6.5 符合数据要求的线性线性平方-interactive

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  Linear Equations That Fit the Data
  ::符合数据的线性公式

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  In the section , global warming was discussed and how data can influence national and global policies. You  saw that the scale of a graph could influence our perception of the graph. If some displays show an increase and some windows show no increase, how can  you know how to interpret the information received? In this section,  you will write an equation for a line that will fit the linear trend of the data. This will tell  you how fast a rate is rising and allow  you to predict what will happen in the future if the rate does not change. Understanding the numbers behind a visualization allows  you to see the truth in the data.
  ::本节讨论了全球变暖以及数据如何影响国家和全球政策。您看到,图表的规模会影响我们对图表的感知。如果一些显示显示显示增加,有些窗口没有显示增加,您如何知道如何解释收到的信息?在本节中,您将为符合数据线性趋势的线条写一个方程式。这将告诉您一个比率上升的速度有多快,并允许您预测如果这个比率没有改变,未来会发生什么。了解直观化背后的数字可以让你看到数据中的真相。

   

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  Climate Change
  ::气候变化气候变化

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  Below is a scatter plot displaying the climate data from . This graph shows the mean global temperature in ten year periods from 1890 to 2010. A line has been fit to the data so that you  can measure the increase.
  ::下面是显示气候数据的散射图。此图显示1890年至2010年10年中全球平均温度。一行适合数据,以便测量上升情况。

   

   

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  To find the equation for the line in slope-intercept form , $\begin{array}{r}y=mx+b\end{array}$ , all you  need is the and the $\begin{array}{r}y\text{-}\end{array}$ intercept . From the scatter plot  you can follow the line and estimate that it will cross the $\begin{array}{r}y\text{-}\end{array}$ axis at about 56.4. This means the $\begin{array}{r}b\end{array}$   will be 56.4 and the $\begin{array}{r}y\text{-}\end{array}$ intercept of the line is (0, 56.4). The one change in the scatter plot from section 1 is that the $\begin{array}{r}x\text{-}\end{array}$ axis was changed from “Years” to “Number of Years Since 1890”. If  you were to list the years, the $\begin{array}{r}y\text{-}\end{array}$ intercept would be at year 0. However,  you want the starting point to be the beginning of your data. By adjusting the $\begin{array}{r}x\text{-}\end{array}$ axis to show the number of years since 1890,  you will get an equation for  the line which is more reflective of the sample size.
  ::要找到斜度截面线的方程式, y=mx+b, 您需要的只是“ y ” 和“ y ” 。 您可以从分布区块图中跟随该线, 估计该线将横跨 Y 轴, 大约56.4。 这意味着 b将是56.4, 而该线的 Y 截面是 0, 56.4 。 从第1 节, 散点图的一个变化是, x 轴从“ 年份” 改为“ 1890年以来的年数 ” 。 如果您要列出年数, y 截面将是 0 年 。 但是, 您想要将起始点作为数据起始点。 通过调整 x 轴以显示1890 年以来的年数, 您将获得一个公式, 该公式更能反映样本大小 。

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  To find the slope,  you will need 2 points from the line. You  already have one point from the $\begin{array}{r}y\text{-}\end{array}$ intercept, so all  you need is one more. To find the other point, keep it simple by looking for a point from the data that falls right on the line or for the location where the line crosses through the grid-lines at a spot that is easy to read. None of the data points fall exactly on the line, but the line crosses nearly exactly through the point (110, 57.6). You can now use the points (0, 56.4) and (110, 57.6) to find the slope.
  ::要找到斜坡, 您需要从线条中找到两点。 您已经从 y 界面中找到一个点, 所以您需要的只是另一个点。 要找到另一个点, 请从线条右侧的数据中寻找一个点, 或从容易读取的点通过网格线的位置, 保持简单 。 没有哪个数据点完全落在线上, 但是线点几乎完全穿过了点( 110, 57. 6) 。 现在您可以使用点( 0, 56.4 ) 和 ( 110, 57.6) 来找到斜坡 。

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  $$\begin{array}{rl}m& =\frac{y_2-y_1}{x_2-x_1}\\ \\ m& =\frac{57.6-56.4}{110-0}\\ \\ m& =\frac{1.2}{110}\\ \\ m& =0.0109\end{array}$$

  
  ::my2-y1x2-x1m=57.6-56.4110-0m=1.2110m=0.0109

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  N ow, write  the equation:  $\begin{array}{r}y=0.0109x+56.4\end{array}$    
  ::现在,写下方程:y=0.0109x+56.4

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  A  rate of 0.0109 degrees per year may seem insignificant. However, this is 1. 09 degrees every hundred years. There are concerns about this being linked to the melting polar ice caps, an increase in extreme weather events, and a rise in CO2 emissions. However, because points on a scatter plot have a positive linear trend, this does not mean that there is guaranteed to be a relationship between the variables. Further scientific testing must be done to prove causation, but this is the first step in the process.
  ::每年0.0109摄氏度的速率似乎微不足道,然而,这是每100年1.09摄氏度。人们担心这与极地冰盖融化、极端天气事件增加和二氧化碳排放量增加有关。然而,由于散地上的点数呈正线性趋势,这并不意味着保证变量之间的关系。必须进行进一步科学测试以证明因果关系,但这是这一过程的第一步。

   

   

   

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  Baseball Salaries
  ::基薪球薪金

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  The lesson   looked at the salaries of professional baseball players over the course of 32 years. The scatter plot below displays this data fitted with the linear equation  $\begin{array}{r}y=134,191x-25.\end{array}$
  ::该课程考察了32年来职业棒球运动员的工资情况。下面的散射图显示了与线性公式y=134,191x-25相匹配的数据。

   

   

   

   

   

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  Hit the Brakes
  ::打刹车

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  It's time to  put it all together. Now  you are going to construct a line to fit the data displayed in the scatterplot below. Find the equation of the line and use it to analyze the graph. This data was obtained by testing the distance it took 5 different cars to brake at various speeds, before coming to a stop. The scatter plot compares the average braking distance to speed . Use the interactive to construct a line to fit the data and find the equation.
  ::现在是时候将其全部组合在一起了。 现在您要构造一条线以适应下面的散射图中显示的数据。 找到线的方程式, 并用它来分析图形 。 此数据是通过测试它用5辆不同的汽车以不同速度刹车的距离获得的, 然后再停下来 。 散射图将平均制动距离与速度进行比较 。 使用互动来构造一条线以适应数据并找到方程式 。

   

  

  INTERACTIVE

  Hit the Brakes

  

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  • Drag the red points to construct an approximate line to fit the data.
    ::拖曳红色点以构建符合数据的大致线条。
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  • Click the red points or green points to use see their coordinates.
    ::单击红点或绿点以使用它们的坐标。
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  • Press the check button to see if your approximation of the line of best fit is close to the actual line of best fit.
    ::按下复选按钮, 检查您是否接近最合适线的近似值 是否接近最合适的线 。

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     Summary
  ::摘要

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  • Use the formula $\begin{array}{r}m=\frac{y_2-y_1}{x_2-x_1}\end{array}$  to find the slope of a line of best fit.
    ::使用公式m=y2-y1x2-x1来找到最适合的线的斜度。
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  • Use the line of best fit to make predictions.
    ::使用最合适的线进行预测。