统计代写|数据可视化代写Data visualization代考|STAT1100

统计代写|数据可视化代写Data visualization代考|The Origin and Development of the Scatterplot

As we saw in Chapter 5, most modern forms of data graphics-pie charts, line graphs, and bar charts-can generally be attributed to William Playfair in the period 1785-1805. All of these, even though presented as two-dimensional graphs, were essentially one-dimensional in their view of data. They showed a single quantitative variable (such as land area or value of trade) broken down by a categorical variable, as in a pie chart or bar chart, or plotted over time (perhaps with separate curves for imports and exports), as in a line graph.

In the development of a language and taxonomy of graphs, Playfair’s graphs and other visual representations of data in this time can considered $1.5 \mathrm{D}-$ more than just a single variable shown, but not quite enough to qualify for $2 \mathrm{D}$ status. In Playfair’s visual understanding, the horizontal axis in his plots most often bound to time, forcing him to use other means to show relations with other variables.

The next major invention in data graphics-the first fully two-dimensional one-was the scatterplot. Indeed, among all forms of statistical graphics, the scatterplot may be considered the most versatile and generally useful invention in the entire history of statistical graphics. ${ }^1$

Essential characteristics of a scatterplot are that two quantitative variables are measured on the same observational units (workers); the values are plotted as points referred to perpendicular axes; and the goal is to show something about the relation between these variables, typically how the ordinate variable, $y$, varies with the abscissa variable, $x$.

Figure $6.1$ shows a typical, if simplistic, modern scatterplot. It relates the number of years of experience of some workers on the horizontal $(x)$ axis to their current annual salary on the vertical $(y)$ axis.

统计代写|数据可视化代写Data visualization代考|Early Displays That Were Not Scatterplots

The history of statistical graphics includes quite a few displays that resemble a scatterplot in some respects but don’t quite meet our definition. The first prerequisite for a scatterplot was the idea of a coordinate system. Abstract, mathematical coordinate systems and the relations between graphs and functional equations, $y=f(x)$, such as the linear equation of a line, $y=a+b x$, were introduced in the 1630 s (by Descartes and Fermat). The idea of twodimensional, map-based coordinates, as systematized by Mercator, had been used since antiquity. What was new here was that Cartesian geometry introduced the idea of an abstract $(x, y)$ plane, where equations could characterize all kinds of functional relations whose properties could be studied mathematically, in what is now called analytic geometry.

In the 1660 s, the first proto-line graphs, showing weather data (barometric pressure) recorded over time, were introduced by Robert Plot (see Figure 1.4). Plot called this a “history of the weather,” but it is little more than a tracing recorded by a pen on a moving paper chart. In 1669 , Christiaan Huygens plotted survival versus age from John Graunt’s data (see Figure 1.5), producing the first graph of an empirical continuous distribution function. This was an early cxample of turning a table into a graph, but not yct a scatterplot.

In 1686, Edmund Halley prepared the first known bivariate plot (perhaps derived from observational data, but not showing the data directly) of a theoretical curve relating barometric pressure to altitude (see Figure 6.2). The curve is simply a hyperbola, showing the inverse mathematical relation between these variables. The labeled horizontal and vertical lines attest to Halley’s effort to explain visually how pressure decreases with altitude.

统计代写|数据可视化代写Data visualization代考|Early Displays That Were Not Scatterplots

1686 年，埃德蒙·哈雷（Edmund Halley）绘制了第一个已知的双变量图（可能来自观测数据，但没有直接显示数据），将气压与高度相关联的理论曲线（见图 6.2）。曲线只是一条双曲线，显示了这些变量之间的反数学关系。标记的水平线和垂直线证明了哈雷在视觉上解释压力如何随高度降低的努力。

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