Data Visualization Web Page
Is Your Process Data Spread Smooth or Chunky?

Author

DOFPro group

  • Video links go directly to the YouTube video.
  • JTF (Just the Facts) videos are the streamlined versions: greenscreen LaTeX equations, clean graphics, minimal narrative. Think efficient and to the point. Each has a companion TFS video.
  • TFS (The Full Story) videos include interviews, additional explanation, and equations written on whiteboards. Same math, more context, more personality. Each has a matching JTF version.
  • Info Page links lead to definitions, expanded explanations, and related material—because sometimes you really do need to explain it.
  • Visuals links contain the greenscreen or whiteboard materials used in the video, for those who like to see the scaffolding.
  • Wondering about the titles? See Appendix B: If you have to explain it, it’s no longer funny.
  • Videos marked This is NOT a DOFPro video were not produced by DOFPro but are included because they are relevant to the topic. They are shown in red so no one calls the academic integrity police.

Purpose of Data Visualization

Is Your Process Data Spread Smooth or Chunky?

Presenting and analyzing process data is one of the fundamental activities of chemical and thermal process engineers. When trying to determine the functional relationship between variables, the human visual system is remarkably good at recognizing whether a plotted data set follows a straight line—or something close to one.

If a plot of the data does not appear linear, it may still represent a simple relationship that becomes linear after a change of coordinates. Transformations such as logarithmic or semi-logarithmic scaling often reveal linear trends that correspond to exponential or power-law relationships.

This video introduces common coordinate transformations used to visualize process data and to identify useful mathematical models.

Just the Facts

The Just the Facts video presents core data visualization techniques and demonstrates how coordinate transformations produce linear, semi-log, and log-log plots. It also shows how model parameters can be estimated from transformed data.

Visuals

The Full Story

The Full Story video explores both correct practices and common misconceptions in plotting and interpreting process data. It explains how coordinate transformations produce linear, semi-log, and log-log plots and demonstrates how model parameters can be extracted from experimental data.

Visuals

Examples and Definitions

Definitions

Data Visualization
The graphical representation of data to make trends, patterns, and relationships easier to interpret.
Linear Plot
A plot in which both the \(x\)-axis and \(y\)-axis use linear scales. Data may appear as a straight line if the underlying relationship follows

\[ y = mx + b \]

or another function that is approximately linear over the plotted range.

Semi-log Plot
A plot where one axis uses a logarithmic scale and the other uses a linear scale. Semi-log plots are commonly used when the data follow an exponential relationship such as

\[ y = ae^{bx} \]

or

\[ y = a10^{bx}. \]

Log-Log Plot
A plot in which both axes are logarithmic. Data that follow a power-law relationship,

\[ y = ax^{b}, \]

appear as a straight line on a log-log plot.

Exponential Function
A function in which the independent variable appears in the exponent, typically written

\[ y = ae^{bx} \]

or

\[ y = a10^{bx}, \]

where \(a\) and \(b\) are constants.

Power Law
A relationship of the form

\[ y = ax^{b} \]

where \(a\) and \(b\) are constants. Power-law relationships appear as straight lines on log-log plots.

Nonlinear Least-Squares Fit
A method for estimating parameters in a model that is nonlinear in the fitting parameters. Unlike linear regression, nonlinear least-squares problems typically require iterative numerical methods and are usually solved with computer software.