxgcf6+q8DkesMsVVcXPlLwUmGC+2/z66m2Qu+sIE6mYyAi459NV0Df7rz4RQ22LWtfDR1Xh8xASW02rip8peRGFuhSYgE4O+Ih+xYEmtxZx316oBRhgMmu2s+zxo6rweQyL5eZVxY/Ie3mKucsin3E8L70rtTMLrws0uenzVrMqE4beCLc8MlrzU5734FxIn/fIf8xoy6Jkv6Cqwmd/pN7UUBU/U/KGi9mMGtUoSgcvgNuUd0iTDCQuBsDjgy6GxUVH/QYmfLrrKPxp9VeQ1DQa5r87VyNu5oTnYVubbj5CX9faG4kTWlVV+DwHxuILVMXPlLyq36TBQ/BwHo28j3hwfL+Utpp/MXfux8ifJvXO+iUvblBNfWMjTP/rs9B539c+Udm4EdI/Pc3+nPfQANK85Nts8SfEuJiUk4b+Div0dcYGQ/0OKz1xuTbV30zBiSo68nMzGgl9TZNq/yGBBQWwb/D/gY75eVDcLBHWPvwsrG3cls0C08YTbpOeOCsNqKo5rIwtGGVUxc+y5tVnTOCgmt0MaQV8r46KOCm5RkXT+f2cPSxgXQyXE7Usv33CVPMKAQZI3CXDpsB37a9jw8Ud5/TBKUExmfF9qgqfFdkIRhlV8Qtr8vLrZqaPSdNkgK9vRRNZXPOiVi4tq2JrXn4bBU4u3hG1Y28RHCwsgZiiH2DgKxkspA9zBh3+Yidr/8vdRyGpaZOgkZYPSlXhCwYxrbxDVfxMyWtl8LJlvNK8ZmtZ8Y4n/W6zmOtHTOQVf6IQHnncl5rl6E9vhNa7fI4rVh+eHQGz+OHTv0c7Wzdn+HuPqsJnFTOvy6mKX1iTF2NdV+d+z+Ze3EHGf/sLVEez+tSZSmjapFENQr25+jM4UnIBxNQjB7veAHhtjb/bKnCtXXq2stZNjmJ2BC6Q4pGUUyFVVficjtfteqriF5C84k5z165dgac/cWOdK06AV5oX3+HvGKhfj7aGF5j7E4x5b22ANvnf1Eg9svqPS1i2A9H8RvIvW7tTO2biPxpjhnRn17LyHxKsg3mJNu04xMqaXe1qJqyqCp/ZuIL1var4GZJXPN/NyspimyJiChOV7m3mGhWFAZ0u7D7ZMxfBsNn/5at2OYiea1ExkwH/DLVpu6Q4KCmrZJtjSM6UTomMvOINF/qbJO32i5dXVficjtfteqriZ5qrCNNzDhkyhGnd5ORkFkmUnZ0Ny5cvZ9fjuHF3s5eaV3qihQCD7wb8En7MfJU1yZ06RPNbv0Em3ieF2hbriFpWPMoSN9Xs9llV4bM7Tq/Kq4qfKXn5WW5aWhqgBkYSI2lVJ6+4cYRa0u8F5QJxP540Az676fYa8iNqXSMtyo+cftW3C/xj8x7NUaRdYhxsyjvINLPsfVOqCp9XZLTbrqr4WTKbEYyUlBR466234PXXXweM6Z09e3bIO2kYTaLRxhFegq49GM6H5AWA4y++CA0nTmHr1oOFpRAX0wh6dEqssaml17L4/Sc7DrJ1MT6oWf29F7+TvaJVVeGzSzKvyquKX8ANK8yzO3LkSMjLy9O0LnpbHT161LVAfJyQYJrN4g60fuNI06QCcdHdcX/btpYuXRfbFgWNa1YkOJ4V4zERrofbJcXX+hFwIqCqCp+TsXpRR1X8wvqoyN9E8/NcfxtHbD36/H9pAQY8pM/O5KI5jo4caA4H6yZHO/3zQvjN2qT+mSEU+Hsp32a5V5vXdkPz8h1lPF/FJzkp3q/zAz86EsnLNeaElx+H5tu/8HV440Yo6HoDO689c+oEXN+tk7QzhTkSzkoQOZzhxmupip+nmhfN7qVLl0JGRkbAu65kySvu2vIJMcqUJ24sde/kS1a9c28RDH12PEs9gu6OePvFsqpmWtIuTCeCl5oHSnAtJz5ytVUVPrlRu1dbVfw8Iy8m4MYdaivnwbLkNTpfNcqUJ7pCorvj0Dfm1SDuJ007aEdBqKELjhRCvYgo0yTX7omTvZZUFT57o/SutKr4eUJedPBYv349oFdWMDQvP18de0cKnDxdDg3q12fHMvgY7eSiqXx8+7dw3ZynfOk1UeMeOMDqiOGAmHkAJ/fwmQhGaNljHS9EUFXh8wILJ22qip8n5OUA+jObUSPn5OTUwnjECJ+zv92nrLIa/rapAE6dqYKmTSK16sdLKqBZbCMYelMbuLpZ7etpI44cgbb9+7PyFX36wLG339bqfrKrCPJ/OAP9r2sJna+OZZ9/te8kbNt3Elo1bQS/7N3GbjepPCEghUCHDrUT3QWdvP5GIGs2j1/wAZSfq4aE2CgYeEM7+Ozbo3Dk+BmIbhgBL064tfZGk8lF6HxTC81u9EvGa3Byvi9ja2DRl1lqNlysrKrmcBECqaZUxS8syDvp5XVwurwKOrSKh4gG9aH6wkXYf6yEkfn3v76ppj+zxQwG3DMKpYJvWIVStnlRWlUVPinGuVhZVfyUJy8eEb307udw+mwV9Lw2UTtfLTxZBo0ir6q55rVIXJQLbBc9pNCj6ofjp+Dm65NDJmWmXm5VFT4X+SfVlKr4eUpeq4jKms18w4of5fhNMC2RekTVybWKv9flCD85hMPaScPILVGL4JFMPULC543wybXqXm1V5zcsNC9OI24yobMFv3sqLiYSxgzuDpCR4csVhI+F1CP4QxDXuFGN2zRUnVz3xFuuJcLPG/zChrx+4dEFGARKPaK/cQPb4zvLJHzeCJ9cq+7VVnV+w5e8mIUe17n4mOQMEomLThi4SWUlY4J74iPXkqrCJzdq92qril94ktcGcVEE/F1pY3pvs3uyI92SqsInPXCXGlAVv/AjLyfu5QADK1n6HGdMcEl4ZJtRVfhkx+1WfVXxCz/y4gYV7i7j5pTF9Jri/c54AwZe/7omN5+ZzoFyFbklPLLtqCp8suN2q76q+IUfeXFGMRUJal6Lj7/NKqwqZkzw51tqsXnPi6kqfJ4DY/EFquIXnuS1OGliMfGoCT/HjavuHRNN8/M6eJXrVVQVPteBcNigqvgReS1MuKqTa2FoQSlC+MnBHNYeVnLQmNcm4TPHKFAJws8b/EjzWsCVhM8CSAGKEH7e4EfktYArCZ8FkIi8ciA5wI/IawFyIq8FkBwIn1yr7tVWdX6JvBZkQNXJtTC0oBQh/ORgpg0rCfxI+CTAA2AX+NE5uXMMibzOsSPhk8AOqxJ55QAk8krgR8InAR6RVw68APjRmtcCtEReCyDRhpUcSA7wI/JagJzIawEkB8In16p7tVWdXyKvBRlQdXItDC0oRQg/OZhpzSuBHwmfBHi05pUDj9a8cvgReQk/OQTkapPmlcCPyCsBHmleOfBI88rhR+Ql/OQQkKtNmlcCPyKvBHikeeXAI80rhx+Rl/CTQ0CuNmleCfyIvBLgkeaVA480rxx+RF7CTw4BudqkeSXwI/JKgEeaVw480rxy+BF5CT85BORqk+aVwI/IKwEeaV458K6E5p0zZw7MmDEDUlJSYOXKldClSxfDQcgm15ZGx6QBIq8cwoSfN/h5EpiQm5sLGzZsgOnTp8OePXtg6dKlkJGRAVFRUX5HQeT1ZnLlWnWvNpFXDsugms0rVqyA5ORkSE1NhYqKCliwYAFMnDgREhISiLxy8+i3NpFDDlRV8fNE8+rJO3PmTBg3bhwznVEr5+Tk1EC7YcOGcO7cObkZoNqEQJgi0LJlS7gfE8XrnqCQV3XNG+pmPfVPjrWq4ucJecNtzavq5MqJtHu1CT85LI3w84S82NVw2m0m4fNG+ORada+2qvPrGXntQKsqeHbG6GVZwk8OXVXxCwnyopmNO9Oh+lD/5GaG8PMGv5Agr9zQqDYhUDcRIPLWzXmnUYcBAkTeMJhEGkLdREAJ8qKXlujoEaypwvc++uijsGTJEhg8eDCg84mRl1iw+uTvPeLR3JXsh/7dxcXFcO+998K6dess+bgHu+9i/0JtfrnspaenG+4HhTx5OcCFhYWmAQ5uTz6SFR8UwFAlCPZx9OjRMHv2bOZLHkoPHhcOHDiQCZ8VH/dg9130BBTnOtj98Pc+ftSK3ohGm7khT96PPvoIunXrBosWLdJcLIMFbmZmJtx5553MrRN/RF577TV44oknDAMsgtUv/h7s07Zt2yA6OloLBAl2H6y+LxTxE/seSuTligL7x3/8/OEcEuQVzRfeyfHjxwOSByORrpTZrCfvtGnTYO7cuSFnOoeqVSD+yEyePBlmzZoVMDTU6g+Bm+W47GGbobAsEi0UdCsOefKaTUaokDfUNC/HLZTJi8KIpF28eHHI/eiJchcqlgFfBvG+BYqHDwnNG6rkVWHNi9iFKnmxX8uXL9csKLN5Dvb3ob4mF/sXsmaz2aRdKc1Lu81mM2P8vYidv6WQ85bdqxnqu+FhQV73potaIgTCBwElzObwgZtGQgi4hwCR1z0sqSVCIKgIEHmDCje9jBBwDwEir3tYUkuEQFARIPIGFW56GSHgHgJEXvewpJYIgaAiQOSVgNufW6eX0Sl47nf06FFTpwfR4d5qHaswoOMFtmnHlVDsA7r88TEY/W10Ob/VPorl+Bxh0EYo39biZGxEXieoXa7DBQPDtjDyiP8bhcSLCB8rRER3xJEjR8Krr77qurByx4vWrVs7Hp8Rkd0krH5KreAmIQZXrCqRVwJ6PXmxKVFQ8N88Hhj/5mF7vB5mlSgoKGDxrvw71GxpaWnsYvqePXuy+vhgkISoqfy1jVkpePwsfp+VlQWYDYBrOqP+cFLi97w/YmAIh0j/w4DaF90fcRw85hktj8cee4xV4eFsTjSv6OMrWjPY1rfffsvaf+edd7Q4a4ys8oc1lkNMJ02aFPSQUgnRslSVyGsJJv+FzDQvChoKDgriiRMnmEZ88sknYciQIYxk+IjfobbExwp5s7OzYfPmzYzUGBbIhRPri5pXTxx//Rk2bBgTfCQu9mf37t1aH0RTU08CTjAkafPmzdl7hw8fzsImjX50rJjNOJ5AGKxatYoRkY8VMcUfEF4HPxfJ6qU1IiE+0lWJvBIQBlrzYrNIUG5Si1oZTWpM/8LNa9HcxhAwK+RFM5MLZV5ennZThRF5+Tv99WfevHkwdepU4OawkbBzTcvXu+K/xR8nHLddbRto/Sv+aLz77ruaJVFeXq5h3KtXL/bjgVhwq4P/QPqzkCSmPWSqEnklpiKQUAQyqd0gLwo710BIHDPNG+7k5UTlN1CIBCbySgh5uFY1EwonZjM3P0XzGk1Ccc3LNSXiip+jCT1//vwapiTfsLJjNptpXn9mM6559csCWc1rZjbzNbyoeREj/gOGGIpWD5nN4cpAiXGZkVcfFmdlw0qsM2rUKNa7uLi4WhtWXMDx+0GDBkFRURHbYe7atau2aWV3w8qMvEYbVm6TF5cEgTas/JGX/2BgQnd8xA032rCSEHKqWhMBr4+UvMLbjaMir/oWqF06KroSqIfpO1UlL06HEyeNKzmN5KRxJdGndxMChIBfBGi3mQSDEFAUASKvohNH3SYEiLwkA4SAogj8f3looH3IjWvOAAAAAElFTkSuQmCC"
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(let ((edu-spending (map-columns (select edu-spending t '(spending population))\n",
    "\t\t\t\t  #'(lambda (x)\n",
    "\t\t\t\t      (elog x))))\n",
    "      (l-population (elog edu-spending:population))\n",
    "      (l-spending   (elog edu-spending:spending)))\n",
    "  (ips:plot\n",
    "   (vega:defplot log-education-spending\n",
    "     `(:title \"Education Spending\"\n",
    "       :data (:values ,edu-spending)\n",
    "       :layer #((:mark :point\n",
    "\t   :encoding (:x (:field :population  :type \"quantitative\" :title \"Population (millions)\")\n",
    "                  :y (:field :spending    :type \"quantitative\" :title \"Spending ($ billions)\")))\n",
    "\t\t,(sctplt:fit-line l-population l-spending))))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37cf7ac0-b3be-4816-945f-e6af2b665369",
   "metadata": {},
   "source": [
    "## Adding categorical variables to scatterplots\n",
    "In example 2.10 we investigated the relationship between the rating and price per load for 52 laundry detergents. Looking more closely, we can see that there are two different types of laundry detergent, liquid and powder.  We can add these categorical variables to the scatter plot by using a different colour for each one.\n",
    "Note how we slice up the data in the `let*` statement, allowing us to plot the elements individually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "acfe4c70-17e7-4d09-8626-1390e4098738",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v4+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
       "data": {
        "values": [
         {
          "price": 12,
          "rating": 32,
          "type": "Liquid"
         },
         {
          "price": 6,
          "rating": 35,
          "type": "Liquid"
         },
         {
          "price": 28,
          "rating": 38,
          "type": "Liquid"
         },
         {
          "price": 28,
          "rating": 40,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 71,
          "type": "Liquid"
         },
         {
          "price": 7,
          "rating": 60,
          "type": "Liquid"
         },
         {
          "price": 29,
          "rating": 37,
          "type": "Liquid"
         },
         {
          "price": 12,
          "rating": 61,
          "type": "Liquid"
         },
         {
          "price": 8,
          "rating": 31,
          "type": "Liquid"
         },
         {
          "price": 11,
          "rating": 51,
          "type": "Liquid"
         },
         {
          "price": 25,
          "rating": 81,
          "type": "Liquid"
         },
         {
          "price": 25,
          "rating": 71,
          "type": "Liquid"
         },
         {
          "price": 19,
          "rating": 68,
          "type": "Liquid"
         },
         {
          "price": 23,
          "rating": 81,
          "type": "Powder"
         },
         {
          "price": 5,
          "rating": 35,
          "type": "Liquid"
         },
         {
          "price": 26,
          "rating": 46,
          "type": "Liquid"
         },
         {
          "price": 26,
          "rating": 47,
          "type": "Powder"
         },
         {
          "price": 13,
          "rating": 61,
          "type": "Powder"
         },
         {
          "price": 25,
          "rating": 43,
          "type": "Powder"
         },
         {
          "price": 8,
          "rating": 42,
          "type": "Liquid"
         },
         {
          "price": 21,
          "rating": 49,
          "type": "Liquid"
         },
         {
          "price": 10,
          "rating": 47,
          "type": "Liquid"
         },
         {
          "price": 11,
          "rating": 42,
          "type": "Liquid"
         },
         {
          "price": 7,
          "rating": 42,
          "type": "Liquid"
         },
         {
          "price": 25,
          "rating": 71,
          "type": "Powder"
         },
         {
          "price": 25,
          "rating": 85,
          "type": "Liquid"
         },
         {
          "price": 20,
          "rating": 74,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 66,
          "type": "Liquid"
         },
         {
          "price": 21,
          "rating": 46,
          "type": "Liquid"
         },
         {
          "price": 22,
          "rating": 64,
          "type": "Liquid"
         },
         {
          "price": 22,
          "rating": 52,
          "type": "Liquid"
         },
         {
          "price": 24,
          "rating": 48,
          "type": "Liquid"
         },
         {
          "price": 26,
          "rating": 53,
          "type": "Liquid"
         },
         {
          "price": 8,
          "rating": 51,
          "type": "Powder"
         },
         {
          "price": 12,
          "rating": 73,
          "type": "Liquid"
         },
         {
          "price": 30,
          "rating": 58,
          "type": "Liquid"
         },
         {
          "price": 11,
          "rating": 70,
          "type": "Liquid"
         },
         {
          "price": 20,
          "rating": 39,
          "type": "Liquid"
         },
         {
          "price": 16,
          "rating": 46,
          "type": "Liquid"
         },
         {
          "price": 12,
          "rating": 44,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 25,
          "type": "Liquid"
         },
         {
          "price": 13,
          "rating": 58,
          "type": "Powder"
         },
         {
          "price": 14,
          "rating": 58,
          "type": "Liquid"
         },
         {
          "price": 13,
          "rating": 65,
          "type": "Liquid"
         },
         {
          "price": 18,
          "rating": 44,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 29,
          "type": "Liquid"
         },
         {
          "price": 8,
          "rating": 41,
          "type": "Liquid"
         },
         {
          "price": 10,
          "rating": 57,
          "type": "Liquid"
         },
         {
          "price": 12,
          "rating": 53,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 60,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 58,
          "type": "Liquid"
         },
         {
          "price": 14,
          "rating": 60,
          "type": "Liquid"
         }
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"
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(let* ((liquids (filter-rows detergents-2 '(string= \"Liquid\" type)))\n",
    "       (powders (filter-rows detergents-2 '(string= \"Powder\" type)))\n",
    "       (l-price  (select liquids t 'price))\n",
    "       (l-rating (select liquids t 'rating))\n",
    "       (p-price  (select powders t 'price))\n",
    "       (p-rating (select powders t 'rating)))\n",
    "  (ips:plot\n",
    "   (vega:defplot detergents-plot-2\n",
    "     `(:title \"Detergents\"\n",
    "       :data (:values ,detergents-2)\n",
    "       :layer #((:mark :point\n",
    "\t             :encoding (:x (:field :price  :type \"quantitative\" :title \"Price per load (cents)\")\n",
    "\t\t\t                :y (:field :rating :type \"quantitative\" )\n",
    "\t\t\t                :color (:field \"type\" :type \"nominal\")))\n",
    "\t\t        ,(sctplt:fit-line l-price l-rating :color :orange)\n",
    "\t\t        ,(sctplt:fit-line p-price p-rating :color :steelblue))))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aefe5605-ddaf-4b2c-bf33-0e7340bc0ce6",
   "metadata": {},
   "source": [
    "## Scatterplot smoothers\n",
    "In this above example, we fit a line to the curve, but some data isn't linear.  To fit a smooth line to these, we can use various smoothers, the most common of which is `lowess`, seen in the calcium retention plots.  There is a variable you should be aware of, call the **smoothing parameter** that determines how closely the curve follows the data.  Let's see this by repeating the calcium plots with two different values for the smoothing parameter.\n",
    "\n",
    "### Example 2.16 Laundry rating vs. price with a smooth fit\n",
    "First, the plot with a small value of the smoothing parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e058b691-430c-4bf3-9815-565b83cdafdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v4+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
       "data": {
        "values": [
         {
          "caintake": 1834.8001,
          "caretention": 581.7,
          "logret": 6.365955
         },
         {
          "caintake": 1816.3,
          "caretention": 344.6,
          "logret": 5.842384
         },
         {
          "caintake": 1792,
          "caretention": 735.10003,
          "logret": 6.600007
         },
         {
          "caintake": 1777.7,
          "caretention": 640,
          "logret": 6.461468
         },
         {
          "caintake": 1715,
          "caretention": 592.60005,
          "logret": 6.3845193
         },
         {
          "caintake": 1666.9,
          "caretention": 307,
          "logret": 5.7268476
         },
         {
          "caintake": 1662.8,
          "caretention": 519,
          "logret": 6.251904
         },
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"
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ips:plot\n",
    " (vega:defplot calcium-retention-plot-smooth\n",
    "   `(:title \"Calcium Retention\"\n",
    "     :data (:values ,calcium-retention)\n",
    "     :width 350\n",
    "     :layer #((:mark :point\n",
    "               :encoding (:x (:field :caintake  :type \"quantitative\" :title \"Calcium intake (mg/d)\" :scale (domain #(500 2000)))\n",
    "                          :y (:field :caretention :type \"quantitative\" :title \"Calcium retention (mg/d)\")))\n",
    "              ,(sctplt:fit-lowess calcium-retention:caintake calcium-retention:caretention :span 1/3)))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e19c46b-74ad-47cb-ae38-85665631054c",
   "metadata": {},
   "source": [
    "And now with the default value (2/3):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "fa39349b-f660-4ae1-90d7-47b85affafbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v4+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
       "data": {
        "values": [
         {
          "caintake": 1834.8001,
          "caretention": 581.7,
          "logret": 6.365955
         },
         {
          "caintake": 1816.3,
          "caretention": 344.6,
          "logret": 5.842384
         },
         {
          "caintake": 1792,
          "caretention": 735.10003,
          "logret": 6.600007
         },
         {
          "caintake": 1777.7,
          "caretention": 640,
          "logret": 6.461468
         },
         {
          "caintake": 1715,
          "caretention": 592.60005,
          "logret": 6.3845193
         },
         {
          "caintake": 1666.9,
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"
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ips:plot\n",
    " (vega:defplot calcium-retention-plot\n",
    "   `(:title \"Calcium Retention\"\n",
    "     :data (:values ,calcium-retention)\n",
    "     :width 350\n",
    "     :layer #((:mark :point\n",
    "               :encoding (:x (:field :caintake  :type \"quantitative\" :title \"Calcium intake (mg/d)\" :scale (domain #(500 2000)))\n",
    "                          :y (:field :caretention :type \"quantitative\" :title \"Calcium retention (mg/d)\")))\n",
    "              ,(sctplt:fit-lowess calcium-retention:caintake calcium-retention:caretention)))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95f4c5e3-4fb2-40e9-bc42-5216140b455f",
   "metadata": {},
   "source": [
    "### Example 2.17 A smooth fit for education spanding and population with logs\n",
    "This scatterplot of log education spending versus log population with a smooth curve suggests that the relationship is approximately linear except for states with relatively small populations.  For them, spending is relatively flat.  Note that this is the same plot as Example 1.14, except using the lowess smoother instead of a linear fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "a2d55dbb-517c-4b98-be26-3b8000f40f8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.vegalite.v4+json": {
       "$schema": "https://vega.github.io/schema/vega-lite/v5.json",
       "data": {
        "values": [
         {
          "population": -0.51082563,
          "spending": 0.9932518
         },
         {
          "population": 1.7578581,
          "spending": 2.939162
         },
         {
          "population": 0.5877867,
          "spending": 1.7917594
         },
         {
          "population": 1.9740811,
          "spending": 3.054001
         },
         {
          "population": 2.1282318,
          "spending": 3.2148677
         },
         {
          "population": -0.51082563,
          "spending": 0.9162907
         },
         {
          "population": 1.0986123,
          "spending": 2.3025851
         },
         {
          "population": 3.310543,
          "spending": 4.4931206
         },
         {
          "population": 1.8870696,
          "spending": 2.7663192
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"
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(let ((edu-spending (map-columns (select edu-spending t '(spending population))\n",
    "\t\t\t\t                  #'(lambda (x)\n",
    "\t\t\t\t                      (elog x))))\n",
    "      (l-population (elog edu-spending:population))\n",
    "      (l-spending   (elog edu-spending:spending)))\n",
    "  (ips:plot\n",
    "   (vega:defplot log-education-spending-smooth\n",
    "     `(:title \"Education Spending\"\n",
    "       :data (:values ,edu-spending)\n",
    "       :layer #((:mark :point\n",
    "\t             :encoding (:x (:field :population  :type \"quantitative\" :title \"Population (millions)\")\n",
    "                            :y (:field :spending    :type \"quantitative\" :title \"Spending ($ billions)\")))\n",
    "\t\t        ,(sctplt:fit-lowess l-population l-spending :span 1/4))))))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Common Lisp",
   "language": "common-lisp",
   "name": "common-lisp"
  },
  "language_info": {
   "codemirror_mode": "text/x-common-lisp",
   "file_extension": ".lisp",
   "mimetype": "text/x-common-lisp",
   "name": "common-lisp",
   "pygments_lexer": "common-lisp",
   "version": "2.3.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}