tpotce/collector/CollectorWEB/templates/registration/_attack_trend.html

<div id="attack-trend-title"
     class="stat-sec-title center">
  <table class="fullwidth">
    <tr>
      <td class="fullwidth">
        Attack Trend
      </td>
      <td class="section-controls">
        <span id="attack-trend-hide" class="button"
             onclick="toggle('attack-trend-body')"> Toggle </span>
      </td>
    </tr>
  </table>
</div>
<div id="attack-trend-body" class="stat-body">
  <div id="attack-trend-filters" class="stat-sec-filters center">
    <table>
      <tr>
        <td class="filter-fields">
          <table>
            <tr>
              <td>
                <label for="attack-trend-filters-startD"
                       class="filter-label">Start Date: </label>
              </td>
              <td>
                <input
                    class="datepicker"
                    id="attack-trend-filters-startD"
                    onchange="setIfLess('attack-trend-filters-startD', 'attack-trend-filters-endD')">
              </td>
            </tr>
            <tr>
              <td>
                <label for="attack-trend-filters-endD"
                        class="filter-label"> End Date: </label>
              </td>
              <td>
                <input
                    class="datepicker"
                    id="attack-trend-filters-endD"
                    onchange="setIfGreater('attack-trend-filters-endD', 'attack-trend-filters-startD')">
              </td>
            </tr>
            <tr>
              <td>
                <label for="attack-trend-filters-resolution"
                        class="filter-label"> Resolution: </label>
              </td>
              <td>
              <select class="select" id="attack-trend-filters-resolution">
                <option value="hour"> Hour </option>
                <option value="day" selected> Day </option>
                <option value="week"> Week </option>
              </select>
            </td></tr>
            <tr>
              <td> <label
                    for="attack-trend-filters-bg_only"
                    class="filter-label"> Bulgarian IPs Only: </label> </td>
              <td>
                <input id="attack-trend-filters-bg_only" type="checkbox">
              </td>
            </tr>
          </table>
        </td>
        <td>
          <table class="filter-buttons">
            <tr>
              <td>
                <span id="attack-trend-filters-clear" class="button"
                      onclick="clearFilters(['attack-trend-filters-startD',
                                             'attack-trend-filters-endD'])"> Clear </span>
              </td>
            </tr>
            <tr>
              <td>
                <span id="attack-trend-filters-apply" class="button"
                      onclick="updateAttackTrend()"> Apply </span>
              </td>
            </tr>
          </table>
        </td>
      </tr>
    </table>
  </div>
  <div id="attack-trend-canvas" class="ga-charts center canvas" onclick="resizeEChart($('#attack-trend-canvas'))"></div>
  <div id="attack-trend-info-panel" class="info-panel"> </div>

  <table id="attack-trend-parameters" class="parameter-table">
    <tr><td class="column-title">Parameter</td><td class="column-title">Value</td></tr>
    <tr><td>a</td><td id="attack-trend-param-value-a"></td></tr>
    <tr><td>b</td><td id="attack-trend-param-value-b"></td></tr>
    <tr><td>\(\sigma_a\)</td><td id="attack-trend-param-value-sigma_a"></td></tr>
  </table>

  <div class="details">
    <details>
      <summary>Details</summary>
      <p> All numbers in the results are rounded to 2 digits after the decimal point. </p>
      <p>
        For modelling the trend of the attacks is used a linear model,
        $$ y = a t + b + \epsilon$$
        $$ \epsilon \sim N(0, \mu)$$
        where y is the number of attacks, t is the time step, a is scale, and b is offset.
        The time-step is determined by the resolution, which can be hour, day or week.
      </p>

      <p>
        The parameters of the model are fit according to
        $$ a = \frac{\sum_i (y - \mu_y)(t_i - \mu_t)}{\sum_i(t_i - \mu_t)^2} $$
        $$ b = \mu_y - a \mu_t $$
        $$ \mu_t = \frac{1}{n} \sum_{i=1}^n t_i $$
        $$ \mu_y = \frac{1}{n} \sum_{i=1}^n y_i $$
        Then the uncertainty of the scale is estimated by assuming Gaussian distribution of the errors, according to
        $$ \sigma_a = \sqrt{\frac{\sum_i (y_i - a x_i - b)^2}{(n-2)\sum_i (x_i - \mu_x)^2}} $$
      </p>

      <p> For further details, please check <a href="https://en.wikipedia.org/wiki/Simple_linear_regression"> linear regression</a>. </p>
    </details>
  </div>
</div>