**lessR** provides many versions of a scatter plot with
its `Plot()`

function for one or two variables with an option
to provide a separate scatterplot for each level of one or two
categorical variables. Access all scatterplots with the same simple
syntax. The first variable listed without a parameter name, the
`x`

parameter, is plotted along the x-axis. Any second
variable listed without a parameter name, the `y`

parameter,
is plotted along the y-axis. Each parameter may be represented by a
continuous or categorical variable, a single variable or a vector of
variables.

Illustrate with the Employee data included as part of
**lessR**.

```
##
## >>> Suggestions
## 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 53788.26 94494.58 ... 56508.32 57562.36
## 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
## ------------------------------------------------------------------------------------------
```

As an option, **lessR** also supports variable labels.
The labels are displayed on both the text and visualization output. Each
displayed label consists of the variable name juxtaposed with the
corresponding label. Create the table formatted as two columns. The
first column is the variable name and the second column is the
corresponding variable label. Not all variables need to be entered into
the table. The table can be stored as either a `csv`

file or
an Excel file.

Read the variable label file into the *l* data frame,
currently the only permissible name for the label file.

```
##
## >>> Suggestions
## Details about your data, Enter: details() for d, or details(name)
##
## Data Types
## ------------------------------------------------------------
## character: Non-numeric data values
## ------------------------------------------------------------
##
## Variable Missing Unique
## Name Type Values Values Values First and last values
## ------------------------------------------------------------------------------------------
## 1 label character 8 0 8 Time of Company Employment ... Test score on legal issues after instruction
## ------------------------------------------------------------------------------------------
```

Display the available labels.

```
## label
## Years Time of Company Employment
## Gender Man or Woman
## Dept Department Employed
## Salary Annual Salary (USD)
## JobSat Satisfaction with Work Environment
## Plan 1=GoodHealth, 2=GetWell, 3=BestCare
## Pre Test score on legal issues before instruction
## Post Test score on legal issues after instruction
```

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 `Plot()`

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.

```
## --- 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.

`## [Ellipse with Murdoch and Chow's function ellipse from their ellipse package]`

```
## --- 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
##
##
## >>> Outlier analysis with Mahalanobis Distance
##
## MD ID
## ----- -----
## 8.14 18
## 7.84 34
##
## 5.63 31
## 5.58 19
## 3.75 4
## ... ...
```

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.

```
##
## Fit: Mean Squared Error, MSE = 100,834,065
##
```

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.

```
##
## Regressed linearized data of transformed data values of Salary with log()
## For predicted values, back transform with exp() of regression model
##
## Line: b0 = 10.777 b1 = 0.041 Fit: MSE = 0.022 Rsq = 0.722
##
```

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.

Map a continuous variable, such as *Pre*, to the plotted
points with the `size`

parameter, a bubble plot.

```
## --- 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
##
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## radius: 0.12 size of largest bubble
## power: 0.50 relative bubble sizes
```

Indicate 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.

```
## --- 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
##
```

Multiple variables for the first parameter value, `x`

, and
no values for `y`

, plot as a scatterplot matrix. Pass a
single 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"`

.

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. `Plot()`

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.

```
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
```

```
## --- 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 turning on the `smooth`

parameter. 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"`

.

```
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
```

```
## --- 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 = 1.030687568 b1 = 7.919636637 Fit: MSE = 917.032 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.

```
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
```

```
## --- 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`

. Plot() 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 `Plot()`

parameters `fill`

,
`color`

, `size`

and `segments`

also
apply.

```
## >>> 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 25.696
```

The default plot for a single continuous variable includes not only the scatterplot, but also the superimposed violin plot and box plot, with outliers identified. Call this plot the VBS plot.

```
## [Violin/Box/Scatterplot graphics from Deepayan Sarkar's lattice package]
##
## >>> Suggestions
## Plot(Salary, out_cut=2, fences=TRUE, vbs_mean=TRUE) # Label two outliers ...
## Plot(Salary, box_adj=TRUE) # Adjust boxplot whiskers for asymmetry
```

```
## --- Salary ---
## Present: 37
## Missing: 0
## Total : 37
##
## Mean : 73795.557
## Stnd Dev : 21799.533
## IQR : 31012.560
## Skew : 0.190 [medcouple, -1 to 1]
##
## Minimum : 46124.970
## Lower Whisker: 46124.970
## 1st Quartile : 56772.950
## Median : 69547.600
## 3rd Quartile : 87785.510
## Upper Whisker: 122563.380
## Maximum : 134419.230
##
##
## --- Outliers --- from the box plot: 1
##
## Small Large
## ----- -----
## 134419.23
##
## Number of duplicated values: 0
##
## Parameter values (can be manually set)
## -------------------------------------------------------
## size: 0.61 size of plotted points
## out_size: 0.82 size of plotted outlier points
## jitter_y: 0.45 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
## bw: 9529.04 set bandwidth higher for smoother edges
```

Control the choice of the three superimposed plots â€“ violin, box, and
scatter â€“ with the `vbs_plot`

parameter. The default setting
is `"vbs"`

for all three plots. Here, for example, obtain
just the box plot. Or, use the alias `BoxPlot()`

in place of
`Plot()`

.

```
## [Violin/Box/Scatterplot graphics from Deepayan Sarkar's lattice package]
##
## >>> Suggestions
## Plot(Salary, out_cut=2, fences=TRUE, vbs_mean=TRUE) # Label two outliers ...
## Plot(Salary, box_adj=TRUE) # Adjust boxplot whiskers for asymmetry
```

```
## --- Salary ---
## Present: 37
## Missing: 0
## Total : 37
##
## Mean : 73795.557
## Stnd Dev : 21799.533
## IQR : 31012.560
## Skew : 0.190 [medcouple, -1 to 1]
##
## Minimum : 46124.970
## Lower Whisker: 46124.970
## 1st Quartile : 56772.950
## Median : 69547.600
## 3rd Quartile : 87785.510
## Upper Whisker: 122563.380
## Maximum : 134419.230
##
##
## --- Outliers --- from the box plot: 1
##
## Small Large
## ----- -----
## 134419.23
##
## Number of duplicated values: 0
```

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_yx`

of `"+"`

for an
ascending plot. Set to `"-"`

for a descending plot and
`"0"`

for no sorting.

```
##
## --- Salary ---
##
## n miss mean sd min mdn max
## 37 0 73795.6 21799.5 46125.0 69547.6 134419.2
##
##
## --- Outliers --- from the box plot: 1
##
## Small Large
## ----- -----
## 134419.2
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## size: 0.80 size of plotted points
## jitter_y: 0.00 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
```

The standard scatterplot version of a Cleveland dot plot follows, with no sorting and no line segments.

```
##
## --- Salary ---
##
## n miss mean sd min mdn max
## 37 0 73795.6 21799.5 46125.0 69547.6 134419.2
##
##
## --- Outliers --- from the box plot: 1
##
## Small Large
## ----- -----
## 134419.2
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## size: 0.80 size of plotted points
## jitter_y: 0.00 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
```

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.

```
##
## --- Pre ---
##
## n miss mean sd min mdn max
## 37 0 78.8 12.0 59.0 80.0 100.0
##
##
## --- Post ---
##
## n miss mean sd min mdn max
## 37 0 81.0 11.6 59.0 84.0 100.0
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## size: 0.80 size of plotted points
## jitter_y: 0.00 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
```

A mixture of categorical and continuous variables can be plotted a variety of ways, as illustrated below.

Plot a scatterplot of two continuous variables for each level of a
categorical variable on the same panel with the `by`

parameter. Here, plot *Years* and *Salary* each for the
two levels of *Gender* in the data. Colors and geometric plot
shapes can distinguish between the plots. For all variables except an
ordered factor, the default plots according to the default qualitative
color palette, `"hues"`

, with the geometric shape of a
point.

Change the plot colors with the `fill`

(interior) and
`color`

(exterior or edge) parameters. Because there are two
levels of the `by`

variable, specify two fill colors and two
edge colors each with an R vector defined by the `c()`

function. Also, include the regression line for each group with the
`fit`

parameter and increase the size of the plotted points
with the `size`

parameter.