Continuous Variables
Two Variables
A typical scatterplot visualizes the relationship of two continuous
variables, here Years worked at a company, and annual
Salary. Following is the function call to XY() for
the default visualization.
Because d is the default name of the data frame that
contains the variables for analysis, the data parameter
that names the input data frame need not be specified. That is, no need
to specify data=d, though this parameter can be explicitly
included in the function call if desired.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(Years, Salary, enhance=TRUE) # many options
## XY(Years, Salary, fill="skyblue") # interior fill color of points
## XY(Years, Salary, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## XY(Years, Salary, out_cut=.10) # label top 10% from center as outliers
##
##
## >>> Pearson's product-moment correlation
##
## Years: Time of Company Employment
## Salary: Annual Salary (USD)
##
## Number of paired values with neither missing, n = 36
## Sample Correlation of Years and Salary: r = 0.852
##
## Hypothesis Test of 0 Correlation: t = 9.501, df = 34, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.727 to 0.923
## Enhance the default scatterplot with parameter enhance.
The visualization includes the mean of each variable indicated by the
respective line through the scatterplot, the 95% confidence ellipse,
labeled outliers, least-squares regression line with 95% confidence
interval, and the corresponding regression line with the outliers
removed.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
## [Ellipse with Murdoch and Chow's function ellipse from their ellipse package]
##
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(Years, Salary, color="red") # exterior edge color of points
## XY(Years, Salary, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## XY(Years, Salary, out_cut=.10) # label top 10% from center as outliers
##
## >>> Outlier analysis with Mahalanobis Distance
##
## MD ID
## ----- -----
## 8.34 Skrotzki, Sara
## 7.73 Billing, Susan
##
## 5.83 Fulton, Scott
## 5.77 Correll, Trevon
## 3.92 Downs, Deborah
## ... ...
##
##
## >>> Pearson's product-moment correlation
##
## Years: Time of Company Employment
## Salary: Annual Salary (USD)
##
## Number of paired values with neither missing, n = 36
## Sample Correlation of Years and Salary: r = 0.852
##
## Hypothesis Test of 0 Correlation: t = 9.501, df = 34, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.727 to 0.923
## The default for formatting both axis labels is to round numeric
values of thousands, such as 100000 to 100K. With parameter
axis_fmt, this default of to {"K"} can be
changed. Also can specify {","} to insert commas in large
numbers with a decimal point or {"."} to insert periods, or
{""} to turn off formatting. The value of
{"K"} can also be combined with {","} or
{"."} by forming a vector of values, such as
c("K", ",").
Axis labels can also be formatted by adding a prefix to a numeric
value with the parameters axis_x_prefix and
axis_y_prefix, such as $ or €.
The specified value can be multiple characters, such as for the
Brazilian currency, R$.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(Years, Salary, enhance=TRUE) # many options
## XY(Years, Salary, fill="skyblue") # interior fill color of points
## XY(Years, Salary, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## XY(Years, Salary, out_cut=.10) # label top 10% from center as outliers
##
##
## >>> Pearson's product-moment correlation
##
## Years: Time of Company Employment
## Salary: Annual Salary (USD)
##
## Number of paired values with neither missing, n = 36
## Sample Correlation of Years and Salary: r = 0.852
##
## Hypothesis Test of 0 Correlation: t = 9.501, df = 34, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.727 to 0.923
## A variety of fit lines can be plotted. The available values:
"loess" for general non-linear fit, "lm" for
linear least squares, "null" for the null (flat line)
model, "exp" for the exponential growth and decay,
"quad" for the quadratic model, and power for
the general power beyond 2. Setting fit to
TRUE plots the "loess" line. With the value of
power, specify the value of the root with parameter
fit_power.
Here, plot the general non-linear fit. For emphasis set
plot_errors to TRUE to plot the residuals from
the line. The sum of the squared errors is displayed to facilitate the
comparison of different models.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
##
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(Years, Salary, enhance=TRUE) # many options
## XY(Years, Salary, color="red") # exterior edge color of points
## XY(Years, Salary, MD_cut=6) # Mahalanobis distance from center > 6 is an outlier
##
## Loess Model MSE = 100,834,065.368
## Next, plot the exponential fit and show the residuals from the exponential curve. These data are approximately linear so the exponential curve does not vary far from a straight line. The function displays the corresponding sum of squared errors to assist in comparing various models to each other.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
##
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(Years, Salary, enhance=TRUE) # many options
## XY(Years, Salary, fill="skyblue") # interior fill color of points
## XY(Years, Salary, out_cut=.10) # label top 10% from center as outliers
##
## Regressed linearized data of transformed data values of Salary with log()
## Line: b0 = 10.959 b1 = 0.036
## Linear Model MSE = 0.0168 Rsq = 0.725
##
## Fit to the data with back transform exp() of linear regression model
## Model MSE = 127,930,074.484
##
## The parameter transforms the y variable to the specified
power from the default of 1 before doing the regression
analysis. The availability of this parameter provides for a wide range
of modifications to the underlying functional form of the fit curve.
Three Variables
Map a continuous variable, such as Pre, to the plotted points with
the size parameter, a bubble plot.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
##
##
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## radius: 0.12 size of largest bubble
## power: 0.50 relative bubble sizesIndicate multiple variables to plot along either axis with a vector
defined according to the base R function c(). Plot the
linear model for each variable according to the fit
parameter set to "lm". By default, when multiple lines are
plotted on the same panel, the confidence interval is turned off by
internally setting the parameter fit_se set to
0. Explicitly override this parameter value as needed.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
##
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(c(Pre, Post), Salary, enhance=TRUE) # many options
## XY(c(Pre, Post), Salary, color="red") # exterior edge color of points
## XY(c(Pre, Post), Salary, MD_cut=6) # Mahalanobis distance from center > 6 is an outlier
##
##
## >>> Pearson's product-moment correlation
##
## Post: Test score on legal issues after instruction
## Salary: Annual Salary (USD)
##
## Number of paired values with neither missing, n = 37
## Sample Correlation of Post and Salary: r = -0.070
##
## Hypothesis Test of 0 Correlation: t = -0.416, df = 35, p-value = 0.680
## 95% Confidence Interval for Correlation: -0.385 to 0.260
## VBS Plot of 5 Variables
Read the data and convert the values of numerically valued categorical variables to meaningful labels.
##
## >>> Suggestions
## Recommended binary format for data files: feather
## Create with Write(d, "your_file", format="feather")
## More details about your data, Enter: details() for d, or details(name)
##
## Data Types
## ------------------------------------------------------------
## character: Non-numeric data values
## integer: Numeric data values, integers only
## double: Numeric data values with decimal digits
## ------------------------------------------------------------
##
## Variable Missing Unique
## Name Type Values Values Values First and last values
## ------------------------------------------------------------------------------------------
## 1 Make character 93 0 32 Acura Acura ... Volvo Volvo
## 2 Type character 93 0 6 Small Midsize ... Compact Midsize
## 3 MinPrice double 93 0 79 12.9 29.2 25.9 ... 22.9 21.8 24.8
## 4 MidPrice double 93 0 81 15.9 33.9 29.1 ... 23.3 22.7 26.7
## 5 MaxPrice double 93 0 79 18.8 38.7 32.3 ... 23.7 23.5 28.5
## 6 MPGcity integer 93 0 21 25 18 20 ... 18 21 20
## 7 MPGhiway integer 93 0 22 31 25 26 ... 25 28 28
## 8 Airbags integer 93 0 3 0 2 1 ... 0 1 2
## 9 DriveTrain integer 93 0 3 1 1 1 ... 1 0 1
## 10 Cylinders integer 92 1 5 4 6 6 ... 6 4 5
## 11 Engine double 93 0 26 1.8 3.2 2.8 ... 2.8 2.3 2.4
## 12 HP integer 93 0 57 140 200 172 ... 178 114 168
## 13 RPM integer 93 0 24 6300 5500 5500 ... 5800 5400 6200
## 14 RevMile integer 93 0 78 2890 2335 2280 ... 2385 2215 2310
## 15 Manual integer 93 0 2 1 1 1 ... 1 1 1
## 16 FuelCap double 93 0 38 13.2 18 16.9 ... 18.5 15.8 19.3
## 17 PassCap integer 93 0 6 5 5 5 ... 4 5 5
## 18 Length integer 93 0 51 177 195 180 ... 159 190 184
## 19 Wheelbase integer 93 0 27 102 115 102 ... 97 104 105
## 20 Width integer 93 0 16 68 71 67 ... 66 67 69
## 21 Uturn integer 93 0 14 37 38 37 ... 36 37 38
## 22 RearSeat double 91 2 24 26.5 30 28 ... 26 29.5 30
## 23 LugCap integer 82 11 16 11 15 14 ... 15 14 15
## 24 Weight integer 93 0 81 2705 3560 3375 ... 2810 2985 3245
## 25 Source integer 93 0 2 0 0 0 ... 0 0 0
## ------------------------------------------------------------------------------------------d$Airbags <- factor(d$Airbags, levels=0:2, labels=c("none", "driver", "drv+pas"))
d$DriveTrain <- factor(d$DriveTrain, levels=0:2, labels=c("rear", "front", "all"))
d$Manual <- factor(d$Manual, levels=0:1, labels=c("Not_Avail", "Available"))Visualize the scatterplot of MPGhiway and HP, stratified against three categorical variables: Airbags plotted in different colors for each scatterplot, and separate scatterplots for all six combinations of the levels of DriveTrain and Manual.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
## [Trellis (facet) graphics from Deepayan Sarkar's lattice package]
##
## ---------- Summary Statistics for MPGhiway
##
## Airbags n Mean Median SD IQR Min Max
## none 34 31 30 6 6 20 50
## driver 43 28 28 5 4 20 46
## drv+pas 16 27 28 2 2 23 31
##
## DriveTrain n Mean Median SD IQR Min Max
## rear 16 26 26 2 3 22 30
## front 67 30 29 5 6 21 50
## all 10 26 24 6 9 20 37
##
## Manual n Mean Median SD IQR Min Max
## Not_Avail 32 26 26 3 3 20 31
## Available 61 31 30 6 6 20 50Scatterplot Matrix
To plot a scatterplot matrix, specify multiple variables for the
first parameter value, x, repeated for the second
parameter, y. Define these multiple variables as a vector,
such as defined by c(). Request the non-linear fit line and
corresponding confidence interval by specifying TRUE or
loess for the fit parameter. Request a linear
fit line with the value of "lm".
##
## >>> Suggestions
## Recommended binary format for data files: feather
## Create with Write(d, "your_file", format="feather")
## More details about your data, Enter: details() for d, or details(name)
##
## Data Types
## ------------------------------------------------------------
## character: Non-numeric data values
## integer: Numeric data values, integers only
## double: Numeric data values with decimal digits
## ------------------------------------------------------------
##
## Variable Missing Unique
## Name Type Values Values Values First and last values
## ------------------------------------------------------------------------------------------
## 1 Years integer 36 1 16 7 NA 7 ... 1 2 10
## 2 Gender character 37 0 2 M M W ... W W M
## 3 Dept character 36 1 5 ADMN SALE FINC ... MKTG SALE FINC
## 4 Salary double 37 0 37 63788.26 104494.58 ... 66508.32 67562.36
## 5 JobSat character 35 2 3 med low high ... high low high
## 6 Plan integer 37 0 3 1 1 2 ... 2 2 1
## 7 Pre integer 37 0 27 82 62 90 ... 83 59 80
## 8 Post integer 37 0 22 92 74 86 ... 90 71 87
## ------------------------------------------------------------------------------------------## [Interactive chart from the Plotly R package (Sievert, 2020)]
Smoothed, Contoured, and Binned Scatterplots
Smoothing and binning are two procedures for visualizing a relationship with many data values.
To obtain a larger data set, in this example generate random data
with base R rnorm(), then plot. XY() first
checks the presence of the specified variables in the global environment
(workspace). If not there, then from a data frame, of which the default
value is d. Here, randomly generate values from normal
populations for x and y in the workspace.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(x, y, enhance=TRUE) # many options
## XY(x, y, color="red") # exterior edge color of points
## XY(x, y, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## XY(x, y, out_cut=.10) # label top 10% from center as outliers
##
##
## >>> Pearson's product-moment correlation
##
## Number of paired values with neither missing, n = 4000
## Sample Correlation of x and y: r = 0.251
##
## Hypothesis Test of 0 Correlation: t = 16.397, df = 3998, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.222 to 0.280
## With large data sets, even for continuous variables there can be much
over-plotting of points. One strategy to address this issue smooths the
scatterplot by setting the type parameter to
smooth. The individual points superimposed on the smoothed
plot are potential outliers. The default number of plotted outliers is
100. Turn off the plotting of outliers completely by setting parameter
smooth_points to 0. Show the linear trend with
fit set to "lm".
## [Interactive chart from the Plotly R package (Sievert, 2020)]
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
##
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(x, y, enhance=TRUE) # many options
## XY(x, y, fill="skyblue") # interior fill color of points
## XY(x, y, MD_cut=6) # Mahalanobis distance from center > 6 is an outlier
##
##
## >>> Pearson's product-moment correlation
##
## Number of paired values with neither missing, n = 4000
## Sample Correlation of x and y: r = 0.251
##
## Hypothesis Test of 0 Correlation: t = 16.397, df = 3998, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.222 to 0.280
##
##
## Line: b0 = 1.03068757 b1 = 7.91963664
## Linear Model MSE = 917.03180812 Rsq = 0.063
## Another strategy for alleviating over-plotting makes the fill color
mostly transparent with the transparency parameter, or turn
off completely by setting fill to "off". The
closer the value of trans is to 1, the more transparent is
the fill.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(x, y, enhance=TRUE) # many options
## XY(x, y, color="red") # exterior edge color of points
## XY(x, y, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## XY(x, y, MD_cut=6) # Mahalanobis distance from center > 6 is an outlier
##
##
## >>> Pearson's product-moment correlation
##
## Number of paired values with neither missing, n = 4000
## Sample Correlation of x and y: r = 0.251
##
## Hypothesis Test of 0 Correlation: t = 16.397, df = 3998, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.222 to 0.280
## Contour plots are another effective way to visualize scatter plots
with much data. By default, the parameter contours_n is set
at 10. XY() provides a threshold for deleting points for
consideration of plotting the contour curves. Otherwise, if there are
extreme outliers, the axes extend to their maximum and minimum values,
typically resulting in much white space that surrounds the visible
contour plot. The extreme values of outlier points with low density
round down to zero on the color scale. The parameter
contours_pad, with a default value of 0, can adjust the
white space to pad the resulting contour curve. Increase the parameter
value to add more padding to the plot.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(x, y, enhance=TRUE) # many options
## XY(x, y, color="red") # exterior edge color of points
## XY(x, y, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## XY(x, y, out_cut=.10) # label top 10% from center as outliers
##
##
## >>> Pearson's product-moment correlation
##
## Number of paired values with neither missing, n = 4000
## Sample Correlation of x and y: r = 0.251
##
## Hypothesis Test of 0 Correlation: t = 16.397, df = 3998, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.222 to 0.280
## Another way to visualize a relationship when there are many data
points is to bin the x-axis. Specify the number of bins with
parameter n_bins. XY() then computes the mean of y
for each bin and connects the means by line segments. This procedure
plots the conditional means by default without any assumption of form
such as linearity. Specify the stat parameter for
median to compute the median of y for each bin. The
standard XY() parameters fill,
color, size and segments also
apply.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
##
## Table: Summary Stats
##
## x y
## ------- ------- ---------
## n 4000 4000
## n.miss 0 0
## min -3.239 -104.740
## max 3.589 112.460
## mean -0.003 1.006
##
##
## Table: mean of y for levels of x
##
## bin n midpt mean
## --- ---------------- ----- ------- --------
## 1 [-3.246,-1.873] 116 -2.560 -16.734
## 2 (-1.873,-0.508] 1090 -1.191 -5.699
## 3 (-0.508,0.858] 2001 0.175 0.848
## 4 (0.858,2.223] 743 1.541 12.374
## 5 (2.223,3.596] 50 2.909 25.696Cleveland Dot Plot
Create a Cleveland dot plot when one of the variables has unique (ID)
values. In this example, for a single variable, row names are on the
y-axis. The default plots sorts by the value plotted with the default
value of parameter sort of "+" for an
ascending plot. Set to "-" for a descending plot and
"0" for no sorting.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(Salary, row_names, sort="0") # do not sort y-axis variable by x-axis variable
## XY(Salary, row_names, segments_y=FALSE) # drop the line segments
## XY(Salary, row_names, fill="red") # red point interiors
## The standard scatterplot version of a Cleveland dot plot follows, with no sorting and no line segments.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(Salary, row_names, segments_y=FALSE, sort="0", fill="red") # red point interiors
## This Cleveland dot plot has two x-variables, indicated as a standard
R vector with the c() function. In this situation, the two
points on each row are connected with a line segment. By default the
rows are sorted by distance between the successive points.
## [Interactive chart from the Plotly R package (Sievert, 2020)]
##
## >>> Suggestions or enter: style(suggest=FALSE)
## XY(c(Pre, Post), row_names, sort="0") # do not sort y-axis variable by x-axis variable
## XY(c(Pre, Post), row_names, segments_y=FALSE) # drop the line segments
## XY(c(Pre, Post), row_names, fill="red") # red point interiors
##
##
## n diff Row
## ---------------------------
## 1 -4.0 Gvakharia, Kimberly
## 2 -4.0 Downs, Deborah
## 3 -3.0 Anderson, David
## 4 -3.0 Correll, Trevon
## 5 -3.0 Kralik, Laura
## 6 -3.0 Jones, Alissa
## 7 -2.0 Capelle, Adam
## 8 -2.0 Stanley, Emma
## 9 -2.0 Adib, Hassan
## 10 -2.0 Skrotzki, Sara
## 28 6.0 LaRoe, Maria
## 29 7.0 Cassinelli, Anastis
## 30 7.0 Hamide, Bita
## 31 7.0 Sheppard, Cory
## 32 8.0 Campagna, Justin
## 33 10.0 Ritchie, Darnell
## 34 12.0 Anastasiou, Crystal
## 35 12.0 Wu, James
## 36 13.0 Korhalkar, Jessica
## 37 13.0 Cooper, Lindsay
