Equation, p-value, $R^2$, AIC and BIC of fitted polynomial

stat_poly_eq fits a polynomial, by default with stats::lm(), but alternatively using robust, resistant or generalized least squares. Major axis regression and segmented linear regression are also supported. Using the fitted model it generates several labels including the fitted model equation, p-value, F-value, coefficient of determination (R^2) and its confidence interval, 'AIC', 'BIC', number of observations and method name, if available.

Usage

stat_poly_eq(
  mapping = NULL,
  data = NULL,
  geom = "text_npc",
  position = "identity",
  ...,
  orientation = NA,
  formula = NULL,
  method = "lm",
  method.args = list(),
  n.min = 2L,
  fit.seed = NA,
  eq.with.lhs = TRUE,
  eq.x.rhs = NULL,
  small.r = getOption("ggpmisc.small.r", default = FALSE),
  small.p = getOption("ggpmisc.small.p", default = FALSE),
  CI.brackets = c("[", "]"),
  rsquared.conf.level = 0.95,
  coef.digits = 3,
  coef.keep.zeros = TRUE,
  decreasing = getOption("ggpmisc.decreasing.poly.eq", FALSE),
  rr.digits = 2,
  f.digits = 3,
  p.digits = 3,
  label.x = "left",
  label.y = "top",
  hstep = 0,
  vstep = NULL,
  output.type = NULL,
  na.rm = FALSE,
  parse = NULL,
  show.legend = FALSE,
  inherit.aes = TRUE
)

Arguments

mapping: The aesthetic mapping, usually constructed with aes. Only needs to be set at the layer level if you are overriding the plot defaults.
data: A layer specific dataset, only needed if you want to override the plot defaults.
geom: The geometric object to use display the data
position: The position adjustment to use for overlapping points on this layer.
...: other arguments passed on to layer. This can include aesthetics whose values you want to set, not map. See layer for more details.
orientation: character Either "x" or "y" controlling the default for formula. The letter indicates the aesthetic considered the explanatory variable in the model fit.
formula: a formula object. Using aesthetic names x and y instead of original variable names.
method: function or character If character, "lm", "rlm", "lts". "gls" "ma", "sma", or the name of a model fit function are accepted, possibly followed by the fit function's method argument separated by a colon (e.g. "rlm:M"). If a function is different to lm(), rlm(), ltsReg(), gls(), ma, sma, it must have formal parameters named formula, data, weights, and method. See Details.
method.args: named list with additional arguments. Not data or weights which are always passed through aesthetic mappings.
n.min: integer Minimum number of distinct values in the explanatory variable (on the rhs of formula) for fitting to the attempted.
fit.seed: RNG seed argument passed to set.seed(). Defaults to NA, indicating that set.seed() should not be called.
eq.with.lhs: If character the string is pasted to the front of the equation label before parsing or a logical (see note).
eq.x.rhs: character this string will be used as replacement for "x" in the model equation when generating the label before parsing it.
small.r, small.p: logical Flags to switch use of lower case r and p for coefficient of determination and p-value.
CI.brackets: character vector of length 2. The opening and closing brackets used for the CI label.
rsquared.conf.level: numeric Confidence level for the returned confidence interval. Set to NA to skip CI computation.
coef.digits, f.digits: integer Number of significant digits to use for the fitted coefficients and F-value.
coef.keep.zeros: logical Keep or drop trailing zeros when formatting the fitted coefficients and F-value.
decreasing: logical It specifies the order of the terms in the returned character string; in increasing (default) or decreasing powers.
rr.digits, p.digits: integer Number of digits after the decimal point to use for $R^2$ and P-value in labels. If Inf, use exponential notation with three decimal places.
label.x, label.y: numeric with range 0..1 "normalized parent coordinates" (npc units) or character if using geom_text_npc() or geom_label_npc(). If using geom_text() or geom_label() numeric in native data units. If too short they will be recycled.
hstep, vstep: numeric in npc units, the horizontal and vertical step used between labels for different groups.
output.type: character One of "expression", "LaTeX", "text", "markdown" or "numeric".
na.rm: a logical indicating whether NA values should be stripped before the computation proceeds.
parse: logical Passed to the geom. If TRUE, the labels will be parsed into expressions and displayed as described in ?plotmath. Default is TRUE if output.type = "expression" and FALSE otherwise.
show.legend: logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes.
inherit.aes: If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. borders.

Value

A data frame, with a single row per group and columns as described under Computed variables. In cases when the number of observations is less than n.min a data frame with no rows or columns is returned, and rendered as an empty/invisible plot layer.

Details

This statistic can be used to automatically annotate a plot with $R^2$, adjusted $R^2$, the fitted model equation, $P$, and other parameters from a fitted model. It supports linear regression and polynomial fits with lm(), segmented linear regression with package 'segmented' and major axis and standardized major axis regression with package 'smatr', robust and resistant regression with packages 'MASS' and 'robustbase'. The list is not exhaustive, and depends on the availability of methods for the model fit objects. Lack of methods or explicit support results in individual parameters and matching labels being set to NA. As some model fitting results can depend on the RNG, fit.seed if different to NA is used as argument in a call to set.seed() immediately ahead of model fitting.

While strings for $R^2$, adjusted $R^2$, $F$, and $P$ annotations are returned for all valid linear models, A character string for the fitted model is returned only for polynomials (see below). When not generated automatically, the equation can still be assembled by the user within the call to aes(). In addition, a label for the confidence interval of $R^2$, based on values computed with function ci_rsquared from package 'confintr' is returned when possible.

Model formulas can use poly() or be defined algebraically including the intercept indicated by +1, -1, +0 or implicit. If defined using poly() the argument raw = TRUE must be passed. The model formula is checked, and if not recognized as a polynomial with no missing terms and terms ordered by increasing powers, no equation label is generated. Thus, as the value returned for eq.label can be NA, the default aesthetic mapping to label is $R^2$.

The character strings mapped to the label aesthetic are encoded differently depending on argument passed to output.type, or if none passed based on the geom used. The argument of parse is set automatically based on output.type. However, if labels manually assembled from numeric output need parsing, the default needs to be overridden.

This statistic only generates annotation labels, the predicted values/line need to be added to the plot as a separate layer using stat_poly_line (or stat_smooth). Passing the same arguments in stat_poly_line() and in stat_poly_eq() to parameters method and formula, and if used also to method.args ensures that the plotted curve and equation are consistent. Thus, it is best to save these arguments as named objects and pass them as arguments to the two statistics.

A ggplot statistic receives as data a data frame that is not the one passed as argument by the user, but instead a data frame with the variables mapped to aesthetics. stat_poly_eq() mimics how stat_smooth() works. Thus, the model formula should be defined based on the names of aesthetics x and y, not the names of the variables in the data. Before fitting the model, data are split based on groupings created by any other mappings present in a plot panel: fitting is done separately for each group in each plot panel.

With method "lm", singularity results in terms being dropped with a message if more numerous than can be fitted with a singular (exact) fit. In this case or if the model results in a perfect fit due to a low number of observations, estimates for various parameters are NaN or NA. When this is the case the corresponding labels are set to character(0L) and thus not visible in the plot. With methods other than "lm", the model fit functions simply fail in case of singularity, e.g., singular fits are not implemented in rlm().

A requirement for a minimum number of observations with distinct values in the explanatory variable can be set through parameter n.min. The default n.min = 2L is the smallest suitable for method "lm" but too small for method "rlm" for which n.min = 3L is needed. Anyway, model fits with very few observations are of little interest and using larger values of n.min than the default is usually wise. This can be useful as when this threshold is not reached an empty data frame is returned resulting in an empty plot layer.

R option OutDec is obeyed based on its value at the time the plot is rendered, i.e., displayed or printed. Set options(OutDec = ",") for languages like Spanish or French.

When possible, i.e., nearly allways, the formula used to build the equation label is extracted from the returned fitted model object. Most fitted model objects follow the example of lm() and include the model that has been formula fitted. Thus, this model formula can safely differ from the argument passed to parameter formula in the call to stat_poly_eq(). Consequently, user-defined methods can implement any or all of method selection, model formula selection, dynamically adjusted method.args and conditional skipping of labelling on a by group basis.

Note

stat_poly_eq() understands x and y, to be referenced in the formula and weight passed as argument to parameter weights. All three must be mapped to numeric variables.

If the model formula includes a transformation of x, a matching argument should be passed to parameter eq.x.rhs as its default value "x" will not reflect the applied transformation. In plots, transformation should never be applied to the left hand side of the model formula, but instead in the mapping of the variable within aes, as otherwise plotted observations and fitted curve will not match. In this case it may be necessary to also pass a matching argument to parameter eq.with.lhs.

For backward compatibility a logical is accepted as argument for eq.with.lhs. If TRUE, the default is used, either "x" or "y", depending on the argument passed to formula. However, "x" or "y" can be substituted by providing a suitable replacement character string through eq.x.rhs. Parameter orientation is redundant as it only affects the default for formula but is included for consistency with ggplot2::stat_smooth().

Computed variables

If the model fit function used does not returns NA or no value, the label is set to character(0L). The position of the columns in the data frame can change between package versions, extract values always by name.

For all output.type arguments the following values are returned.

x,npcx: x position
y,npcy: y position
coefs: fitted coefficients, named numeric vector as a list member
r.squared, rr.confint.level, rr.confint.low, rr.confint.high, adj.r.squared, f.value, f.df1, f.df2, p.value, AIC, BIC, n, knots, knots.se: numeric values, from the model fit object
grp.label: Set according to mapping in aes.
knots: list containing a numeric vector of knot or "psi" x-value for linear splines
fm.method: name of method used, character
fm.class: most derived class or the fitted model object, character
fm.formula.chr: formatted model formula, character

If output.type is not "numeric" the returned tibble contains in addition to those above the columns listed below, each containing a single character string. The markup used depends on the value of output.type.

eq.label: equation for the fitted polynomial as a character string to be parsed or NA
rr.label: $R^2$ of the fitted model as a character string to be parsed
adj.rr.label: Adjusted $R^2$ of the fitted model as a character string to be parsed
rr.confint.label: Confidence interval for $R^2$ of the fitted model as a character string to be parsed
f.value.label: F value and degrees of freedom for the fitted model as a whole.
p.value.label: P-value for the F-value above.
AIC.label: AIC for the fitted model.
BIC.label: BIC for the fitted model.
n.label: Number of observations used in the fit.
knots.label: The knots or change points in segmented regression.
grp.label: Set according to mapping in aes.
method.label: Set according method used.

If output.type is "numeric" the returned tibble contains columns listed below in addition to the base ones. If the model fit function used does not return a value, the variable is set to NA_real_.

coef.ls: list containing the "coefficients" matrix from the summary of the fit object
b_0.constant: TRUE is polynomial is forced through the origin
b_i: One or more columns with the coefficient estimates

To explore the computed values returned for a given input we suggest the use of geom_debug as shown in the last examples below.

Model fit methods supported

Several model fit functions are supported explicitly (see tables), and some of their differences smoothed out. Compatibility is checked late, based on the class of the returned fitted model object. This makes it possible to use wrapper functions that do model selection or other adjustments to the fit procedure on a per panel or per group basis. Moreover, if the value returned as model fit object is NULL no layer is added to the plot on a per group within panel basis.

In the case of fitted model objects of classes not explicitly supported an attempt is made to find the usual accessors and/or fitted object members, and if found, either complete or partial support is frequently achieved. In this case a message is issued encouraging users to check the valisdity of the values extracted.

The argument to parameter method can be either the name of a function object, possibly using double colon notation, or a character string matching the function name. This approach makes it possible to support model fit functions that are not dependencies of 'ggpmisc'. Either by attaching the package where the function is defined and passing it by name or as string, or using double colon notation when passing the name of the function. User-defined functions can be passed as argument to parameter method as long as they have parameters formula, data subset and possibly weights. Additional arguments can be passed to any method as a named list as an argument to parameter method.args. As in stat_smooth() prior weights are passed to the model fit functions' weights (plural!) parameter by mapping a numeric variable to plot aesthetic weight (singular!).

The table below lists natively supported model fit functions, with the caveat that only some 'broom' methods' specializations have been actually tested with statistics from 'ggpmisc'. In addition, the statistics based on 'broom' methods require the user to tailor their behaviour by passing additional arguments in the call.

Statistic	$f$	Supported model fit methods
`stat_poly_line()`	G	"lm", "rlm", "lts", "sma", "ma", "gls", others with methods `predict()` or `fitted()`
`stat_poly_eq()`	G	"lm", "rlm", "lts", "sma", "ma", "gls", others with needed accesors
`stat_quant_line()`	G	"rq", "rqss"
`stat_quant_band()`	G	"rq", "rqss"
`stat_quant_eq()`	G	"rq", "rqss"
`stat_ma_line()`	G	"SMA", "MA", "RMA", "OLS"
`stat_ma_eq()`	G	"SMA", "MA", "RMA", "OLS"
`stat_fit_residuals()`	G	"lm", "rlm", "lts", "sma", "ma", "gls", "rq", "rqss" others with method `residuals()`
`stat_fit_fitted()`	G	"lm", "rlm", "lts", "gls", "rq", "rqss" others with method `fitted()`
`stat_fit_deviations()`	G	"lm", "rlm", "lts", "gls", "rq", "rqss" others with methods `fitted()` and `weights()`
`stat_fit_augment()`	G	any with 'broom' method `augment()`
`stat_fit_glance()`	G	any with 'broom' method `glance()`
`stat_fit_tidy()`	G	any with 'broom' method `tidy()`
`stat_fit_tb()`	P	any with 'broom' method `tidy()`

The table below lists the names for fit methods coded in the statistics as given in the table above. The single colon notation is based on parsing the name and is available whenever passing the name of the fit method as a character string. In a string such as "head:tail" the "head" gives the name of the model fit function and the "tail" gives the argument to pass it's method parameter. In some cases the default formula = y ~ x needs to be overridden with an explicit argument.

Predefined method names	Model fit methods	R package	Object class
"lm", "lm:qr"	`lm()`	'stats'	"lm"
"rlm", "rlm:M", "rlm:MM"	`rlm()`	'MASS'	"rlm" ("lm")
"lts", "ltsReg"	`ltsReg()`	'robustbase'	"lts"
"ma", "sma", "sma:SMA", "sma:MA", "sma:OLS"	`sma()`	'smatr'	"ma" or "sma"
"gls", "gls:REML", "gls:ML"	`gls()`	'nlme'	"gls"
"rq", "rq:sfn", "rq:sfnc", "rq:lasso"	`rq()`	'quantreg'	"rq"
"rqss", "rqss:sfn", "rqss:sfnc", "rqss:lasso"	`rqss()`	'quantreg'	"rqss"
"SMA", "MA", "RMA", "OLS"	`lmodel2()`	'lmodel2'

Output types

The formatting of character strings to be displayed in plots are marked as mathematical equations. Depending on the geom used, the mark-up needs to be encoded differently, or in some cases mark-up not applied.

"expression": The labels are encoded as character strings to be parsed into R's plotmath expressions.
"LaTeX", "TeX", "tikz", "latex": The labels are encoded as 'LaTeX' maths equations, without the "fences" for switching in math mode.
"latex.eqn": Same as "latex" but enclosed in single $, i.e., as in-line maths.
"latex.deqn": Same as "latex" but enclosed in double $$, i.e., as display maths.
"markdown": The labels are encoded as character strings using markdown syntax, with some embedded HTML.
"marquee": The labels are encoded as character strings using markdown syntax, with 'marquee' supported spans.
"text": The labels are plain ASCII character strings.
"numeric": No labels are generated. This value is accepted by the statistics, but not by the label formatting functions.
NULL: The value used, expression, latex.eqn or markup depends on the argument passed to geom.

If geom = "latex" (package 'xdvir') the output type used is "latex.eqn". If geom = "richtext" (package 'ggtext') or geom = "textbox" (package 'ggtext') the output type used is "markdown". If geom = "marquee" (package 'marquee') the output type used is "marquee". For all other values of geom the default is "expression" unless the user passes an argument. Invalid values as argument trigger an Error.

References

Originally written as an answer to question 7549694 at Stackoverflow but enhanced based on suggestions from users and my own needs.

Aesthetics

stat_poly_eq() understands the following aesthetics. Required aesthetics are displayed in bold and defaults are displayed for optional aesthetics:

•	`x`
•	`y`
•	`group`	→ inferred
•	`grp.label`
•	`hjust`	→ `"inward"`
•	`label`	→ `after_stat(rr.label)`
•	`npcx`	→ `after_stat(npcx)`
•	`npcy`	→ `after_stat(npcy)`
•	`vjust`	→ `"inward"`
•	`weight`	→ `1`

Learn more about setting these aesthetics in vignette("ggplot2-specs").

Examples

# generate artificial data
set.seed(4321)
x <- 1:100
y <- (x + x^2 + x^3) + rnorm(length(x), mean = 0, sd = mean(x^3) / 4)
y <- y / max(y)
my.data <- data.frame(x = x, y = y,
                      group = c("A", "B"),
                      y2 = y * c(1, 2) + c(0, 0.1),
                      w = sqrt(x))

# give a name to a formula
formula <- y ~ poly(x, 3, raw = TRUE)

# using defaults
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line() +
  stat_poly_eq()


# no weights
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(formula = formula)


# other labels
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(use_label("eq"), formula = formula)


# other labels
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(use_label("eq"), formula = formula, decreasing = TRUE)


ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(use_label("eq", "R2"), formula = formula)


ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(use_label("R2", "R2.CI", "P", "method"), formula = formula)


ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(use_label("R2", "F", "P", "n", sep = "*\"; \"*"),
               formula = formula)


# grouping
ggplot(my.data, aes(x, y2, color = group)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(formula = formula)


# rotation
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(formula = formula, angle = 90)


# label location
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(formula = formula, label.y = "bottom", label.x = "right")


ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(formula = formula, label.y = 0.1, label.x = 0.9)


# modifying the explanatory variable within the model formula
# modifying the response variable within aes()
# eq.x.rhs and eq.with.lhs defaults must be overridden!!
formula.trans <- y ~ I(x^2)
ggplot(my.data, aes(x, y + 1)) +
  geom_point() +
  stat_poly_line(formula = formula.trans) +
  stat_poly_eq(use_label("eq"),
               formula = formula.trans,
               eq.x.rhs = "~x^2",
               eq.with.lhs = "y + 1~~`=`~~")


# using weights
ggplot(my.data, aes(x, y, weight = w)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(formula = formula)


# no weights, 4 digits for R square
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(formula = formula, rr.digits = 4)


# manually assemble and map a specific label using paste() and aes()
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(aes(label =  paste(after_stat(rr.label),
                                  after_stat(n.label), sep = "*\", \"*")),
               formula = formula)


# manually assemble and map a specific label using sprintf() and aes()
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(aes(label =  sprintf("%s*\" with \"*%s*\" and \"*%s",
                                    after_stat(rr.label),
                                    after_stat(f.value.label),
                                    after_stat(p.value.label))),
               formula = formula)


# x on y regression
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula, orientation = "y") +
  stat_poly_eq(use_label("eq", "adj.R2"),
               formula = x ~ poly(y, 3, raw = TRUE))


# conditional user specified label
ggplot(my.data, aes(x, y2, color = group)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(aes(label =  ifelse(after_stat(adj.r.squared) > 0.96,
                                   paste(after_stat(adj.rr.label),
                                         after_stat(eq.label),
                                         sep = "*\", \"*"),
                                   after_stat(adj.rr.label))),
               rr.digits = 3,
               formula = formula)


# geom = "text"
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_poly_line(formula = formula) +
  stat_poly_eq(geom = "text", label.x = 100, label.y = 0, hjust = 1,
               formula = formula)


# Inspecting the returned data using geom_debug_group()
# This provides a quick way of finding out the names of the variables that
# are available for mapping to aesthetics with after_stat().

gginnards.installed <- requireNamespace("gginnards", quietly = TRUE)

if (gginnards.installed)
  library(gginnards)

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_poly_line(formula = formula) +
    stat_poly_eq(formula = formula,
                 geom = "debug_group")

#> [1] "PANEL 1; group(s) -1; 'draw_function()' input 'data' (head):"
#>                                                                                                      eq.label
#> 1 italic(y)~`=`~-0.00450 + 0.00109*~italic(x) - 2.14%*% 10^{-05}*~italic(x)^2 + 1.06%*% 10^{-06}*~italic(x)^3
#>                 rr.label                adj.rr.label      rr.confint.label
#> 1 italic(R)^2~`=`~"0.96" italic(R)[adj]^2~`=`~"0.96" "95% CI [0.95, 0.97]"
#>                 AIC.label               BIC.label
#> 1 plain(AIC)~`=`~"-291.9" plain(BIC)~`=`~"-278.8"
#>                    f.value.label         p.value.label           n.label
#> 1 italic(F)[3*","*96]~`=`~"810." italic(P)~`<`~"0.001" italic(n)~`=`~100
#>   knots.label grp.label    method.label
#> 1        <NA>        -1 "method: lm:qr"
#>                                                      coefs
#> 1 -4.495631e-03, 1.089644e-03, -2.139937e-05, 1.055387e-06
#>                                                                              coefs.names
#> 1 (Intercept), poly(x, 3, raw = TRUE)1, poly(x, 3, raw = TRUE)2, poly(x, 3, raw = TRUE)3
#>   rr.confint.level rr.confint.low rr.confint.high f.value f.df1 f.df2 r.squared
#> 1             0.95      0.9464423       0.9696371 810.484     3    96 0.9620171
#>   adj.r.squared      p.value       AIC      BIC   n knots knots.se knots.names
#> 1     0.9608301 5.110349e-68 -291.8639 -278.838 100    NA       NA          NA
#>   fm.method fm.class                 fm.formula             fm.formula.chr x
#> 1     lm:qr       lm y ~ poly(x, 3, raw = TRUE) y ~ poly(x, 3, raw = TRUE) 1
#>   npcx y npcy PANEL group                  label orientation
#> 1   NA 1   NA     1    -1 italic(R)^2~`=`~"0.96"           x

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_poly_line(formula = formula) +
    stat_poly_eq(formula = formula,
                 geom = "debug_group",
                 output.type = "numeric")

#> [1] "PANEL 1; group(s) -1; 'draw_function()' input 'data' (head):"
#>   rr.label
#> 1         
#>                                                                                                                                                                                                                              coef.ls
#> 1 -4.495631e-03, 1.089644e-03, -2.139937e-05, 1.055387e-06, 2.268244e-02, 1.935252e-03, 4.440449e-05, 2.890821e-07, -1.981987e-01, 5.630500e-01, -4.819189e-01, 3.650820e+00, 8.433087e-01, 5.747135e-01, 6.309604e-01, 4.255076e-04
#>   b_0.constant          b_0         b_1           b_2          b_3
#> 1        FALSE -0.004495631 0.001089644 -2.139937e-05 1.055387e-06
#>                                                      coefs
#> 1 -4.495631e-03, 1.089644e-03, -2.139937e-05, 1.055387e-06
#>                                                                              coefs.names
#> 1 (Intercept), poly(x, 3, raw = TRUE)1, poly(x, 3, raw = TRUE)2, poly(x, 3, raw = TRUE)3
#>   rr.confint.level rr.confint.low rr.confint.high f.value f.df1 f.df2 r.squared
#> 1             0.95      0.9464423       0.9696371 810.484     3    96 0.9620171
#>   adj.r.squared      p.value       AIC      BIC   n knots knots.se knots.names
#> 1     0.9608301 5.110349e-68 -291.8639 -278.838 100    NA       NA          NA
#>   fm.method fm.class                 fm.formula             fm.formula.chr x
#> 1     lm:qr       lm y ~ poly(x, 3, raw = TRUE) y ~ poly(x, 3, raw = TRUE) 1
#>   npcx y npcy PANEL group label orientation
#> 1   NA 1   NA     1    -1                 x

# names of the variables
if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_poly_line(formula = formula) +
    stat_poly_eq(formula = formula,
                 geom = "debug_group",
                 dbgfun.data = colnames)

#> [1] "PANEL 1; group(s) -1; 'draw_function()' input 'data' (anonymous function):"
#>  [1] "eq.label"         "rr.label"         "adj.rr.label"     "rr.confint.label"
#>  [5] "AIC.label"        "BIC.label"        "f.value.label"    "p.value.label"   
#>  [9] "n.label"          "knots.label"      "grp.label"        "method.label"    
#> [13] "coefs"            "coefs.names"      "rr.confint.level" "rr.confint.low"  
#> [17] "rr.confint.high"  "f.value"          "f.df1"            "f.df2"           
#> [21] "r.squared"        "adj.r.squared"    "p.value"          "AIC"             
#> [25] "BIC"              "n"                "knots"            "knots.se"        
#> [29] "knots.names"      "fm.method"        "fm.class"         "fm.formula"      
#> [33] "fm.formula.chr"   "x"                "npcx"             "y"               
#> [37] "npcy"             "PANEL"            "group"            "label"           
#> [41] "orientation"     

# only data$eq.label
if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_poly_line(formula = formula) +
    stat_poly_eq(formula = formula,
                 geom = "debug_group",
                 output.type = "expression",
                 dbgfun.data = function(x) {x[["eq.label"]]})

#> [1] "PANEL 1; group(s) -1; 'draw_function()' input 'data' (anonymous function):"
#> [1] "italic(y)~`=`~-0.00450 + 0.00109*~italic(x) - 2.14%*% 10^{-05}*~italic(x)^2 + 1.06%*% 10^{-06}*~italic(x)^3"

# only data$eq.label
if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_poly_line(formula = formula) +
    stat_poly_eq(formula = formula,
                 geom = "debug_group",
                 output.type = "text",
                 dbgfun.data = function(x) {x[["eq.label"]]})

#> [1] "PANEL 1; group(s) -1; 'draw_function()' input 'data' (anonymous function):"
#> [1] "y = -0.00450 + 0.00109  x - 2.14 10^-05  x^2 + 1.06 10^-06  x^3"

Equation, p-value, \(R^2\), AIC and BIC of fitted polynomial