The Business Plot

Examples of The Business Plot in the following topics:

• Contour Plots

  • Contour plots portray data for three variables in two dimensions.
  • The plot contains a number of contour lines.
  • Each contour line is shown in an X-Y plot and has a constant value on a third variable.
  • An alternative way to draw the plot is shown in Figure 2.
  • A contour plot showing calories as a function of fat and carbohydrates

• The Cartesian System

  • To plot the point $(2,3)$, for example, you start at the origin (where the two axes intersect).
  • For example, there is a relationship between the number of cars a car wash cleans and the money the business makes (its revenue).
  • The revenue is plotted on the $y$-axis, and the number of cars washed is plotted on the $x$-axis.
  • Some basic rules about these quadrants can be helpful for quickly plotting points:
  • The Cartesian coordinate system with 4 points plotted, including the origin, at $(0,0)$.

• 3D Plots

  • Just as two-dimensional scatter plots show the data in two dimensions, 3D plots show data in three dimensions.
  • Figure 1 shows a 3D scatter plot of the fat, non-sugar carbohydrates, and calories from a variety of cereal types.
  • Many statistical packages allow you to rotate the axes interactively to view the data from a different vantage point.
  • Figure 3 represents the different manufacturers by using different colors.
  • Interactively rotating 3D plots can sometimes reveal aspects of the data not otherwise apparent.

• Dot Plots

  • The dot plot in Figure 2 shows the number of people playing various card games on the Yahoo website on a Wednesday.
  • The dot plot in Figure 3 shows the number of people playing on a Sunday and on a Wednesday.
  • The dot plot in Figure 4 makes it easy to compare the days of the week for specific games while still portraying differences among games.
  • A dot plot showing the number of M & M's of various colors in a bag of M & M's.
  • A dot plot showing the number of people playing various card games on a Wednesday.

• Segmented bar and mosaic plots

  • Segmented bar and mosaic plots provide a way to visualize the information in these tables.
  • For example, a segmented bar plot representing Table 1.36 is shown in Figure 1.38(a), where we have first created a bar plot using the number variable and then divided each group by the levels of spam.
  • Examine both of the segmented bar plots.
  • Figure 1.39(a) shows a mosaic plot for the number variable.
  • The one-variable mosaic plot for number and the two-variable mosaic plot for both number and spam.

• Plotting Points on a Graph

  • The plot can be drawn by hand or by a mechanical or electronic plotter.
  • Graphs can also be used to read off the value of an unknown variable plotted as a function of a known one.
  • As an example of plotting points on a graph, consider one of the most important visual aids available to us in the context of statistics: the scatter plot.
  • The researcher would then plot the data in a scatter plot, assigning "lung capacity" to the horizontal axis, and "time holding breath" to the vertical axis.
  • The scatter plot of all the people in the study would enable the researcher to obtain a visual comparison of the two variables in the data set and will help to determine what kind of relationship there might be between the two variables.

• Statistical Graphics

  • Statistical graphics allow results to be displayed in some sort of pictorial form and include scatter plots, histograms, and box plots.
  • They include plots such as scatter plots , histograms, probability plots, residual plots, box plots, block plots and bi-plots.
  • In addition, the choice of appropriate statistical graphics can provide a convincing means of communicating the underlying message that is present in the data to others.
  • Many familiar forms, including bivariate plots, statistical maps, bar charts, and coordinate paper were used in the 18th century.
  • A scatter plot helps identify the type of relationship (if any) between two variables.

• Exercises

  • For the following data, plot the theoretically expected z score as a function of the actual z score (a Q-Q plot).
  • For the data in problem 2, describe how the data differ from a normal distribution.
  • For the "SAT and College GPA" case study data, create a contour plot looking at College GPA as a function of Math SAT and High School GPA.
  • For the "SAT and College GPA" case study data, create a 3D plot using the variables College GPA, Math SAT, and High School GPA.

• Graphing Quantitative Variables

  • The upcoming sections cover the following types of graphs: (1) stem and leaf displays, (2) histograms, (3) frequency polygons, (4) box plots, (5) bar charts, (6) line graphs, (7) scatter plots, and (8) dot plots.
  • Graph types such as box plots are good at depicting differences between distributions.
  • Scatter plots are used to show the relationship between two variables.

• Constructing a normal probability plot (special topic)

  • We construct a normal probability plot for the heights of a sample of 100 men as follows:
  • The zi in Table 3.16 are not the Z scores of the observations but only correspond to the percentiles of the observations.
  • Because of the complexity of these calculations, normal probability plots are generally created using statistical software.
  • Construction details for a normal probability plot of 100 men's heights.
  • To create the plot based on this table, plot each pair of points, (zi,xi).