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 "cells": [
  {
   "cell_type": "markdown",
   "id": "14ce8697-1094-4d83-83fe-1ff0921faa84",
   "metadata": {},
   "source": [
    "### Example exercises using skills so far"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53dfaad6-0d90-49cb-ae34-613e22042f1d",
   "metadata": {},
   "source": [
    "We will focus on some relevant exercises that pull together the content from the previous chapters, leveraging all of the skills you have learned so far, and offer some challenges in terms of interpretation as well as coding."
   ]
  },
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   "cell_type": "markdown",
   "id": "466c8d15-d6f5-4b3a-bbb8-c0ed2aeabfb9",
   "metadata": {},
   "source": [
    "## Starting off\n",
    "As usual, import all the libraries and tools we've used so far, including things like the `rmse` function so we can check assumptions with GLMs."
   ]
  },
  {
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   "execution_count": 1,
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   "source": [
    "# Your answer here\n",
    "import pandas as pd\n",
    "import pingouin as pg\n",
    "import statsmodels.formula.api as smf\n",
    "import seaborn as sns\n",
    "import marginaleffects as me\n",
    "import numpy as np\n",
    "import statsmodels.tools.eval_measures as measures\n",
    "\n",
    "sns.set_style('whitegrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddb9f8a7-fe42-446f-939f-cfea9eeaad43",
   "metadata": {},
   "source": [
    "# Case Study One\n",
    "## Men's faces convey information about their bodies and their behavior - what you see is what you get\n",
    "### Shoup & Gallup, 2008, Evolutionary Psychology\n",
    "We will first consider this manuscript and its associated data. \n",
    "\n",
    "You can find the manuscript here, and I suggest giving it a read before beginning: https://journals.sagepub.com/doi/full/10.1177/147470490800600311\n",
    "When you are ready, the data can be found here: https://vincentarelbundock.github.io/Rdatasets/csv/Stat2Data/Faces.csv\n",
    "\n",
    "The paper reports a few correlations between its variables of shoulder to height ratio, number of sexual partners, facial attractiveness, and grip strength. Correlations alone are uninteresting, because they are not really a specified model, and they do not allow us to make claims about the influence of certain predictors while we hold others constant. \n",
    "\n",
    "The authors do report a regression model in the paper. Can you read in the data and fit this regression model (don't worry about the 'semi-partial' correlation content)?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5d7ba60-97e3-4696-8ebc-1a1dcf02fe56",
   "metadata": {},
   "source": [
    "### a. Fitting models"
   ]
  },
  {
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   "id": "f53aa9b3-9ad7-4d98-ad74-b00f23f2fe91",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rownames</th>\n",
       "      <th>MaxGripStrength</th>\n",
       "      <th>SHR</th>\n",
       "      <th>Partners</th>\n",
       "      <th>Attractive</th>\n",
       "      <th>AgeFirstSex</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>44.0</td>\n",
       "      <td>1.352</td>\n",
       "      <td>36</td>\n",
       "      <td>2.333</td>\n",
       "      <td>15.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>58.0</td>\n",
       "      <td>1.349</td>\n",
       "      <td>4</td>\n",
       "      <td>2.375</td>\n",
       "      <td>15.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>57.0</td>\n",
       "      <td>1.431</td>\n",
       "      <td>5</td>\n",
       "      <td>1.857</td>\n",
       "      <td>14.0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>48.0</td>\n",
       "      <td>1.405</td>\n",
       "      <td>6</td>\n",
       "      <td>2.125</td>\n",
       "      <td>18.0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
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       "      <td>34.0</td>\n",
       "      <td>1.307</td>\n",
       "      <td>3</td>\n",
       "      <td>2.500</td>\n",
       "      <td>14.0</td>\n",
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       "   rownames  MaxGripStrength    SHR  Partners  Attractive  AgeFirstSex\n",
       "0         1             44.0  1.352        36       2.333         15.0\n",
       "1         2             58.0  1.349         4       2.375         15.0\n",
       "2         3             57.0  1.431         5       1.857         14.0\n",
       "3         4             48.0  1.405         6       2.125         18.0\n",
       "4         5             34.0  1.307         3       2.500         14.0"
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       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>Attractive</td> <th>  R-squared:         </th> <td>   0.331</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                <td>OLS</td>    <th>  Adj. R-squared:    </th> <td>   0.272</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>   <td>    38</td>   <th>  F-statistic:       </th> <td>   5.614</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>   <td>nonrobust</td> <th>  Prob (F-statistic):</th>  <td>0.00308</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "         <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>       <td>   -0.8901</td> <td>    0.996</td> <td>   -0.893</td> <td> 0.378</td> <td>   -2.915</td> <td>    1.135</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SHR</th>             <td>    2.2248</td> <td>    0.797</td> <td>    2.790</td> <td> 0.009</td> <td>    0.604</td> <td>    3.845</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MaxGripStrength</th> <td>    0.0059</td> <td>    0.011</td> <td>    0.545</td> <td> 0.590</td> <td>   -0.016</td> <td>    0.028</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Partners</th>        <td>    0.0188</td> <td>    0.012</td> <td>    1.590</td> <td> 0.121</td> <td>   -0.005</td> <td>    0.043</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &   Attractive  & \\textbf{  R-squared:         } &     0.331   \\\\\n",
       "\\textbf{Model:}            &      OLS      & \\textbf{  Adj. R-squared:    } &     0.272   \\\\\n",
       "\\textbf{No. Observations:} &         38    & \\textbf{  F-statistic:       } &     5.614   \\\\\n",
       "\\textbf{Covariance Type:}  &   nonrobust   & \\textbf{  Prob (F-statistic):} &  0.00308    \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                         & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Intercept}       &      -0.8901  &        0.996     &    -0.893  &         0.378        &       -2.915    &        1.135     \\\\\n",
       "\\textbf{SHR}             &       2.2248  &        0.797     &     2.790  &         0.009        &        0.604    &        3.845     \\\\\n",
       "\\textbf{MaxGripStrength} &       0.0059  &        0.011     &     0.545  &         0.590        &       -0.016    &        0.028     \\\\\n",
       "\\textbf{Partners}        &       0.0188  &        0.012     &     1.590  &         0.121        &       -0.005    &        0.043     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             Attractive   R-squared:                       0.331\n",
       "Model:                            OLS   Adj. R-squared:                  0.272\n",
       "No. Observations:                  38   F-statistic:                     5.614\n",
       "Covariance Type:            nonrobust   Prob (F-statistic):            0.00308\n",
       "===================================================================================\n",
       "                      coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------\n",
       "Intercept          -0.8901      0.996     -0.893      0.378      -2.915       1.135\n",
       "SHR                 2.2248      0.797      2.790      0.009       0.604       3.845\n",
       "MaxGripStrength     0.0059      0.011      0.545      0.590      -0.016       0.028\n",
       "Partners            0.0188      0.012      1.590      0.121      -0.005       0.043\n",
       "===================================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# Read in data\n",
    "faces = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/Stat2Data/Faces.csv')\n",
    "display(faces.head())\n",
    "\n",
    "# Fit the model as described\n",
    "model = smf.ols('Attractive ~ SHR + MaxGripStrength + Partners', data=faces).fit()\n",
    "model.summary(slim=True)"
   ]
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    "If you have successfully specified the model, you should see a similar set of coefficients as the 'B' reported in the paper. We can interpret this then as a one-unit increase in shoulder to hip ratio increasing attractiveness by 2.22 points. This is somewhat difficult to interpret though, as these particular variables (attractiveness and shoulder-hip ratio) are in rather abstract units (unlike grip strength and number of partners). Can you instead standardise all the values so that it recreates the 'β' coefficients, which represent changes in standard deviations?"
   ]
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       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>scale(Attractive)</td> <th>  R-squared:         </th> <td>   0.331</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>        <th>  Adj. R-squared:    </th> <td>   0.272</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    38</td>       <th>  F-statistic:       </th> <td>   5.614</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>     <th>  Prob (F-statistic):</th>  <td>0.00308</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "             <td></td>               <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>              <td> 5.796e-16</td> <td>    0.140</td> <td> 4.13e-15</td> <td> 1.000</td> <td>   -0.285</td> <td>    0.285</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>scale(SHR)</th>             <td>    0.4263</td> <td>    0.153</td> <td>    2.790</td> <td> 0.009</td> <td>    0.116</td> <td>    0.737</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>scale(MaxGripStrength)</th> <td>    0.0855</td> <td>    0.157</td> <td>    0.545</td> <td> 0.590</td> <td>   -0.233</td> <td>    0.404</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>scale(Partners)</th>        <td>    0.2368</td> <td>    0.149</td> <td>    1.590</td> <td> 0.121</td> <td>   -0.066</td> <td>    0.540</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}         & scale(Attractive) & \\textbf{  R-squared:         } &     0.331   \\\\\n",
       "\\textbf{Model:}                 &        OLS        & \\textbf{  Adj. R-squared:    } &     0.272   \\\\\n",
       "\\textbf{No. Observations:}      &           38      & \\textbf{  F-statistic:       } &     5.614   \\\\\n",
       "\\textbf{Covariance Type:}       &     nonrobust     & \\textbf{  Prob (F-statistic):} &  0.00308    \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                                & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Intercept}              &    5.796e-16  &        0.140     &  4.13e-15  &         1.000        &       -0.285    &        0.285     \\\\\n",
       "\\textbf{scale(SHR)}             &       0.4263  &        0.153     &     2.790  &         0.009        &        0.116    &        0.737     \\\\\n",
       "\\textbf{scale(MaxGripStrength)} &       0.0855  &        0.157     &     0.545  &         0.590        &       -0.233    &        0.404     \\\\\n",
       "\\textbf{scale(Partners)}        &       0.2368  &        0.149     &     1.590  &         0.121        &       -0.066    &        0.540     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:      scale(Attractive)   R-squared:                       0.331\n",
       "Model:                            OLS   Adj. R-squared:                  0.272\n",
       "No. Observations:                  38   F-statistic:                     5.614\n",
       "Covariance Type:            nonrobust   Prob (F-statistic):            0.00308\n",
       "==========================================================================================\n",
       "                             coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------------\n",
       "Intercept               5.796e-16      0.140   4.13e-15      1.000      -0.285       0.285\n",
       "scale(SHR)                 0.4263      0.153      2.790      0.009       0.116       0.737\n",
       "scale(MaxGripStrength)     0.0855      0.157      0.545      0.590      -0.233       0.404\n",
       "scale(Partners)            0.2368      0.149      1.590      0.121      -0.066       0.540\n",
       "==========================================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "# Your answer here\n",
    "# Fit the model as described\n",
    "model_s = smf.ols('scale(Attractive) ~ scale(SHR) + scale(MaxGripStrength) + scale(Partners)', data=faces).fit()\n",
    "model_s.summary(slim=True)"
   ]
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   "source": [
    "These two models are absolutely equivalent, we have just altered the meaning of the coefficients. If you have done this correctly and the values match, then you've just replicated an analysis in a published article. Well done!\n",
    "\n",
    "### b. Model checking\n",
    "Next, we should check the assumptions of:\n",
    "- Linearity\n",
    "- Homoscedasticity\n",
    "- Normality of residuals\n",
    "\n",
    "We can see each row belongs to only one male, so the independence assumption is fine. We will return to *validity* later. First, check the linearity assumption graphically by plotting the variables used in the regression against each other (can be done simply in `seaborn`)."
   ]
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       "<seaborn.axisgrid.PairGrid at 0x103a177d0>"
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",
      "text/plain": [
       "<Figure size 1000x1000 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "sns.pairplot(faces[['Attractive', 'SHR', 'MaxGripStrength', 'Partners']])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ad5b7dc-7510-4102-ad87-df9c626c279e",
   "metadata": {},
   "source": [
    "Next, check the assumption of heteroscedasticity from the fitted model - you can use either instance you've made."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "158e6bc3-0c69-4426-b667-40365bef6b87",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x14f768990>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "axis = sns.scatterplot(x=model.fittedvalues, \n",
    "                       y=model.resid, alpha=.5) # scatter is easy\n",
    "axis.set(xlabel='Predicted Values', ylabel='Residual') # Renaming \n",
    "axis.axhline(0) # Adding a horizontal line at zero"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "643ee8ca-f07c-4a5b-91b6-df2219943e4f",
   "metadata": {},
   "source": [
    "Finally, check the normality of residuals. You can do this graphically, and with a statistical test. Again, either model is fine. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "584f5322-15a3-4229-a8f1-a1a4bce48442",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.9684099822188909, pvalue=0.35074616263990327)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "sns.histplot(model.resid, kde=True)\n",
    "\n",
    "from scipy.stats import shapiro\n",
    "shapiro(model.resid)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "267818b9-d087-46c4-810d-0ba88b6d7439",
   "metadata": {},
   "source": [
    "In your view, are the assumptions all met? "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa828163-e7e8-46f4-ac52-daee48cae754",
   "metadata": {},
   "source": [
    "### c. Model evaluation\n",
    "Before we interrogate the model further, the authors claim in the abstract good things about the variance explained by the model. We've seen how that isn't the best way to evaluate a model. Compute the RMSE for both your initial and second, standardised model to get a sense of how 'wrong' the model is.\n",
    "\n",
    "Hint - for either model, you can access the dependent variable used via `your_model_variable.model.endog`. This is a copy of the data the model is trying to predict and can be handy in the use case of when you let the formula specification transform things."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ee12a709-41e7-4b9c-a2e9-534e92053e74",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5117926409212918"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0.8177619301857805"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "display(\n",
    "    measures.rmse(model.model.endog,\n",
    "                  model.fittedvalues),\n",
    "    measures.rmse(model_s.model.endog,\n",
    "                  model_s.fittedvalues)\n",
    ")\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c992cee-8ebf-464e-881f-7b41be079447",
   "metadata": {},
   "source": [
    "One of your results will be for the non-standardised model, which tells you how wrong the model is, on average, in terms of 1-7 attractiveness rating scale points. The other result for the standardised model will be for the z-scored attractiveness rating scale.\n",
    "\n",
    "In your view, is this a sufficiently accurate model? How wrong on average is it for raw scores and for standardised scores?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cca0921-f1e5-4ad7-8322-a3ba2b65984c",
   "metadata": {},
   "source": [
    "### d. Interpreting model predictions\n",
    "Rather than focus on the coefficients, we will continue to interpret the predictions of this model, as we have done for many others.\n",
    "\n",
    "Using the unstandardised model, consider two males.\n",
    "- One has a SHR of 1, meaning his shoulders and waist are the same width entirely, like a barrel!\n",
    "- One has a SHR of 1.25, his shoulders being 25% wider than his waist, approaching the inverted triangle shape.\n",
    "\n",
    "For these two example males, we can consider them to have the full range of sexual partners and grip strength we see in the data, and we will average over those variables to obtain the marginal predictions of SHR. Can you create a datagrid that will produce this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6ed822ec-6d5d-40a9-bbce-e2a6e6e82581",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr,\n",
       ".dataframe > tbody > tr {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (696, 6)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>SHR</th><th>MaxGripStrength</th><th>Partners</th><th>rownames</th><th>Attractive</th><th>AgeFirstSex</th></tr><tr><td>f64</td><td>f64</td><td>i64</td><td>i64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>1.0</td><td>44.0</td><td>36</td><td>15</td><td>2.435447</td><td>16.16129</td></tr><tr><td>1.0</td><td>44.0</td><td>4</td><td>15</td><td>2.435447</td><td>16.16129</td></tr><tr><td>1.0</td><td>44.0</td><td>5</td><td>15</td><td>2.435447</td><td>16.16129</td></tr><tr><td>1.0</td><td>44.0</td><td>6</td><td>15</td><td>2.435447</td><td>16.16129</td></tr><tr><td>1.0</td><td>44.0</td><td>3</td><td>15</td><td>2.435447</td><td>16.16129</td></tr><tr><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td></tr><tr><td>1.25</td><td>41.0</td><td>8</td><td>15</td><td>2.435447</td><td>16.16129</td></tr><tr><td>1.25</td><td>41.0</td><td>2</td><td>15</td><td>2.435447</td><td>16.16129</td></tr><tr><td>1.25</td><td>41.0</td><td>35</td><td>15</td><td>2.435447</td><td>16.16129</td></tr><tr><td>1.25</td><td>41.0</td><td>11</td><td>15</td><td>2.435447</td><td>16.16129</td></tr><tr><td>1.25</td><td>41.0</td><td>16</td><td>15</td><td>2.435447</td><td>16.16129</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (696, 6)\n",
       "┌──────┬─────────────────┬──────────┬──────────┬────────────┬─────────────┐\n",
       "│ SHR  ┆ MaxGripStrength ┆ Partners ┆ rownames ┆ Attractive ┆ AgeFirstSex │\n",
       "│ ---  ┆ ---             ┆ ---      ┆ ---      ┆ ---        ┆ ---         │\n",
       "│ f64  ┆ f64             ┆ i64      ┆ i64      ┆ f64        ┆ f64         │\n",
       "╞══════╪═════════════════╪══════════╪══════════╪════════════╪═════════════╡\n",
       "│ 1.0  ┆ 44.0            ┆ 36       ┆ 15       ┆ 2.435447   ┆ 16.16129    │\n",
       "│ 1.0  ┆ 44.0            ┆ 4        ┆ 15       ┆ 2.435447   ┆ 16.16129    │\n",
       "│ 1.0  ┆ 44.0            ┆ 5        ┆ 15       ┆ 2.435447   ┆ 16.16129    │\n",
       "│ 1.0  ┆ 44.0            ┆ 6        ┆ 15       ┆ 2.435447   ┆ 16.16129    │\n",
       "│ 1.0  ┆ 44.0            ┆ 3        ┆ 15       ┆ 2.435447   ┆ 16.16129    │\n",
       "│ …    ┆ …               ┆ …        ┆ …        ┆ …          ┆ …           │\n",
       "│ 1.25 ┆ 41.0            ┆ 8        ┆ 15       ┆ 2.435447   ┆ 16.16129    │\n",
       "│ 1.25 ┆ 41.0            ┆ 2        ┆ 15       ┆ 2.435447   ┆ 16.16129    │\n",
       "│ 1.25 ┆ 41.0            ┆ 35       ┆ 15       ┆ 2.435447   ┆ 16.16129    │\n",
       "│ 1.25 ┆ 41.0            ┆ 11       ┆ 15       ┆ 2.435447   ┆ 16.16129    │\n",
       "│ 1.25 ┆ 41.0            ┆ 16       ┆ 15       ┆ 2.435447   ┆ 16.16129    │\n",
       "└──────┴─────────────────┴──────────┴──────────┴────────────┴─────────────┘"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "dg = me.datagrid(model,\n",
    "                 SHR=[1., 1.25],\n",
    "                 MaxGripStrength=faces['MaxGripStrength'].unique(),\n",
    "                 Partners=faces['Partners'].unique())\n",
    "\n",
    "dg"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "135622dc-472b-44df-aa32-053d35f4d87b",
   "metadata": {},
   "source": [
    "Once you have this, make the predictions for it, and average them by SHR, and plot the estimates. A big bonus if you can add the error bars as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a945c691-2861-4c3e-a420-164a46457fb5",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x152165210>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "p = me.predictions(model,\n",
    "                   newdata=dg,\n",
    "                   by='SHR')\n",
    "\n",
    "# Plot\n",
    "ax = sns.scatterplot(data=p, x='SHR', y='estimate')\n",
    "ax.vlines(p['SHR'], p['conf_low'], p['conf_high'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e494817-dcb5-4f86-89a6-6d3ddd2bcbfc",
   "metadata": {},
   "source": [
    "Now, conduct a null-hypothesis test of the differences between both males - i.e. comparing all males to each other. Are any more physically attractive than the rest?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ba1f5d13-7c80-4e81-a13c-58b6bb8e9b92",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr,\n",
       ".dataframe > tbody > tr {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (1, 8)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>term</th><th>estimate</th><th>std_error</th><th>statistic</th><th>p_value</th><th>s_value</th><th>conf_low</th><th>conf_high</th></tr><tr><td>str</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>&quot;Row 1 - Row 2&quot;</td><td>-0.556204</td><td>0.199335</td><td>-2.790292</td><td>0.005266</td><td>7.569062</td><td>-0.946895</td><td>-0.165514</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (1, 8)\n",
       "┌───────────────┬──────────┬───────────┬───────┬─────────┬──────┬────────┬────────┐\n",
       "│ Term          ┆ Estimate ┆ Std.Error ┆ z     ┆ P(>|z|) ┆ S    ┆ 2.5%   ┆ 97.5%  │\n",
       "│ ---           ┆ ---      ┆ ---       ┆ ---   ┆ ---     ┆ ---  ┆ ---    ┆ ---    │\n",
       "│ str           ┆ str      ┆ str       ┆ str   ┆ str     ┆ str  ┆ str    ┆ str    │\n",
       "╞═══════════════╪══════════╪═══════════╪═══════╪═════════╪══════╪════════╪════════╡\n",
       "│ Row 1 - Row 2 ┆ -0.556   ┆ 0.199     ┆ -2.79 ┆ 0.00527 ┆ 7.57 ┆ -0.947 ┆ -0.166 │\n",
       "└───────────────┴──────────┴───────────┴───────┴─────────┴──────┴────────┴────────┘\n",
       "\n",
       "Columns: term, estimate, std_error, statistic, p_value, s_value, conf_low, conf_high"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "p = me.predictions(model,\n",
    "                   newdata=dg,\n",
    "                   by='SHR',\n",
    "                   hypothesis='pairwise')\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "149ab96c-5339-4d19-a436-3e4f5e3e24b4",
   "metadata": {},
   "source": [
    "The results indicate that the step up in SHR does indeed increase physical attractiveness, and the estimate is around 0.55 rating scale units. \n",
    "\n",
    "Consider that this null hypothesis of zero difference might not be very compelling. Let's instead test the hypothesis that the increase in SHR increases attractiveness by *at least* 0.20 rating scale units. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ff7eb0a0-75e4-455a-970d-7038933c0da4",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr,\n",
       ".dataframe > tbody > tr {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (1, 8)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>term</th><th>estimate</th><th>std_error</th><th>statistic</th><th>p_value</th><th>s_value</th><th>conf_low</th><th>conf_high</th></tr><tr><td>str</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>&quot;(b2-b1)=0.2&quot;</td><td>0.356204</td><td>0.199335</td><td>1.786958</td><td>0.073944</td><td>3.757419</td><td>-0.034486</td><td>0.746895</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (1, 8)\n",
       "┌─────────────┬──────────┬───────────┬──────┬─────────┬──────┬─────────┬───────┐\n",
       "│ Term        ┆ Estimate ┆ Std.Error ┆ z    ┆ P(>|z|) ┆ S    ┆ 2.5%    ┆ 97.5% │\n",
       "│ ---         ┆ ---      ┆ ---       ┆ ---  ┆ ---     ┆ ---  ┆ ---     ┆ ---   │\n",
       "│ str         ┆ str      ┆ str       ┆ str  ┆ str     ┆ str  ┆ str     ┆ str   │\n",
       "╞═════════════╪══════════╪═══════════╪══════╪═════════╪══════╪═════════╪═══════╡\n",
       "│ (b2-b1)=0.2 ┆ 0.356    ┆ 0.199     ┆ 1.79 ┆ 0.0739  ┆ 3.76 ┆ -0.0345 ┆ 0.747 │\n",
       "└─────────────┴──────────┴───────────┴──────┴─────────┴──────┴─────────┴───────┘\n",
       "\n",
       "Columns: term, estimate, std_error, statistic, p_value, s_value, conf_low, conf_high"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "p = me.predictions(model,\n",
    "                   newdata=dg,\n",
    "                   by='SHR',\n",
    "                   hypothesis='(b2-b1)=0.2')\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d66c983d-9e08-492f-9545-d9343a8efe27",
   "metadata": {},
   "source": [
    "Does this increase in SHR alter attractiveness ratings by at *least* 0.2 rating scale units? Not quite, according to the model. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f79cbfd6-33f6-453b-9cd0-d7b99ff972c3",
   "metadata": {},
   "source": [
    "### e. Model validity\n",
    "So far we have seen that a step up from 1 to 1.25 SHR, averaged over sexual partners and hand grip strength, leads to an increase of about half a rating scale point. This difference is not significant when consdering an effect of about 0.2 units - whether or not that is a useful null hypothesis is of course a theoretical discussion, but it is worth considering.\n",
    "\n",
    "There is one final, conceptual issue with the analysis as completed in the paper, and it is quite important from a theoretical perspective. \n",
    "\n",
    "Consider the structure of the model we have examined, and consider the introduction of the paper in terms of how it discusses the findings/theory.  Can you propose an alternative model that makes more sense? This is a difficult question, but take some time to consider."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a1e6cb6f-44fc-48c9-972f-60632a566d27",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "# Your answer here\n",
    "# The issue is that the authors talk about attractiveness predicting measures of strength/body size, and sexual behaviour.\n",
    "# they use those measures to predict attractiveness, but this only partially makes sense. \n",
    "# How can number of sexual partners predict facial attractiveness, adjusted for other variables?\n",
    "# this is like saying - having more sexual partners makes you better looking. \n",
    "# But its much more logical to consider that being better looking means you have more sexual partners.\n",
    "# So the model is mis-specified; instead they should be predicting number of partners from the body traits."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c427518d-5013-4e61-b843-ade461ac821b",
   "metadata": {},
   "source": [
    "If you've figured it out, can you fit the more theoretically correct model to the data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "dc12db8c-7498-4fea-b95e-0db64ae8f6db",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>Partners</td>  <th>  R-squared:         </th> <td>   0.175</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>OLS</td>    <th>  Adj. R-squared:    </th> <td>   0.102</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>  <td>    38</td>   <th>  F-statistic:       </th> <td>   2.400</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>  <td>nonrobust</td> <th>  Prob (F-statistic):</th>  <td>0.0849</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "         <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>       <td>  -11.9806</td> <td>   13.977</td> <td>   -0.857</td> <td> 0.397</td> <td>  -40.386</td> <td>   16.425</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SHR</th>             <td>   -0.6747</td> <td>   12.389</td> <td>   -0.054</td> <td> 0.957</td> <td>  -25.851</td> <td>   24.502</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MaxGripStrength</th> <td>    0.1961</td> <td>    0.148</td> <td>    1.327</td> <td> 0.193</td> <td>   -0.104</td> <td>    0.497</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Attractive</th>      <td>    3.6876</td> <td>    2.319</td> <td>    1.590</td> <td> 0.121</td> <td>   -1.025</td> <td>    8.400</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &    Partners   & \\textbf{  R-squared:         } &     0.175   \\\\\n",
       "\\textbf{Model:}            &      OLS      & \\textbf{  Adj. R-squared:    } &     0.102   \\\\\n",
       "\\textbf{No. Observations:} &         38    & \\textbf{  F-statistic:       } &     2.400   \\\\\n",
       "\\textbf{Covariance Type:}  &   nonrobust   & \\textbf{  Prob (F-statistic):} &   0.0849    \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                         & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Intercept}       &     -11.9806  &       13.977     &    -0.857  &         0.397        &      -40.386    &       16.425     \\\\\n",
       "\\textbf{SHR}             &      -0.6747  &       12.389     &    -0.054  &         0.957        &      -25.851    &       24.502     \\\\\n",
       "\\textbf{MaxGripStrength} &       0.1961  &        0.148     &     1.327  &         0.193        &       -0.104    &        0.497     \\\\\n",
       "\\textbf{Attractive}      &       3.6876  &        2.319     &     1.590  &         0.121        &       -1.025    &        8.400     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:               Partners   R-squared:                       0.175\n",
       "Model:                            OLS   Adj. R-squared:                  0.102\n",
       "No. Observations:                  38   F-statistic:                     2.400\n",
       "Covariance Type:            nonrobust   Prob (F-statistic):             0.0849\n",
       "===================================================================================\n",
       "                      coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------\n",
       "Intercept         -11.9806     13.977     -0.857      0.397     -40.386      16.425\n",
       "SHR                -0.6747     12.389     -0.054      0.957     -25.851      24.502\n",
       "MaxGripStrength     0.1961      0.148      1.327      0.193      -0.104       0.497\n",
       "Attractive          3.6876      2.319      1.590      0.121      -1.025       8.400\n",
       "===================================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "m3 = smf.ols('Partners ~ SHR + MaxGripStrength + Attractive', data=faces).fit()\n",
    "m3.summary(slim=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64e65d4f-ce97-44f3-8296-ef5ff777c894",
   "metadata": {},
   "source": [
    "# Case Study Two\n",
    "## Women can judge sexual unfaithfulness from unfamiliar men's faces\n",
    "### Rhodes, Morley, & Simmons, 2013\n",
    "In the next study, we will examine the central claim from this manuscript. \n",
    "\n",
    "The manuscript is available from Canvas, and the data can be found here when you are ready: https://vincentarelbundock.github.io/Rdatasets/csv/Stat2Data/FaithfulFaces.csv\n",
    "\n",
    "The first thing you might notice is that much of the analysis does not make sense! I agree. Unlike the first paper, to test the central claim here, we are going to have to do our own analysis. First, lets download the data, read it in, and print the top 10 and bottom 10 rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "989b8b35-a079-43a3-b177-5cff1e8e2ff5",
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    "slideshow": {
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    {
     "data": {
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       "      <td>4.300</td>\n",
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       "   rownames  SexDimorph  Attract  Cheater  Trust  Faithful FaceSex RaterSex\n",
       "0         1       4.900    2.000        1  4.118     6.294       F        M\n",
       "1         2       2.583    2.083        1  4.000     6.588       F        M\n",
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       "3         4       4.083    2.917        0  4.118     5.412       F        M\n",
       "4         5       4.500    3.500        0  3.235     4.000       F        M"
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      ],
      "text/plain": [
       "     rownames  SexDimorph  Attract  Cheater  Trust  Faithful FaceSex RaterSex\n",
       "165       166       3.833    4.167        0  5.294     5.471       M        F\n",
       "166       167       3.083    2.583        1  5.294     5.824       M        F\n",
       "167       168       5.250    2.917        0  3.000     3.824       M        F\n",
       "168       169       4.750    2.333        0  3.000     3.824       M        F\n",
       "169       170       5.167    3.833        0  2.941     3.353       M        F"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "faith = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/Stat2Data/FaithfulFaces.csv')\n",
    "\n",
    "display(faith.head(), faith.tail())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "283c9110-3265-4c84-9341-0a59ae7be6db",
   "metadata": {},
   "source": [
    "The data contains a dichotomous variable, `Cheater` that codes whether the face belonged to someone who had admitted to infidelity. There are other variables such as `Trust` - how trustworthy that face appears, `Faithful` - ratings of faithfulness, `Attract` - how attractive the face was judged to be, and `RaterSex` - whether the face was rated by females or males. `FaceSex` is irrelevant because female participants rated only male faces and vice versa.\n",
    "\n",
    "The specific claim here is that females can accurately perceive infidelity from men's faces, presumably via their ratings of faithfulness, and this is to be compared to males. \n",
    "\n",
    "Fit the appropriate model to the data that allows us to predict the `Cheater` variable from faithfulness and participant sex. This will need to test the difference between males and females and faithfulness ratings, so an interaction is needed (check 'model 1' in the paper for a clue).\n",
    "\n",
    "Once done, print the summary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "839936a8-abe3-45a9-a058-4b27254a4307",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
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    "tags": [
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.596754\n",
      "         Iterations 5\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Probit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>Cheater</td>     <th>  No. Observations:  </th>  <td>   170</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                <td>Probit</td>      <th>  Df Residuals:      </th>  <td>   166</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>     3</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Fri, 30 Aug 2024</td> <th>  Pseudo R-squ.:     </th>  <td>0.01493</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>21:15:15</td>     <th>  Log-Likelihood:    </th> <td> -101.45</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -102.99</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th>  <td>0.3803</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "             <td></td>               <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>              <td>    0.7160</td> <td>    0.729</td> <td>    0.982</td> <td> 0.326</td> <td>   -0.713</td> <td>    2.145</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>RaterSex[T.M]</th>          <td>   -1.2827</td> <td>    1.276</td> <td>   -1.006</td> <td> 0.315</td> <td>   -3.783</td> <td>    1.217</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Faithful</th>               <td>   -0.2597</td> <td>    0.153</td> <td>   -1.698</td> <td> 0.089</td> <td>   -0.559</td> <td>    0.040</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Faithful:RaterSex[T.M]</th> <td>    0.2571</td> <td>    0.241</td> <td>    1.066</td> <td> 0.287</td> <td>   -0.216</td> <td>    0.730</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}         &     Cheater      & \\textbf{  No. Observations:  } &      170    \\\\\n",
       "\\textbf{Model:}                 &      Probit      & \\textbf{  Df Residuals:      } &      166    \\\\\n",
       "\\textbf{Method:}                &       MLE        & \\textbf{  Df Model:          } &        3    \\\\\n",
       "\\textbf{Date:}                  & Fri, 30 Aug 2024 & \\textbf{  Pseudo R-squ.:     } &  0.01493    \\\\\n",
       "\\textbf{Time:}                  &     21:15:15     & \\textbf{  Log-Likelihood:    } &   -101.45   \\\\\n",
       "\\textbf{converged:}             &       True       & \\textbf{  LL-Null:           } &   -102.99   \\\\\n",
       "\\textbf{Covariance Type:}       &    nonrobust     & \\textbf{  LLR p-value:       } &   0.3803    \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                                & \\textbf{coef} & \\textbf{std err} & \\textbf{z} & \\textbf{P$> |$z$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Intercept}              &       0.7160  &        0.729     &     0.982  &         0.326        &       -0.713    &        2.145     \\\\\n",
       "\\textbf{RaterSex[T.M]}          &      -1.2827  &        1.276     &    -1.006  &         0.315        &       -3.783    &        1.217     \\\\\n",
       "\\textbf{Faithful}               &      -0.2597  &        0.153     &    -1.698  &         0.089        &       -0.559    &        0.040     \\\\\n",
       "\\textbf{Faithful:RaterSex[T.M]} &       0.2571  &        0.241     &     1.066  &         0.287        &       -0.216    &        0.730     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{Probit Regression Results}\n",
       "\\end{center}"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                          Probit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                Cheater   No. Observations:                  170\n",
       "Model:                         Probit   Df Residuals:                      166\n",
       "Method:                           MLE   Df Model:                            3\n",
       "Date:                Fri, 30 Aug 2024   Pseudo R-squ.:                 0.01493\n",
       "Time:                        21:15:15   Log-Likelihood:                -101.45\n",
       "converged:                       True   LL-Null:                       -102.99\n",
       "Covariance Type:            nonrobust   LLR p-value:                    0.3803\n",
       "==========================================================================================\n",
       "                             coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------------------\n",
       "Intercept                  0.7160      0.729      0.982      0.326      -0.713       2.145\n",
       "RaterSex[T.M]             -1.2827      1.276     -1.006      0.315      -3.783       1.217\n",
       "Faithful                  -0.2597      0.153     -1.698      0.089      -0.559       0.040\n",
       "Faithful:RaterSex[T.M]     0.2571      0.241      1.066      0.287      -0.216       0.730\n",
       "==========================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "model = smf.probit('Cheater ~ Faithful * RaterSex', data=faith).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "722790a4-ec36-4581-bac2-83572007840e",
   "metadata": {},
   "source": [
    "With the model fitted, make predictions for male and female raters, for faces of faithfulness ratings of 1 through to 9. Plot those outcomes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b905d9ee-f5f5-4041-999f-06ed4c6f517e",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Faithful', ylabel='estimate'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bP2k8X/sSrHwSHA5zc4mIiLiJioyns1ig9WPQYYLx/PspsORBsGeZm0tERMQNVGS8xQ33Qbd3wGKFbbNh/mDIOmN2KhERkSKlWxR4k4Z9wa8UfH4P/LoE5t4JvWcbZzqJiIi4QJs2bThy5EjOvZWcTicWi4XIyEg++OADt+cxpcgkJyfzzDPPEB8fj81mo0uXLjz22GN53nAqPj6eiRMn8scffxASEkLfvn0ZNmyYCak9RL0u4P8JzOtnXDBvVnfo+6lxDRoRESnenE7jOmHu5BtkHKZQAGPGjKFHjx44nU7S0tIICgrCUsBtuIopRWbkyJFUrFiRDRs2kJSUxP3338+MGTMYMmRIrvV27drFvffey3PPPUe3bt347bffGDRoEFWrVqVDhw5mRPcMNdrAwMUwJxr2xcGMTsaF9EpVMDuZiIhciNMJH7Q3/rntTpVvMO7pZ1IRuVxuP0Zmz549xMfHM3r0aAIDA6lcuTIxMTHMmXP+Rd0+/vhj2rZtS/fu3bFYLNSpU4d58+bRuHFjd8f2PJWvh7u+gODycCjRuHN2yj6zU4mIyEV5Zpkwk9v3yOzcuZPQ0FAqVqyYs6xGjRocOHCAEydOEBISkrN8+/bt3HjjjYwaNYrvvvuOcuXKcdddd9G7d+8Cv6/dbndJ/v9uz9Xbdany9WDQcqxzumM5ugvnB+1x9FsAYbXy9XKPmPEyaD7P5+0zaj7Pd+6MTqcz53FBg1eY89US5Ps6ZE6nkzFjxjB+/Pic5xaLhXXr1hEUFFSgt87+POx2+3l/D/L798LtRebUqVMEBgbmWpb9PC0tLVeROX78ODNnzmTSpEm88sorJCQkMGzYMMqUKVPgr5YSExMvP7wbt+tKvk1e5dpNowk4sQ/H9PbsvGEC6WXyV2bAM2a8HJrP83n7jJrP8+3cuRMfHx/S09NxXPJaX27eK5OVXqDVnU4njz/+OF26dDnvd2lpBSthZ86cITMzkx07dhTodedye5EJCgoiPT33h5b9PDg499k1fn5+tG3bltatWwPQpEkTunbtyooVKwpcZCIiIrDZbIUP/h92u53ExESXb7fI/F8jnB9H43twO3XjRuPoM8/4XvQiPG7GAtJ8ns/bZ9R8ni97xlq1avH3338TGBhIQECA2bEui8Viwc/Pj6CgIJxOJ+np6QQGBhbqYF+r1Yqvry81a9Y873PJ/uwuxe1FplatWqSkpJCUlERYWBhgHNQbHh5O6dKlc61bo0YNMjIyci3L3j1XUDabrUj+j1JU23W5kIpw1zL4uDeWvZuwze4Jd86Gmrdc8qUeM2MhaT7P5+0zaj7PZ7PZsFgsOQ9PltcchZ0r+3WX83fA7Qf7VqtWjcaNGzN+/HhSU1PZt28fU6ZMITo6+rx177zzTr7++msWL16M0+lk8+bNLF26lK5du7o7tncIKAP9FxjlJSsdPr4Tfl5kdioREZFCM+XKvrGxsWRlZdG2bVt69epFy5YtiYkxbn4YGRnJkiVLAGjWrBlTpkxh5syZNG7cmCeeeILHHnuMtm3bmhHbO/gFwZ1zoV43cGQaVwDeOsvsVCIi4iHWrFlDjx49zI6Rw5TryISFhREbG5vn7xISEnI9b9WqFa1atXJHrJLDxw+iP4BlIbB1Jix5AM6cgGbDzU4mIiJSILrXUklltUHnWGj2gPF85ZPwzfh8n34nIiJSHKjIlGQWC9z6IrR52ni+bgJ8+Thc8tRAERGR4kFFpqSzWOCm0dBxovE87l1YPBzsWebmEhERyQcVGTE0vRe6vQsWG/z4MXw2CLLOmJ1KRMSrFObyId7MFZ+Hioz8q2Ef6DUTbH6wYxnWeXdiLeAVH0VE5Hy+vr5Awa986+2yP4/sz6cwTDlrSYqxup2g32cwty+Wv9ZRKyUZIr6AoFCzk4mIeCybzUZoaCiHDx8GjKvce/qF8cDYo3LmzBmsVmuB5nE6naSlpXH48GFCQ0Mv64KIKjJyvuqtYeBinLN7UOrYTzg/jjYupBcQcsmXiohI3sLDwwFyyow3cDqdZGZm4uvrW6hiFhoamvO5FJaKjOStchMc/RfinNkVn783w6zu0P9zCAw1O5mIiEeyWCxUqlSJChUqkJmZaXYcl7Db7ezYsYOaNWsWeK+Kr6+vS25NoSIjF3ZlJL/f8Cp1f3gCy/4fYFY3GLAQAsuanUxExGN5072l7HY7AAEBAabNpIN95aLSQ6/F0X8xBJaDAwkwsyukHTU7loiICKAiI/kRfp1x5+ygMPjnR5jZBU4lm51KRERERUbyqWJ9o8wEl4eDifBRZziVZHYqEREp4VRkJP8q1IW7voBSFeHwzzCjE6R6z9H3IiLieVRkpGDK1zbKTOlKcORXo8ycPGR2KhERKaFUZKTgwmqdLTNXQtJvMON2OPGP2alERKQEUpGRwrmiBgz+AkKuhuSdZ8vMAbNTiYhICaMiI4VXrrpRZspUgaO74MPb4PjfZqcSEZESREVGLk/ZakaZCa0Kx/4yykzKXrNTiYhICaEiI5cvtIpxzEzZayBlD3x4OxzbbXYqEREpAVRkxDVCKxtlplwNOL7XOJvp6J9mpxIRES+nIiOuU+Yqo8xcUQuO7zPKTPIus1OJiIgXU5ER1wqpZJSZsNpwYr9xNlPSTrNTiYiIl1KREdcrXdG4nUH5unDyH6PMHPnd7FQiIuKFVGSkaJSqYJSZCvUh9ZBRZg7/anYqERHxMioyUnSCw2DQUgiPgFOHjWNmDv1sdioREfEiKjJStIKvgIFLoFIDSEsy7pp9MNHsVCIi4iVUZKToBZWDgYvhykhISzbKzD8/mp1KRES8gIqMuEdgWRiwCK6KgvRjRpk5kGB2KhER8XAqMuI+gaEwYCFcfT2cPg4fdYW/t5idSkREPJiKjLhXQAgMWABVmsGZ4zCrG+zbbHYqERHxUCoy4n7+paHffKjaHM6cgFndYW+c2alERMQDqciIOfxLQb/PoFpLyDgJs3vAno1mpxIREQ+jIiPm8QuGvp9C9daQkQqze8JfG8xOJSIiHkRFRszlFwR95kGNNpCZBnPugD/Xmp1KREQ8hIqMmM83EO6cCzXbQVY6fNwbdq0xO5WIiHgAFRkpHnwD4M45cG0HyDoNH98JO78yO5WIiBRzKjJSfPj4Q6+ZUPt2sJ+BeX3g91VmpxIRkWJMRUaKFx9/uGMG1O0M9gyY1xd+W2F2KhERKaZUZKT48fGD6A+hXjdwZMInA+DXZWanEhGRYkhFRoonmy/0nA7X9TTKzGeD4JfFZqcSEZFiRkVGii+bD3R/HyJ6gSMLPhsMPy0wO5WIiBQjKjJSvNl8oPu70KAPOO3w+RBInG92KhERKSZUZKT4s9qg69sQ2d8oMwuGwo+fmJ1KRESKARUZ8QxWG3SeDI0GgdMBC4fBto/NTiUiIiYzpcgkJycTExNDVFQUTZs2Zdy4cWRlZeW57pAhQ4iIiCAyMjLnsX79ejcnlmLBaoVOb0DU3YATFsXA1llmpxIRERP5mPGmI0eOpGLFimzYsIGkpCTuv/9+ZsyYwZAhQ85b96effmL69Olcf/31JiSVYsdqhdtfB6sPxL8PSx4wDgSOGmx2MhERMYHb98js2bOH+Ph4Ro8eTWBgIJUrVyYmJoY5c+act+6+ffs4fvw49erVc3dMKc4sFuj4CjS933i+bCRsnmZqJBERMYfb98js3LmT0NBQKlasmLOsRo0aHDhwgBMnThASEpKzPDExkeDgYB5++GESExMJCwvjrrvuIjo6usDva7fbXZL/v9tz9XaLk2I/Y7sXsVgsWL+fAl88gsOehbPJ0Hy/vNjPd5m8fT7w/hk1n+fz9hmLcr78btPtRebUqVMEBgbmWpb9PC0tLVeRycjIoGHDhjz88MPUqlWLuLg4HnzwQYKDg+nYsWOB3jcxMfHyw7txu8VJsZ4xrCdX1ThK+K55WL98jH379nC4esGKbrGezwW8fT7w/hk1n+fz9hnNnM/tRSYoKIj09PRcy7KfBwcH51rerVs3unXrlvO8RYsWdOvWjRUrVhS4yERERGCz2QoXOg92u53ExESXb7c48ZgZG76N45srsX73OpV/nsJVlcJxNnvgki/zmPkKydvnA++fUfN5Pm+fsSjny972pbi9yNSqVYuUlBSSkpIICwsDYNeuXYSHh1O6dOlc686fP/+8vS8ZGRn4+/sX+H1tNluR/CUqqu0WJx4x4y3Pgo8vrJuA9atnAQe0eDhfL/WI+S6Dt88H3j+j5vN83j6jmfO5/WDfatWq0bhxY8aPH09qair79u1jypQpeR73kpqaytixY/nll19wOBysXbuWZcuW0bt3b3fHluLOYoGbn4TWTxrPv3oe1r9qaiQRESl6ppx+HRsbywsvvEDbtm2xWq1069aNmJgYACIjIxkzZgxdunRh0KBBpKWl8cADD5CcnEzlypWZMGECUVFRZsQWT9D6MeMU7TUvwpqx4LAby0RExCuZUmTCwsKIjY3N83cJCQk5P1ssFmJiYnJKjki+3DTauM7MV8/D2vHGbQ1aP2HstREREa+iWxSId2rxMNz6ovHzugnGHhqn09xMIiLicioy4r1ufBDav2T8vOFVYw+NyoyIiFdRkRHv1iwGOk40fv7uDVj1tMqMiIgXUZER79f0Xrj9NePnTW/ByidVZkREvISKjJQMTYYYd84G+H4KrPifyoyIiBcw5awlEVNEDTbOZlryIMS/j8WeBZX6mp1KREQug/bISMnSaAB0mwJYsG75gCrbJ4HTYXYqEREpJBUZKXka9oXu7+G0WCm/9wssSx40LpwnIiIeR0VGSqYGvXF2M8qMdftcWDAU7JlmpxIRkQJSkZESy3ldT/5s/BxOqy/89DnMHwxZGWbHEhGRAlCRkRItpVJLHL1mgc0ffl0Kn/SHzNNmxxIRkXxSkRGpdSv0mQs+gbBzJczrAxlpZqcSEZF8UJERAajZFvp9Br7BsGsNfNwLzqSanUpERC5BRUYk2zUtYcBC8A+B3Rtgdg84fdzsVCIichEqMiLnqtIUBi6CgDKwLw5mdoP0Y2anEhGRC1CREfmvqxrDoGUQWA4ObIWPOsOpZLNTiYhIHlRkRPJS6f/gri8guAIcTIQZt0PqYbNTiYjIf6jIiFxIxXoweDmUrgRHfoUPb4MTB8xOJSIi51CREbmYsFpGmSlTGZJ3wocdIWWv2alEROQsFRmRSylX3SgzZavBsd3Gnpmjf5qdSkREUJERyZ/QKjB4BVxRE47vgw9vh6SdZqcSESnxVGRE8ivkSrhrOZSvCycPGHtmDv9qdioRkRJNRUakIEpXNM5mCo+AU4eNs5n+2W52KhGREktFRqSggq+AgUvgykaQlmxcZ2b/FrNTiYiUSCoyIoURVM64AnDlpnA6xbgC8N44k0OJiJQ8KjIihRVQBvp/DlVbwJkTMKs77P7W7FQiIiWKiozI5fAvbdw1u/rNkHkKZkcbd88WERG3UJERuVx+QdBnHtS6FbLS4eM74feVZqcSESkRVGREXME3AHrPgTqdwH4G5vWDX5eanUpExOupyIi4io8f3DED6vcARyZ8Ogh++tzsVCIiXk1FRsSVbL7Qcxo06ANOO3w+BLbNNTuViIjXUpERcTWrDbpOgUYDwemARffDlhlmpxIR8UoqMiJFwWqFTm/C9fcCTlj6EMS9b3YqERGvoyIjUlSsVuj4CjR7wHi+YjRsnGxuJhERL6MiI1KULBa49UVo+ajxfNXTsH6iuZlERLyIioxIUbNYoO0zcPPTxvM1LxoPp9PcXCIiXkBFRsRdWo2Gdi8YP6+fCKufVZkREblMKjIi7tT8IeO4GYCNsbDiMZUZEZHLoCIj4m5Nh0GnNwALxL8Hy0aCw2FyKBERz6QiI2KGqMHQbQpYrMY1ZhYPB4fd7FQiIh5HRUbELA37Qo+pYLHBjx/DgqFgzzQ7lYiIR1GRETFTRLRxfyarr3FfpvmDISvD7FQiIh5DRUbEbPW6QO/ZYPMz7pj9SX/IPG12KhERj6AiI1Ic1O4AfeaBTwDsXAnz+kBGmtmpRESKvUIVme+++4777ruPHj16cOTIESZMmEBWVla+X5+cnExMTAxRUVE0bdqUcePGXfL1v//+Ow0aNCAuLq4wkUWKv5ptod988A2GXWvg415wJtXsVCIixVqBi8zSpUsZPXo0tWvXZs+ePQCsWbOG119/Pd/bGDlyJEFBQWzYsIH58+ezadMmZsyYccH109PTeeSRRzh9Wrvbxctd0xIGLAC/0rB7A8zuAaePm51KRKTYKnCRef/995kyZQoPP/wwVquV8uXL895777Fs2bJ8vX7Pnj3Ex8czevRoAgMDqVy5MjExMcyZM+eCrxkzZgy33HJLQaOKeKYqN8DAxRBQBvbFwcxukH7M7FQiIsWST0FfcPDgQRo0aACAxWIBoGrVqqSl5e/7/J07dxIaGkrFihVzltWoUYMDBw5w4sQJQkJCcq2/aNEi9uzZw7hx45gyZUpB4+aw2117jY7s7bl6u8WJt89YrOer1BD6L8I6pyeWA1txzuiMo/8CCLoi35so1vO5iLfPqPk8n7fPWJTz5XebBS4y1apV4+uvv861h2Tjxo1UrVo1X68/deoUgYGBuZZlP09LS8tVZHbt2sWkSZOYO3cuNputoFFzSUxMvKzXu3u7xYm3z1ic5wu4/hWu3TQa30OJZLzfjt+bvUqWf7kCbaM4z+cq3j6j5vN83j6jmfMVuMg8/PDDxMTE0LZtW86cOcPzzz/PsmXLeO211/L1+qCgINLT03Mty34eHBycs+zMmTM8/PDDPPnkk1x55ZUFjXmeiIiIyy5D57Lb7SQmJrp8u8WJt8/oGfM1hHrX4ZzVjcCTu/m/LU/g6L8QQi79/wnPmO/yePuMms/zefuMRTlf9rYvpcBF5sYbb2TevHl88sknNG3aFIfDwQcffMD//d//5ev1tWrVIiUlhaSkJMLCwgBjz0t4eDilS5fOWS8xMZHdu3fz1FNP8dRTT+Usv+++++jatSvPP/98gXLbbLYi+UtUVNstTrx9xmI/X8W6MHg5fNQFS/JObDM7waClEFolXy8v9vO5gLfPqPk8n7fPaOZ8BS4y06dP55577uG5557LtfyNN95g5MiRl3x9tWrVaNy4MePHj+eFF17g2LFjTJkyhejo6FzrRUVFsX379lzLateuzbvvvkvTpk0LGlvEs11R42yZ6QzHdsOHt8GgJVCuutnJRERMla+zlo4ePcrmzZvZvHkzkydP5ocffsh5vnnzZtasWcNHH32U7zeNjY0lKyuLtm3b0qtXL1q2bElMTAwAkZGRLFmypHDTiHizslVh8AooVwOO74MPb4eknWanEhExVb72yPj5+TFixAiOHTNOAe3fv/95v+/du3e+3zQsLIzY2Ng8f5eQkHDB1/3222/5fg8Rr1TmKmPPzMyucGTHv3tmKtQ1O5mIiCnyVWRKlSrFpk2bAOjQoQNffvllkYYSkYsoHQ53fWFcX+ZQIsy4HQYsgkr5O05NRMSbFPiCeBcqMUePHr3sMCKST8Fhxp6YSg0hLdk4dmb/FrNTiYi4XYEP9t2+fTuvvPIKhw4dwuFwAJCZmcnRo0f56aefXB5QRC4gqJxRZmZHw9/xxh6afvOhig6GF5GSo8B7ZF544QXKly9PixYtuOaaa+jfvz82m41HHnmkKPKJyMUElDHuzVS1OZw5AbO6w+5vzU4lIuI2BS4yO3fu5KWXXqJfv37Y7XYGDx7MpEmTWLp0aVHkE5FL8S9t7Imp3hoyTxl7aHatMTuViIhbFLjIhISEEBAQQOXKldm50zj1s2HDhuzfv9/l4UQkn/yCoM8nUOtWyEqHj++EnavMTiUiUuQKXGSqV6/O3Llz8ff3JygoiF9//ZVdu3bl3EBSREziGwC9Z0OdTmA/g/XTAYT+s8HsVCIiRarAReahhx7ijTfeYO/evdxzzz306tWLnj170r1796LIJyIF4eMPd8yA+t2xODKpvmUMlh/nmp1KRKTIFPispUaNGrF+/Xp8fX3p3bs3devW5eTJkzRv3rwo8olIQdl8occ0HDZ/rNvnYVkyHFIPQstHQHtORcTLFLjIgHHNmP379+N0OgHjyr6bN2+mSZMmLg0nIoVk88HZ5S0OnnISvusTWDMWTv4DHV8Bq/feuE5ESp4CF5l33nmHN99887zlFouFX3/91SWhRMQFLFb21xtGhRoNsK56CjZPg5MHoec08A00O52IiEsUuMjMmDGDt99+mzZt2ugAXxEP4Gx6H4RUgoXDYMcy48J5feYaF9QTEfFwBT7Y18fHh9atW6vEiHiS63rAgIXgXwb2fQ8fdICUfWanEhG5bAUuMv369WPSpEmkpqYWRR4RKSrVWsDdX0LpKyHpN5jeDg7qtiIi4tkKdR2ZDz/8kCZNmlC3bt1cDxEp5irWgyGroXxd4+DfDzvCn+vMTiUiUmgFPkbm5Zdf5u677+bGG2/EZtPZDyIep8zVcPcKmNcP9nwHs3tC93chItrsZCIiBVbgInPy5EndIFLE0wWWhf4LYOG98Mti+Pwe44ymGx8wO5mISIEU+Kuldu3asXr16qLIIiLu5BsA0R/C9cOM56uegi+fBIfD3FwiIgVQ4D0yp0+f5qGHHqJGjRqEhobmOntp5syZLg0nIkXMaoOOE6DMVbD6Wfj+bePYme7vGrc7EBEp5gpcZGrWrEnNmjWLIouImMFigeYPQalwWBwDPy+AU0fgzjkQUMbsdCIiF1XgIvPAA/oOXcQrNegNpcrDJwNg9wb48DboN9+4mJ6ISDGV7yLz/PPP8/zzz/PEE09ccJ2XXnrJJaFExCQ12sDg5TDnDjj0k3Gtmf6fQ/naZicTEclTvg/2zb5BpIh4uUoN4J5VcEVNOL4Ppt8KezaZnUpEJE/53iMzZswYAO68804aNGhw3u/Xr1/vulQiYq6y1eDuVTC3N/y9GWZ1M242Wbez2clERHIp8OnXgwcPPm9ZamoqDz30kEsCiUgxEXwFDFwC13aErNPGsTPxU81OJSKSS772yOzZs4fbb78du92O0+nM83YEjRo1cnk4ETGZXxD0ng1fjIKtH8HyR+HEAWj7rHG2k4iIyfJVZKpWrcpnn33GiRMnuPfee5k6Nfd/lfn7+3PttdcWSUARMZnNBzq/adza4Jtx8O3rxrVmukwGm6/Z6USkhMv3MTLZe2GWLVtG5cqVc5anpqbi5+eHn5+f69OJSPFgsUCr/0HpcFg6En6cC6mHoddH4F/a7HQiUoIV+BiZjIwMhg8fDsDq1au54YYbaNmyJVu2bHF5OBEpZhoNhD5zwTcIdn0NMzoZhUZExCQFLjLjx48nJCQEp9PJ66+/zogRIxgxYgQvv/xyUeQTkeLm2vYwaBkEXQH/bINpt0DyLrNTiUgJVeAi89tvv/HCCy+wf/9+9u7dS9++fenbty+7dukfZCIlxtWN4Z7VxmnaKXuMC+f9rb2yIuJ+BS4yWVlZOJ1OvvvuO+rXr0+pUqU4duwY/v66wZxIiXJFDaPMVGoIacnwUSf4faXZqUSkhClwkbnxxht58MEHmTJlCp06dWLfvn0MHz6c1q1bF0E8ESnWSlWAu76AGm0hMw3m9oGtM81OJSIlSIGLzNixY7nuuuvo378/nTp14tSpU9SvX59nn322KPKJSHHnXwr6fgIN+oLTDksehLUTQLc1ERE3KHCR8ff3JzMzk3fffZc2bdoQFBREQkICqampRZFPRDyBzRe6TYGWjxjP146HZSPBnmVqLBHxfgUuMpMnTyYuLo7Y2Fh8fX0JCwsjPDycF198sSjyiYinsFiMK/7e9ipggS0z4JP+kJFmdjIR8WIFLjJLly4lNjaW5s2bY7FYCAoK4qWXXuL7778vinwi4mmuHwq9Z4FPAPy+AmZ2gVPJZqcSES9V4CKTlpZGuXLlAHCe/Q48ICAAq7XAmxIRb1W3MwxcDAGhxt2zP7gVju02O5WIeKECt4+GDRvy1ltvAWA5e9O4WbNmERER4dpkIuLZqtwAd6+EkKsh+Q+Yfiv886PZqUTEyxS4yDz11FMsXbqUm266iVOnTnHbbbcxc+ZMHn/88aLIJyKerEIdGLIaKl4HqYfgw9tg1xqzU4mIF8n3TSOzVa5cmS+++IK1a9eyf/9+wsPDad26NaVKlSqKfCLi6UKuhMHLYV4/2L0B5twBXadAg95mJxMRL1DgIgMQGBhIx44dXZ1FRLxVQBno/zksuh9++hwW3gsn/4HmDxlnO4mIFJKO0BUR9/Dxhx7ToNkDxvOvnoMvHweH3dxcIuLRVGRExH2sVmg/Dm4dZzyPexfmD4bM0+bmEhGPZUqRSU5OJiYmhqioKJo2bcq4cePIyjr/CqAOh4PJkyfTqlUrIiMj6dy5M8uXLzchsYi41I0PQM/pYPODXxbD7B6QfszsVCLigUwpMiNHjiQoKIgNGzYwf/58Nm3axIwZM85bb86cOSxatIhZs2aRkJDAqFGjeOSRR9i7d6/7Q4uIa0VEG8fN+IfAnu/gg45w/G+zU4mIh3F7kdmzZw/x8fGMHj2awMBAKleuTExMDHPmzDlv3X79+rF06VKqVKlCRkYGR48eJTAwkICAAHfHFpGicM1NMHgFlK4ER36Fae3g0C9mpxIRD1Kos5Yux86dOwkNDaVixYo5y2rUqMGBAwc4ceIEISEhOcutVitBQUF8++23DB06FKfTyRNPPEGFChUK/L52u2sPKMzenqu3W5x4+4yar5goXxcGr8T6cTSWpN9xftAeR+85ULX5JV/qMTMWkubzfN4+Y1HOl99tWpzZ9xlwk8WLFzNp0iTWrl2bs2zv3r20a9eOdevWER4eft5rMjIysFqtbN68mZiYGMaNG8dtt92Wr/ez2+1s27bNRelFpKjYMk5QM/5pSh37CYfVl78inyDlytZmxxIRkzVs2BCbzXbB37t9j0xQUBDp6em5lmU/Dw4OzvM1fn5+ADRr1oyuXbuydOnSfBeZbBERERf9IArKbreTmJjo8u0WJ94+o+YrhiJX4lw0DOuOZVTfMhZnWCDO64ddcHWPnLEANJ/n8/YZi3K+7G1fituLTK1atUhJSSEpKYmwsDAAdu3aRXh4OKVLl8617ssvvwyQ6/YHGRkZhIaGFvh9bTZbkfwlKqrtFifePqPmK0ZspaDXTFjxGJbNU7GsfMK4cN4tY4xTty/0Mk+asRA0n+fz9hnNnM/tB/tWq1aNxo0bM378eFJTU9m3bx9TpkwhOjr6vHWjoqKYN28emzdvxuFwsGbNGpYvX84dd9zh7tgi4i5WG9w2Edo+ZzzfGAsLh0FWhrm5RKRYMuX069jYWLKysmjbti29evWiZcuWxMTEABAZGcmSJUsAuOWWW3j66ad5+umnadKkCW+//TaTJ0+mUaNGZsQWEXexWKDlKOj2Llh9IPFT+PgOOH3C7GQiUsy4/aslgLCwMGJjY/P8XUJCQq7n0dHRee6tEZESoGEfKFUePhkIf66FGbdBv/lQ+vyTAkSkZDKlyHiDTLuDP49l4nvgBD42GzarBasFLBbjf60WCzarBcvZn62Wf39fkHVFSryat8DgL4y7Zh9MhOntoP8CCKtldjIRKQZUZArpwbnbWP1rMny1sUjfJ8/SYzlbeqz/KUjn/Gy1/mfdswXJck5x+u92rdZzfrZYsOAkNfUkodu3nC1a/1333+cWC2ff33jv7HWN9z9n3f+8Lu9yd/a1/33PPGY2ZsnOkDv/v1nP/XzOKYlOB38mZeDYewwfm+3f11nPL5TZec79DAu8rspp4V0ZCfesNm5lcPRPo8z0/RSubGx2MhExmYpMIV1/TTkS9iTh4+OL3QlOpxOHExxOJw7HOT+fXe50OrGfXV4QdocT45JAbr3cT24Hj5j33u7wTZzb3srynwJnPacA5i6n55c9q/U/6+aUqTzWPfs87VQqpX+IzylWF1r339J48TJ4ueX0Qhnyt24Afi3m0PjbYZQ5uh37jE78fOMkfjxzDad2JeNrs52T55yie+7nZSWPGc/97M+d75xSn+dn/29GETGPikwh3d28Go2CUy55oZ68nFt67A4nzv+UHqMI/VuAHE6wny1Iudc9tzxx3rKc157d3r+vzf0e2evaz9mG0wmZdju79+yh8tVVwGLJXc4c57727CzZP59X5P6zruOcdS8wd67tXuIzuuS6OZnPXzf99Gl8/fxxcv5neOHP7/wM+f+zN/4s3VpOk466533cJJCRvOU7mbYkUH/9cBZkDeCF9e0B8wpFrtJzgT2I5+41PH+P3fnFzWKxYAVOn06j1KZNee+BLdDeyDzWvUipdPm6eeTF6WTv/tMc8Ttk7BW15i6guYq59b8z5i6oeRbQcz7rS+6BzmNvtXgGFRkTGP+nBhsWfIvxZQXsdjvbLEdo2PBqr7z+QfZVnwtTRv+rIKXn4uU07+JlzymY524v7/KaXUjtdju7/txN1WpVwWK9aHnNtUfxEkX3vHXPK7bOs3nPzurg/NlybTf353J+hvP3ar7lGIM99S1uPbOK531n0iroLyYFDOcUgbmKtcORx3bPKeO51v1PBmcBemb2a4qsnB47XjTbLS42Jlx6HRPkKk7WvMvq+V+B5y5QFiDjzGkC1317zp7R88tfXnsOs/9dcX5RLHhBvfDX8Hl/ZX+hr/f/uwcVpxOOZ9LQxD8nFRkRF8gpp8Xoawa73c62zIM0jKjklUUU5004Nk3BsvoZbs7cwM1lDhkX06tQ1zWb/0/xOXdP3vnFK/cevYKs+9+Sdu66WXY7f+zaRbVq1XP2ip5bhJ0XKb3/FskLlch/947+u90LldN/X293nL+uM58l/vzPxsmJk6kEBQfjzP4c/jNPrr2958x7XmG+yF7Zwn61n6ugXu6thE6mXuYGii+bBW5tlkVosDn/nFGRERHPZLHgbHofv58qRe3tL2FJ+h2mtoHOsfB/l3/RzHP3nJrFbrdTJm0/DetW8Moy6sq9ovlVkNKTr3UvWLyMdTKz7OzcuZPqNWrm+oo+997K3HsNs4tifvaYnlsqjYznbyv3PHkX0PN+f9ECem5GJ+Ws6ZTyN+/vp4qMiHi0U+WuwzF0LbZFw4xrzSwYAns3QYeXwMff7HhSzLj7q3273Y7/cX8a1rjCq8uomccUmXJlXxERlwoub1xb5qb/Gc9/mA4ftIdje8zNJSJFTkVGRLyD1QZtnjKu/BtYFg4kwHs3we+rzE4mIkVIRUZEvEutdjBsPVzZCE6nGPdo+nosOC73aE0RKY5UZETE+4RWgbu/hCZDjecbXoVZ3SDVyy/uKFICqciIiHfy8YfbX4We08E3GP5aD++1hL3fm51MRFxIRUZEvFtENAxdA2G14eQ/8OFtsPEtCnTFOxEptlRkRMT7VahjlJnrosFph1VPwacD4LSXXzFXpARQkRGRksG/FPScBre9ClZf+HUpvN8aDv5kdjIRuQwqMiJSclgscP1QuHsllKkMR/+EaW0hYY7ZyUSkkFRkRKTkubqxcYp2zXaQdRoWx8CSByEz3exkIlJAKjIiUjIFlYO+n8LNTwMW2DoTpt9q7KUREY+hIiMiJZfVCq1Gw4CFEHQFHNwO77WGHV+YnUxE8klFRkSkxs0wbANUbgpnjsO8vrD6WbBnmZ1MRC5BRUZEBKDMVXDXF3DDcOP5d2/CzC5w8qC5uUTkolRkRESy2Xyhw3i44yPwKw17voN3W8JfG8xOJiIXoCIjIvJf9bvBvWuhQn04ddjYM/PtJHA4zE4mIv+hIiMikpewmjDkK2jQB5wO+Op5+KQfpB8zO5mInENFRkTkQvyCoNs70PlNsPnDb8vhvVZwYJvZyUTkLBUZEZGLsVig8V1wzyoIrQope4zrzWyZoRtPihQDKjIiIvlxZUMYtg6u7Qj2M7D0IVh0P2SkmZ1MpERTkRERya/AsnDnx3DL82Cxwo9zYdotkPSH2clESiwVGRGRgrBaocXDMHAJBFeAwz8bd9H+eZHZyURKJBUZEZHCuKYl3LcBqjaHjJPw2SD48kmwZ5qdTKREUZERESms0uHGnpnmDxnPv38bZtwOx/ebm0ukBFGRERG5HDYfaPeCceyMfxnYFwfv3QS7vjE7mUiJoCIjIuIKdW6HYWshPALSkmBWd1j3iq4GLFLEVGRERFylXHW4ZzU0Ggg44Ztx8HEvSDtqdjIRr6UiIyLiSr6B0GUydJ0CPgHwx2rjq6a/t5idTMQrqciIiBSFyH4w5GtjL83xffBBe4ifqqsBi7iYioyISFEJv864i3bdzuDIhOWPwudD4Eyq2clEvIaKjIhIUQooA71mwa3jwGKDn+bD1DZw5Dezk4l4BRUZEZGiZrHAjQ/AXV9A6UqQ9Bu8fzMkzjc7mYjHU5EREXGXqs1g2Aa45ibIPAWf3wNfPApZZ8xOJuKxVGRERNypVHkYsAhuGm083zwVPuwIKXtNjSXiqVRkRETczWqDNk9D388gIBT2bzFO0d75ldnJRDyOKUUmOTmZmJgYoqKiaNq0KePGjSMrKyvPdefOnUv79u2JjIykffv2zJkzx81pRUSKyLW3wrD1cGUkpB+DOdGwZhw47GYnE/EYphSZkSNHEhQUxIYNG5g/fz6bNm1ixowZ56331Vdf8frrrzNhwgS2bt3Kyy+/zBtvvMHKlSvdH1pEpCiUrQp3r4SoewAnrH8FZveAU0lmJxPxCG4vMnv27CE+Pp7Ro0cTGBhI5cqViYmJyXNPy6FDhxg6dCgNGzbEYrEQGRlJ06ZN2bx5s7tji4gUHR9/6PQ69JgKvkHw51p4t6VxA0oRuSgfd7/hzp07CQ0NpWLFijnLatSowYEDBzhx4gQhISE5y/v165frtcnJyWzevJknnniiwO9rt7t2V2329ly93eLE22fUfJ7P62as3xPK18M6/y4syTuxzuxMhTpDsNevB/iZnc7lvO7PLw/ePmNRzpffbVqcTvdeL3vx4sVMmjSJtWvX5izbu3cv7dq1Y926dYSHh+f5uiNHjjBs2DDKli3Le++9h49P/jqY3W5n27ZtLkguIuIe1qw0qv74GuUOfAPAqTK12ft/D5MWeq3JyUTcr2HDhthstgv+3u17ZIKCgkhPT8+1LPt5cHBwnq/Ztm0bDz30EFFRUbz00kv5LjHnioiIuOgHUVB2u53ExESXb7c48fYZNZ/n8+oZGzcja8sMWP0swcd/o863MTibDMHZ+knwD7nkyz2BV//5neXtMxblfNnbvhS3F5latWqRkpJCUlISYWFhAOzatYvw8HBKly593vrz58/nxRdfZMSIEdx9992Ffl+bzVYkf4mKarvFibfPqPk8n7fOaI8azE9ZVYn4Zx7Wn+ZjiX8fflkCHV+Get2MKwZ7AW/98zuXt89o5nxuP9i3WrVqNG7cmPHjx5Oamsq+ffuYMmUK0dHR5627cuVKnn/+eSZPnnxZJUZExFNlBZTD2f194yJ65WpA6kH47C7jVO2jf5kdT8R0ppx+HRsbS1ZWFm3btqVXr160bNmSmJgYACIjI1myZAkAb731Fna7nREjRhAZGZnzePbZZ82ILSJinho3w/0bofUTYPODP76CKTfA+om6xYGUaG7/agkgLCyM2NjYPH+XkJCQ8/PSpUvdFUlEpPjzDYDWj8N10fDFKPhrHax5EbZ/Cre/Dte0NDuhiNvpFgUiIp4mrCYMXAw9pkFweUj6HT7qBAvv04X0pMRRkRER8UQWC/zfHfDAD2evCmyBH+fC5Maw5SNwOMxOKOIWKjIiIp4sMNS4KvCQryA8Ak6nwNIR8GEHOPSz2elEipyKjIiIN7g6CoauhfYvgV8p4/YG77aEVc9Aximz04kUGRUZERFvYfOBZjEwPB7qdgGnHTbGwttNYcdys9OJFAkVGRERb1PmKug9C/p+CqFV4Pg+mNcH5vaFlH1mpxNxKRUZERFvdW17iImDFg+D1Qd++wLevh6+iwV7ptnpRFxCRUZExJv5BcEtz8N930KVZpCZBqufgfdbw754s9OJXDYVGRGRkqBCXbhrOXR9GwLLwaGfYHo7WPoQpB01O51IoanIiIiUFFYrRPY3rj0T2d9YtmUGvNUEfpwHTqep8UQKQ0VGRKSkCb7C2DMzeAWUrwNpSbBwGHzUGY78bnY6kQJRkRERKamq3gjDNkDb58AnEHZvgHduNO7flJludjqRfFGREREpyXz8oOUoGP491LoVHJnGHbWn3GDcYVukmFORERERKFvNuO5Mr1lQ+ko4thtm94TP7oIT/5gcTuTCVGRERMRgsUC9LvBAPNwwHCxW+Hmhce2ZuPfBYTc7och5VGRERCQ3/9LQYTzcuxauagxnTsCK0TC1DRxIMDudSC4qMiIikrdKDeCe1XD76+BfBv7ZZpSZ5f+D08fNTicCqMiIiMjFWG3Q5B54YDNE9AKnA+Lfg7euh58W6NozYjoVGRERubTSFaHnVBi4GMrVgNSDMH+wcUDw0T/NTiclmIqMiIjkX/XWcP9GaP0E2Pxg19cwpRmsmwhZZ8xOJyWQioyIiBSMbwC0fhxivjeKTdZp+OZFeKc5/LXe7HRSwqjIiIhI4VxRAwYsgp7TIbgCJO80bnOwYBikHjE7nZQQKjIiIlJ4FgtERBsHAzcZAlhg+zx4K8q4IaXDYXZC8XIqMiIicvkCQ+H212DI1xAeAadTYOlD8EF7OPiT2enEi6nIiIiI61zdGIauhfYvgV8p+Dse3rsJVj0NZ1LNTideSEVGRERcy+YDzWJgeDzU7QJOO2ycDG83hR1fmJ1OvIyKjIiIFI0yV0HvWcbNKEOrwIm/YV5fmNsHUvaanU68hIqMiIgUrWvbQ0wctBgFVh/4bTm83RTLxlhwZJmdTjycioyIiBQ9vyC45Tm471uociNkpmH9+nnqrR8GO5bp7CYpNBUZERFxnwp1YfBy6DoFZ2A5Ak/+he2zgfD29bB1pq4OLAWmIiMiIu5lsUBkPxwx8fxTqx/OgDLGxfSWPAhv/B98+wacPmF2SvEQKjIiImKOoHIcqHMPjhHb4dYXofSVxs0ov3oOJtWH1c/ByYNmp5RiTkVGRETM5V8abnwQHvoRur4NYdfCmRPw3RvwRgQsGQHJu8xOKcWUioyIiBQPPn4Q2d84w+nOuVC5KdgzYOtHMLkxfDIA9m8xO6UUMyoyIiJSvFitUOc2uGcVDP4Sru0AOOHXJTC1DczoBH98BU6n2UmlGPAxO4CIiMgFVW1mPA79AhtjIfEz2L3BeIRHQPORUK+bcTVhKZG0R0ZERIq/ivWg+7swYhvcEAO+wXAwET6/ByY3gvipkJFmdkoxgYqMiIh4jtDK0OElePgnuPkpCLoCUvbA8kfhjetg3SuQdtTslOJGKjIiIuJ5gspBq//ByJ/gtleNezmlJcM342DSdbDicUjZZ3ZKcQMVGRER8Vx+QXD9UHgwAXpOh4oRkHkK4t6B2IawYJhxfI14LRUZERHxfDYfiIiG+zZA/8+hWkvjhpTb58E7zWBOL9izUWc6eSEVGRER8R4WC9S8Be5aBkPXQL2ugAV2roQPO8L0W2HHF7pJpRdRkREREe90VWPoNRMe3AKN7wKbH/wdD/P6wpSmsHUWZGWYnVIuk4qMiIh4tytqQOc3jQODWzwM/iGQ9DsseQDe/D/4LlY3qfRgphSZ5ORkYmJiiIqKomnTpowbN46srKyLvmblypW0bdvWTQlFRMTrlK4ItzwPD/8M7V6AUuFw8h9Y/YxxptNXYyD1sNkppYBMKTIjR44kKCiIDRs2MH/+fDZt2sSMGTPyXDczM5OpU6cyatQonDpIS0RELldACDR/CEZuhy6T4YpacOY4fPu6UWiWjtRNKj2I24vMnj17iI+PZ/To0QQGBlK5cmViYmKYM2dOnuvffffdxMXFMXToUDcnFRERr+bjD40GwvB46D0brooC+xnY8iG8FQWfDoIDCWanlEtw+80pdu7cSWhoKBUrVsxZVqNGDQ4cOMCJEycICQnJtf7EiRMJDw9nwYIFl/W+drv9sl5/oe25ervFibfPqPk8n7fPqPnc6NrboFZH2LsR68Y3sfzxFfyyCH5ZhPOaVjhuHAHXtDbOiiqAYjVjESjK+fK7TbcXmVOnThEYGJhrWfbztLS084pMeHi4S943MTHRJdtx13aLE2+fUfN5Pm+fUfO5UzDUfZLAq3pT8Y9PKHdgDZa/1mH7ax1pITU5WLMPxyrdBFZbgbZavGZ0PTPnc3uRCQoKIj09Pdey7OfBwcFF9r4RERHYbAX7i3cxdrudxMREl2+3OPH2GTWf5/P2GTWfmRrCTT1xpOzDEvc2loTZBJ34g+pbx+IsWw3nDcNxNugLvoEX3UrxnvHyFeV82du+FLcXmVq1apGSkkJSUhJhYWEA7Nq1i/DwcEqXLl1k72uz2YrkL1FRbbc48fYZNZ/n8/YZNZ+JrqgGt02EVo/D5qkQ9x6WY7uxrBgN6yZA0/vg+iEQWPaimynWM7qAmfO5/WDfatWq0bhxY8aPH09qair79u1jypQpREdHuzuKiIhI/gRfAa0fN+663fEVKFMF0pLgmxfh9frw5ZNw/G+zU5ZIppx+HRsbS1ZWFm3btqVXr160bNmSmJgYACIjI1myZIkZsURERC7OLxiaDoMRW6HHVKhQ37hJ5fdvw5sNYOH9cHiH2SlLFLd/tQQQFhZGbGxsnr9LSMj7VLcePXrQo0ePoowlIiKSPzZf+L9eEHEH/PEVfPsG7PkWfvzYeFzbEVqMhKuamJ3U65lSZERERLyCxQK12hmPv3+AbycZN6X8fQX8vgJr5aaUDbsF6laHoIsfRyOFoyIjIiLiCldHwZ1zIGknfPcmbP8Ey744qu+Lw7l9ItRoY9yNu3bHSx4cLPmnIiMiIuJKYbWg61tw81M4Nk8jY+snBJzaB79/aTysPnBNK6PU1OlkHEgshaYiIyIiUhRCKuFs/SQ/l+lIw6sCsP22DH5ZAod/hl1fG49lD0O15mdLTWfjxpZSICoyIiIiRcligQp1odJ1xincSTvhl8Xw6xL450f4a73x+OJRqNLMKDV1O0OZq8xO7hFUZERERNwprBbc9KjxOPqXUWh+WQL7f4C9G43Hl4/B1ddDvS5QtwuUrWp26mJLRUZERMQs5a6B5g8Zj5R98OtSo9js/R7+jjceq56GKyONQlOvK1xRw+zUxYqKjIiISHEQWhmaxRiPE//AjmXGV1B7voMDCcbj6zFQMcLYU1OvK5SvbXZq06nIiIiIFDchleD6ocYj9YhRan5dAn+ug0OJxuObcVC+ztljarpAxfrG8TgljIqMiIhIcVaqPEQNNh5pR+G35cYxNbvWwJEdsG6HcQPLcjX+3VNTqWGJKTUqMiIiIp4iqBxE9jce6Snw+0rj66c/voKju4wrC387CUKrnD2mphtc1Risptxa0S1UZERERDxRYCg06G08zpyEnauMUrNzNaTshU1vGY+Qq4zTuet1hcpNwWozO7lLqciIiIh4Ov/ScF1P45GRZuyh+WWxscfmxH6Ie9d4lKpolJq6XaBqc7B5fg3w/AlERETkX35BZ4+V6QKZp+HPb4xSs2M5pB6CzdOMR9AVxi0S6nUxbplg8zU7eaGoyIiIiHgr3wDjJpW1O0JWhnEF4V8WGXfoTkuGrR8Zj4BQqHO7saemxs3g42928nxTkRERESkJfPyg1i3Go9MbsOfbs7dKWAqnjsC2OcbDPwSu7WAcU1OzLfgGmp38olRkREREShqbD1RvbTxue9W4knD2/Z9O/gOJnxoP32C49tazpaYd+JcyO/l5VGRERERKMqvNuAN3tebQ4WX4e/PZ+z8thuP74OeFxsMnAGreYpzSfW17CAgxOzmgIiMiIiLZrFao0tR43PqicVuEXxYbj2N/GVcY3rEMbH5Qow2WOp2xZVY2NbKKjIiIiJzPYoGrGhmPW56HQz/9W2qSfoffv8T6+5fU878CGm4HmzlfO6nIiIiIyMVZLBAeYTzaPA2Hd8Avi3H+uoQzmRaCLOZdOVhFRkRERAqmQh2oUAdHy0f5fds2Gpp4urb33nxBREREvJ6KjIiIiHgsFRkRERHxWCoyIiIi4rFUZERERMRjqciIiIiIx1KREREREY+lIiMiIiIeS0VGREREPJaKjIiIiHgsFRkRERHxWCoyIiIi4rFUZERERMRjqciIiIiIx/IxO0BRczqdANjtdpduN3t7rt5uceLtM2o+z+ftM2o+z+ftMxblfNnbzP73+IVYnJdaw8NlZGSQmJhodgwREREphIiICPz8/C74e68vMg6Hg6ysLKxWKxaLxew4IiIikg9OpxOHw4GPjw9W64WPhPH6IiMiIiLeSwf7ioiIiMdSkRERERGPpSIjIiIiHktFRkRERDyWioyIiIh4LBUZERER8VgqMiIiIuKxVGQuw9GjR2nXrh1xcXFmR3GpHTt2MHjwYK6//nqaN2/O//73P44ePWp2LJfatGkTd9xxB40aNaJ58+aMHTuW06dPmx3L5ex2OwMGDODxxx83O4pLLV++nHr16hEZGZnzGD16tNmxXColJYX//e9/NG3alCZNmhATE8Phw4fNjuUSS5YsyfVnFxkZyXXXXcd1111ndjSX+fnnn+nXrx9RUVG0aNGCF198kYyMDLNjudSuXbu45557iIqKonXr1rzzzjs4HA6351CRKaQtW7bQu3dv9u7da3YUlzp9+jRDhgwhMjKSb7/9lmXLlpGSksKTTz5pdjSXOXr0KMOGDaNPnz788MMPLFy4kPj4eN5//32zo7ncW2+9xQ8//GB2DJdLTEyka9euJCQk5DwmTpxodiyXevDBB0lLS2P16tV888032Gw2nnnmGbNjuUSXLl1y/dl9+eWXhIaGMm7cOLOjuYTD4WDYsGG0b9+e+Ph45s+fz7fffsvUqVPNjuYyp06dYsiQIVSqVIn169czZ84cli9fzpQpU9yeRUWmEBYuXMijjz7Kww8/bHYUlztw4AB16tRh+PDh+Pn5UbZsWXr37s3mzZvNjuYy5cqVY+PGjfTo0QOLxUJKSgpnzpyhXLlyZkdzqU2bNrFq1SpuvfVWs6O4XGJiolf91/t//fTTT/z444+8/PLLhISEUKpUKcaOHcujjz5qdjSXczqdjB49mtatW9O1a1ez47jE8ePHOXLkCA6HI+eGh1arlcDAQJOTuc6WLVtITk7m2WefJSgoiKuuuor777+fuXPnXvImj66mIlMILVq0YPXq1dx2221mR3G56tWrM23aNGw2W86ylStXUr9+fRNTuV6pUqUAaNWqFZ07d6Z8+fL06NHD5FSuk5yczFNPPcVrr73mVf/wBOO/dn/++WfWrl3LzTffzE033cQzzzzD8ePHzY7mMtu3b6dmzZp8+umntGvXjhYtWjBhwgTKly9vdjSXW7x4MX/88YdXff1ZtmxZ7rrrLiZMmEBERAStWrWiWrVq3HXXXWZHcxmHw4Gvry++vr45yywWC0lJSZw4ccKtWVRkCqF8+fL4+PiYHaPIOZ1OJk2axDfffMNTTz1ldpwisWrVKtavX4/VamXEiBFmx3EJh8PB6NGjGTx4MHXq1DE7jssdPXqUevXq0b59e5YvX868efPYvXu3Vx0jc/z4cX777Td2797NwoULWbRoEYcOHeKxxx4zO5pLORwO3nnnHe67776c/7jwBg6Hg4CAAJ555hm2bdvGsmXL2LVrF7GxsWZHc5lGjRoREBDAa6+9Rnp6Ovv372f69OkAbj/eUEVG8pSamsqIESNYunQps2fPpnbt2mZHKhIBAQFUrFiR0aNHs2HDBq/4r/r33nsPPz8/BgwYYHaUIhEWFsacOXOIjo4mMDCQK6+8ktGjR7N+/XpSU1PNjucSfn5+ADz11FOUKlWKsLAwRo4cybp16zh16pTJ6VwnLi6Ow4cPEx0dbXYUl1q9ejUrV66kb9+++Pn5UatWLYYPH87cuXPNjuYyISEhTJ06lR9//JHWrVszcuRIunXrlvM7d1KRkfPs3buXnj17kpqayvz5872uxGzdupUOHTrkOoMgIyMDX19fr/gaZvHixcTHxxMVFUVUVBTLli1j2bJlREVFmR3NJXbs2MGrr76a63v4jIwMrFZrTgHwdDVr1sThcJCZmZmzLPtsEHcff1CUVq5cSbt27QgKCjI7ikv9888/552h5OPjk+trGE+XkZFBVlYWM2fOJC4ujs8++wyr1UrNmjXd/s9RFRnJ5fjx4wwaNIhGjRoxffp0rzsAFqB27dqcPn2a1157jYyMDPbv38+ECROIjo72in8Rfvnll2zdupUffviBH374gU6dOtGpUyevOXspNDSUOXPmMG3aNLKysjhw4AATJ06ke/fuXvHnB3DjjTdSuXJlnnzySU6dOsXRo0eZNGkSt9xyi1d9BbNlyxaaNGlidgyXa9GiBUeOHOHdd9/Fbrezb98+3nnnHTp37mx2NJe65557mD9/Pk6nk59++ol3332XQYMGuT2HiozksmDBAg4cOMCKFSto3Lhxrus8eIvg4GCmTZvGzp07ad68OQMGDODGG2/0qlPMvVl4eDjvvfceX3/9Nddffz09e/YkIiKCZ5991uxoLuPr68usWbOw2Wy0b9+e9u3bEx4ezvjx482O5lJ///03FSpUMDuGy9WsWZP33nuPNWvW0LRpUwYOHEibNm286kxXPz8/pkyZwty5c2nUqBEjR45k6NCh9OrVy+1ZLE5v2k8pIiIiJYr2yIiIiIjHUpERERERj6UiIyIiIh5LRUZEREQ8loqMiIiIeCwVGREREfFYKjIiIiLisVRkRMTj7Nmzx+wIIlJMqMiIiFu0adOGiIiIXFeLjoyM5O67777kayMjI3NusTBhwgTeeeednN/Vrl2buLi4C752xowZNGnShCZNmrBjx46Lvs/kyZO99mabIt7Kx+wAIlJyjBkzhh49ehT4dQkJCTk/Hzt2rECv/fjjj4mJiWHw4MEFfl8RKf60R0ZETHfo0CFGjhxJmzZtaNCgAW3btmX+/Pk5v8/e6/L222+zdOlSli5dSpcuXXJ+/91339G1a1ciIyOJjo7m999/B6B58+bs3buX119/nYEDBxIXF3fe3dwff/xxHn/8cfcMKiIupyIjIqZ7+umn8fX15YsvvmDr1q3079+fsWPHcurUqVzrDR8+nM6dO9O5c2eWLFmSszw+Pp7p06ezadMmypYty4QJEwCj4Fx55ZWMGTOGmTNnunUmEXEPfbUkIm4zZsyY8+7gvH79el588UWCg4Px9fXlwIEDBAcHc/r0aY4fP05wcPAltzt48GDCwsIAuOWWW5g2bVqR5BeR4kdFRkTc5rnnnsvzGJlffvmFV155hd27d1OtWjWqVq0KgMPhyNd2Q0NDc3729fXFbre7JK+IFH/6aklETJWZmcmwYcPo2rUrcXFxfPrppwwaNKhI3stmswGQkZGRs6ygBw+LSPGiIiMipsrMzOT06dMEBARgsVg4cOAAEydOzPndf/n5+XHy5MlCvVeVKlXw8fHhiy++AGDjxo18//33hQ8vIqZTkRERUwUFBTF+/HjefvttIiMjGThwIM2bNycsLCzn7KNz3XbbbWzdupXWrVsX+L0qVKjAk08+yZQpU2jUqBGzZ88u1OngIlJ8WJxOp9PsECIiIiKFoT0yIiIi4rFUZERERMRjqciIiIiIx1KREREREY+lIiMiIiIeS0VGREREPJaKjIiIiHgsFRkRERHxWCoyIiIi4rFUZERERMRjqciIiIiIx/p/nGK0xG2XrpsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "dg = me.datagrid(model, \n",
    "                 RaterSex=['M', 'F'],\n",
    "                 Faithful=np.arange(1, 10))\n",
    "\n",
    "# Predict\n",
    "p = me.predictions(model, newdata=dg)\n",
    "\n",
    "# Plot\n",
    "sns.lineplot(data=p,\n",
    "             x='Faithful', \n",
    "             y='estimate',\n",
    "             hue='RaterSex')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "752e08a9-379d-4cea-bcc0-5399f83e8403",
   "metadata": {},
   "source": [
    "From examining the plot, what looks to be happening? Is the pattern at least from the plot similar to what the article claims?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "05e30a89-bf93-4195-8a41-e981aa549265",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "# Your answer here\n",
    "# Yes - it suggests that cheating accuracy is highest for females who make low faithfulness ratings. Males don't have any accuracy across the board."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d517fe0e-872f-4f72-b172-bb4253f09221",
   "metadata": {},
   "source": [
    "Given the appearance of the plot, can we get an estimate of the slopes of both of the lines? This will tell us the unique relationship between faithfulness ratings for males and females."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "cb717d91-0fa8-49fa-ab25-a76bb341265d",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr,\n",
       ".dataframe > tbody > tr {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (2, 10)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>RaterSex</th><th>term</th><th>contrast</th><th>estimate</th><th>std_error</th><th>statistic</th><th>p_value</th><th>s_value</th><th>conf_low</th><th>conf_high</th></tr><tr><td>str</td><td>str</td><td>str</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>&quot;F&quot;</td><td>&quot;Faithful&quot;</td><td>&quot;mean(dY/dX)&quot;</td><td>-0.075793</td><td>0.031296</td><td>-2.421799</td><td>0.015444</td><td>6.016821</td><td>-0.137133</td><td>-0.014454</td></tr><tr><td>&quot;M&quot;</td><td>&quot;Faithful&quot;</td><td>&quot;mean(dY/dX)&quot;</td><td>-0.00089</td><td>0.062949</td><td>-0.01414</td><td>0.988718</td><td>0.016369</td><td>-0.124267</td><td>0.122487</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (2, 10)\n",
       "┌──────────┬──────────┬─────────────┬──────────┬───┬─────────┬────────┬────────┬─────────┐\n",
       "│ RaterSex ┆ Term     ┆ Contrast    ┆ Estimate ┆ … ┆ P(>|z|) ┆ S      ┆ 2.5%   ┆ 97.5%   │\n",
       "│ ---      ┆ ---      ┆ ---         ┆ ---      ┆   ┆ ---     ┆ ---    ┆ ---    ┆ ---     │\n",
       "│ str      ┆ str      ┆ str         ┆ str      ┆   ┆ str     ┆ str    ┆ str    ┆ str     │\n",
       "╞══════════╪══════════╪═════════════╪══════════╪═══╪═════════╪════════╪════════╪═════════╡\n",
       "│ F        ┆ Faithful ┆ mean(dY/dX) ┆ -0.0758  ┆ … ┆ 0.0154  ┆ 6.02   ┆ -0.137 ┆ -0.0145 │\n",
       "│ M        ┆ Faithful ┆ mean(dY/dX) ┆ -0.00089 ┆ … ┆ 0.989   ┆ 0.0164 ┆ -0.124 ┆ 0.122   │\n",
       "└──────────┴──────────┴─────────────┴──────────┴───┴─────────┴────────┴────────┴─────────┘\n",
       "\n",
       "Columns: RaterSex, term, contrast, estimate, std_error, statistic, p_value, s_value, conf_low, conf_high"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "slopes = me.slopes(model,\n",
    "                   newdata=dg,\n",
    "                   variables='Faithful',\n",
    "                   by='RaterSex')\n",
    "slopes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cba9e34e-18e6-4ed3-99d5-f5ae52232ebb",
   "metadata": {},
   "source": [
    "If you've successfully estimate the slopes, conduct a hypothesis test to see if they are statistically significantly different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c524f78a-92a3-49b5-8887-c91df379eede",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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       "  text-align: right;\n",
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       "</style>\n",
       "<small>shape: (1, 8)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>term</th><th>estimate</th><th>std_error</th><th>statistic</th><th>p_value</th><th>s_value</th><th>conf_low</th><th>conf_high</th></tr><tr><td>str</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>&quot;Row 1 - Row 2&quot;</td><td>-0.074903</td><td>0.070291</td><td>-1.065619</td><td>0.286596</td><td>1.802909</td><td>-0.21267</td><td>0.062864</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (1, 8)\n",
       "┌───────────────┬──────────┬───────────┬───────┬─────────┬─────┬────────┬────────┐\n",
       "│ Term          ┆ Estimate ┆ Std.Error ┆ z     ┆ P(>|z|) ┆ S   ┆ 2.5%   ┆ 97.5%  │\n",
       "│ ---           ┆ ---      ┆ ---       ┆ ---   ┆ ---     ┆ --- ┆ ---    ┆ ---    │\n",
       "│ str           ┆ str      ┆ str       ┆ str   ┆ str     ┆ str ┆ str    ┆ str    │\n",
       "╞═══════════════╪══════════╪═══════════╪═══════╪═════════╪═════╪════════╪════════╡\n",
       "│ Row 1 - Row 2 ┆ -0.0749  ┆ 0.0703    ┆ -1.07 ┆ 0.287   ┆ 1.8 ┆ -0.213 ┆ 0.0629 │\n",
       "└───────────────┴──────────┴───────────┴───────┴─────────┴─────┴────────┴────────┘\n",
       "\n",
       "Columns: term, estimate, std_error, statistic, p_value, s_value, conf_low, conf_high"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "me.slopes(model,\n",
    "          newdata=dg,\n",
    "          variables='Faithful',\n",
    "          by='RaterSex',\n",
    "          hypothesis='pairwise')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d16f3477-5e35-4427-8626-802fa993ca00",
   "metadata": {},
   "source": [
    "The answer appears to be incompatible with the claim of the manuscript.\n",
    "\n",
    "Let us be at least charitable to the authors. Have the model make a prediction about the probability of a face being a cheater, given males and females rate it with a faithfulness of 1, the lowest possible rating. Is there a difference there?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f8dc13ef-ac08-4d55-ab2a-835c411b3fd4",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<small>shape: (2, 16)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>RaterSex</th><th>Faithful</th><th>rowid</th><th>estimate</th><th>std_error</th><th>statistic</th><th>p_value</th><th>s_value</th><th>conf_low</th><th>conf_high</th><th>rownames</th><th>SexDimorph</th><th>Attract</th><th>Cheater</th><th>Trust</th><th>FaceSex</th></tr><tr><td>str</td><td>i64</td><td>i32</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>i64</td><td>f64</td><td>f64</td><td>i64</td><td>f64</td><td>str</td></tr></thead><tbody><tr><td>&quot;M&quot;</td><td>1</td><td>0</td><td>0.284553</td><td>0.292498</td><td>0.972837</td><td>0.330634</td><td>1.596691</td><td>-0.288732</td><td>0.857837</td><td>156</td><td>4.162171</td><td>2.9927</td><td>0</td><td>4.323206</td><td>&quot;M&quot;</td></tr><tr><td>&quot;F&quot;</td><td>1</td><td>1</td><td>0.675911</td><td>0.208502</td><td>3.241746</td><td>0.001188</td><td>9.717251</td><td>0.267254</td><td>1.084567</td><td>156</td><td>4.162171</td><td>2.9927</td><td>0</td><td>4.323206</td><td>&quot;M&quot;</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (2, 9)\n",
       "┌──────────┬──────────┬──────────┬───────────┬───┬─────────┬──────┬────────┬───────┐\n",
       "│ RaterSex ┆ Faithful ┆ Estimate ┆ Std.Error ┆ … ┆ P(>|z|) ┆ S    ┆ 2.5%   ┆ 97.5% │\n",
       "│ ---      ┆ ---      ┆ ---      ┆ ---       ┆   ┆ ---     ┆ ---  ┆ ---    ┆ ---   │\n",
       "│ str      ┆ str      ┆ str      ┆ str       ┆   ┆ str     ┆ str  ┆ str    ┆ str   │\n",
       "╞══════════╪══════════╪══════════╪═══════════╪═══╪═════════╪══════╪════════╪═══════╡\n",
       "│ M        ┆ 1        ┆ 0.285    ┆ 0.292     ┆ … ┆ 0.331   ┆ 1.6  ┆ -0.289 ┆ 0.858 │\n",
       "│ F        ┆ 1        ┆ 0.676    ┆ 0.209     ┆ … ┆ 0.00119 ┆ 9.72 ┆ 0.267  ┆ 1.08  │\n",
       "└──────────┴──────────┴──────────┴───────────┴───┴─────────┴──────┴────────┴───────┘\n",
       "\n",
       "Columns: RaterSex, Faithful, rowid, estimate, std_error, statistic, p_value, s_value, conf_low, conf_high, rownames, SexDimorph, Attract, Cheater, Trust, FaceSex"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "}\n",
       "</style>\n",
       "<small>shape: (1, 8)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>term</th><th>estimate</th><th>std_error</th><th>statistic</th><th>p_value</th><th>s_value</th><th>conf_low</th><th>conf_high</th></tr><tr><td>str</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>&quot;b1=b2&quot;</td><td>-0.391358</td><td>0.359205</td><td>-1.089513</td><td>0.275928</td><td>1.857639</td><td>-1.095387</td><td>0.31267</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (1, 8)\n",
       "┌───────┬──────────┬───────────┬───────┬─────────┬──────┬──────┬───────┐\n",
       "│ Term  ┆ Estimate ┆ Std.Error ┆ z     ┆ P(>|z|) ┆ S    ┆ 2.5% ┆ 97.5% │\n",
       "│ ---   ┆ ---      ┆ ---       ┆ ---   ┆ ---     ┆ ---  ┆ ---  ┆ ---   │\n",
       "│ str   ┆ str      ┆ str       ┆ str   ┆ str     ┆ str  ┆ str  ┆ str   │\n",
       "╞═══════╪══════════╪═══════════╪═══════╪═════════╪══════╪══════╪═══════╡\n",
       "│ b1=b2 ┆ -0.391   ┆ 0.359     ┆ -1.09 ┆ 0.276   ┆ 1.86 ┆ -1.1 ┆ 0.313 │\n",
       "└───────┴──────────┴───────────┴───────┴─────────┴──────┴──────┴───────┘\n",
       "\n",
       "Columns: term, estimate, std_error, statistic, p_value, s_value, conf_low, conf_high"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "dg = me.datagrid(model,\n",
    "                 RaterSex=['M', 'F'],\n",
    "                 Faithful=[1])\n",
    "\n",
    "# Predict\n",
    "display(me.predictions(model, newdata=dg))\n",
    "\n",
    "# Contrast\n",
    "display(me.predictions(model, newdata=dg, hypothesis='b1=b2'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0688b743-fa7a-43e9-b613-82049c32fd37",
   "metadata": {},
   "source": [
    "Not even at the lowest level of accuracy is there a sex difference.\n",
    "\n",
    "Repeat the predictions for males and females above, at the lowest level of faithfulness rating. Before taking the difference, set the null hypothesis to .50. This will tell us whether the predictions are actually better than chance or not. So now we are focusing not on the difference between males and females, but on the absolute probability their low faithfulness rating corresponds to a face that has actually cheated is better than a 50/50 coin flip."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "115d31fd-e361-4a22-a361-eac493789b2b",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr,\n",
       ".dataframe > tbody > tr {\n",
       "  text-align: right;\n",
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       "}\n",
       "</style>\n",
       "<small>shape: (2, 16)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>RaterSex</th><th>Faithful</th><th>rowid</th><th>estimate</th><th>std_error</th><th>statistic</th><th>p_value</th><th>s_value</th><th>conf_low</th><th>conf_high</th><th>rownames</th><th>SexDimorph</th><th>Attract</th><th>Cheater</th><th>Trust</th><th>FaceSex</th></tr><tr><td>str</td><td>i64</td><td>i32</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>i64</td><td>f64</td><td>f64</td><td>i64</td><td>f64</td><td>str</td></tr></thead><tbody><tr><td>&quot;M&quot;</td><td>1</td><td>0</td><td>0.284553</td><td>0.292498</td><td>-0.736579</td><td>0.461379</td><td>1.115977</td><td>-0.288732</td><td>0.857837</td><td>156</td><td>4.162171</td><td>2.9927</td><td>0</td><td>4.323206</td><td>&quot;M&quot;</td></tr><tr><td>&quot;F&quot;</td><td>1</td><td>1</td><td>0.675911</td><td>0.208502</td><td>0.843689</td><td>0.398843</td><td>1.326105</td><td>0.267254</td><td>1.084567</td><td>156</td><td>4.162171</td><td>2.9927</td><td>0</td><td>4.323206</td><td>&quot;M&quot;</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (2, 9)\n",
       "┌──────────┬──────────┬──────────┬───────────┬───┬─────────┬──────┬────────┬───────┐\n",
       "│ RaterSex ┆ Faithful ┆ Estimate ┆ Std.Error ┆ … ┆ P(>|z|) ┆ S    ┆ 2.5%   ┆ 97.5% │\n",
       "│ ---      ┆ ---      ┆ ---      ┆ ---       ┆   ┆ ---     ┆ ---  ┆ ---    ┆ ---   │\n",
       "│ str      ┆ str      ┆ str      ┆ str       ┆   ┆ str     ┆ str  ┆ str    ┆ str   │\n",
       "╞══════════╪══════════╪══════════╪═══════════╪═══╪═════════╪══════╪════════╪═══════╡\n",
       "│ M        ┆ 1        ┆ 0.285    ┆ 0.292     ┆ … ┆ 0.461   ┆ 1.12 ┆ -0.289 ┆ 0.858 │\n",
       "│ F        ┆ 1        ┆ 0.676    ┆ 0.209     ┆ … ┆ 0.399   ┆ 1.33 ┆ 0.267  ┆ 1.08  │\n",
       "└──────────┴──────────┴──────────┴───────────┴───┴─────────┴──────┴────────┴───────┘\n",
       "\n",
       "Columns: RaterSex, Faithful, rowid, estimate, std_error, statistic, p_value, s_value, conf_low, conf_high, rownames, SexDimorph, Attract, Cheater, Trust, FaceSex"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# Predict, just set hypothesis to .50\n",
    "display(me.predictions(model, newdata=dg, hypothesis=.50))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b7c9892-26b9-42a4-bdbe-dbcfe3bb68f7",
   "metadata": {},
   "source": [
    "No luck there either!"
   ]
  }
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