Line chart
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In the experimental sciences, data collected from experiments are often visualized through the use of a particular scatter graph that includes an overlaid mathematical function that depicts the best-fit trend of the scattered data. This layer is referred to as a best-fit layer and the graph containing this layer is often referred to as a line graph.
For example, if one were to collect data on the speed of a body at certain points in time, one could visualize the data by a data table such as the following:
| Elapsed Time (s) | Speed (ms-1) |
|---|---|
| 0 | 0 |
| 1 | 3 |
| 2 | 7 |
| 3 | 12 |
| 4 | 20 |
| 5 | 30 |
| 6 | 45 |
The table "visualization" is a good way of displaying precision values, but a very poor way of understanding the underlying patterns that those values represent. Because of these qualities of a table, the table display is often erroneously conflated with the data itself; whereas, it is just another visualization of the data.
Understanding the process described by the data in the table is aided by producing a graph or line chart of Speed versus Time. In this context, Versus (or the abbreviations vs and VS), separates the parameters appearing in an X-Y (two-dimensional) graph. The first argument indicates the dependent variable, usually appearing on the Y-axis, while the second argument indicates the independent variable, usually appearing on the X-axis. Thus the graph of Speed versus Time would plot time along the x-axis and speed up the y-axis. Mathematically, if we denote time by the variable t, and speed by v, then the function plotted in the graph would be denoted v(t) indicating that v (the dependent variable) is a function of t.
It is simple to construct a "best-fit" layer consisting of a set of line segments connecting adjacent data points; however, such a "best-fit" is usually not an ideal representation of the trend of the underlying scatter data for the following reasons:
(1)It is highly improbable that the discontinuities in the slope of the best-fit would correspond exactly with the positions of the measurement values. (2)It is highly unlikely that the experimental error in the data is negligible, yet the curve falls exactly through each of the data points.
A true best-fit layer should depict a continuous mathematical function whose parameters are determined by using a suitable error-minimization scheme, which appropriately weights the error in the data values.
In either case, the best-fit layer can reveal trends in the data. Further, measurements such as the gradient or the area under the curve can be made visually, leading to more conclusions from the data.
