Section outline

  • lesson content
    Pollen is necessary for plants to produce fruit, nuts, and seeds, both for our enjoyment and to enable the plants to reproduce. In the process of pollination, a yellowish powder is transported from plant to plant by wind,  insects, or e ven people, either accidentally or purposely. Yet m any people are sensitive to p ollen . In fact, during the springtime, when airborne   are at their highest levels , some people suffer . The level of discomfort depends on the geographic location and type of pollen in the environment. Pollen sensitivity causes inflammation and irri tation in the nasal passage, itchy eyes, fatigue, and other symptoms.

    The Asthma and Allergy Foundation of America and its research partner, IMS Health, produce a website, pollen.com, which monitor s pollen levels in many locations throughout the year.
    ::美国麻风病和过敏基金会及其研究伙伴IMS Health,制作了一个网站,poolen.com,全年监测许多地点的花粉水平。

    This dataset was taken from the pollen.com website:
    ::此数据集取自花粉. com网站:

    Day Date Pollen Level
    1 3/3/2016 10.7
    2 3/4/2016 9.3
    3 3/5/2016 8.9
    4 3/6/2016 8.4
    5 3/7/2016 7.6
    6 3/8/2016 6.7
    7 3/9/2016 2.3
    8 3/10/2016 3.1
    9 3/11/2016 4
    10 3/12/2016 8.2
    11 3/13/2016 10.9
    12 3/14/2016 10.9
    13 3/15/2016 10.6
    14 3/16/2016 10
    15 3/17/2016 9.3
    16 3/18/2016 7.6
    17 3/19/2016 10.8
    18 3/20/2016 10
    19 3/21/2016 8.4
    20 3/22/2016 9.1
    21 3/23/2016

    9.7

    1. Plot the data and label the axes.
      ::绘制数据并标注轴。
    2. During which time periods did the pollen level decrease? Increase?
      ::花粉水平在什么时期内下降? 增加?
    3. On which days was the pollen level  highest? Lowest? What were those extreme levels?
      ::花粉水平是哪几天最高的?最低?那些极端水平是什么?
    4. Using either a graphing calculator or a website, such as Desmos.com, create a regression analysis to fit a polynomial function to the data. Desmos.com allows the user to create an account to store work. It also offers a step-by-step tutorial to guide the user through a regression. The steps are:
      1. Create a new graph.
        ::创建新图形 。
      2. Add a table to the graph. Enter the above dataset. Use the day number for x and the allergy index for y.
        ::向图形添加表格。输入上面的数据集。使用x的日数和y的过敏指数。
      3. Add a regression equation in the form  y 1  ~  a x 1 2 + b x 1 + c .  This creates a quadratic function that best fits the data.
        ::以 y1 ~ ax12+bx1+c 的形式添加回归方程式。 这将产生最适合数据的二次函数 。
      4. Change the scale of the axes until both the data and graph are visible.
        ::更改轴的尺度,直到数据和图形都可见。
      5. Export the graph to an image file and add it to your report.
        ::将图形导出为图像文件,并将其添加到报表中。

      ::使用图形计算器或网站, 如 Desmos. com , 创建回归分析, 以适应数据中的多元函数 。 Desmos. com 允许用户创建账户以存储工作。 它还提供一步步练习指导用户通过回归。 步骤是 : 创建一个新图形, 添加一个表格到图形中 。 输入上述数据集 。 使用 x 的日数和 y 的过敏指数 。 以 y1 格式添加一个回归方程式 y1 ~ ax12+bx1+c 。 这样可以创建最适合数据的二次函数 。 更改轴的尺度, 直至数据和图形都可见 。 将图形导出为图像文件, 并将其添加到您的报表中 。
    5. Create a 2nd regression model. Use a cubic function,  y 1  ~  a x 1 3 + b x 1 2 + c x 1 + d .  Export an image and add it to your report.
      ::创建 2nd 回归模型。 使用一个立方函数, y1 ~ ax13+bx12+cx1+d。 导出一个图像并将其添加到报表中 。
    6. Compare the two regression models.
      1. Consider intervals where each increases or decreases, and the extreme values. Do these correspond with the data?
        ::考虑每次增减的间隔和极端值。 这些值是否与数据相符?
      2. Which model best fits the data?
        ::哪一种模型最适合数据?
      3. Why would a straight line not fit the data?
        ::为什么一条直线不符合数据?

      ::比较两个回归模型。 考虑每个增减的间隔和极端值。 这些与数据是否相符?哪个模型最适合数据? 为什么直线与数据不匹配?

    Reference:
    ::参考:

    Asthma and Allergy Foundation of America,  N.p., n.d. Web. 02 Apr. 2016.
    ::美国气喘和过敏基金会,N.p.,n.d.Web. 02 Apr.2016年4月2日。