Compute and plot 'grand' regression over multiple smaller regressions - r

Question

I have grouped Area values, for each of which I can compute and plot regressions:
set.seed(123)
df <- data.frame(
Group = c(rep("A",8), rep("B",10), rep("C",7)),
Area = c(1,3,2,4,3,5,7,9, rnorm(10), sample(7)),
x = c(1:8,1:10,1:7)
)
library(ggplot2)
ggplot(df,
aes(x = x, y = Area, group = factor(Group))) +
geom_smooth(method = "lm", se = FALSE)
But what I'm looking for is how to compute and plot what could be called a 'grand' regression for all Area groups. Is this possible and how would it be possible?
EDIT:
My guess is that it's not enough to simply disregard the group variable by running a model over all Area and all x values and excluding the groupvariable. This would treat the different groups as irrelevant. In actual fact each group represents a distribution in its own right. Consider each group as collecting the values of an independent event . What I need is a model that incorporates the distinction between the groups/events while at the same time summarizing over them.

Answer 1

I would be wary of the answers using stat_smooth/geom_smooth to plot a fitted line for the disaggregated values. This simply draws a best fit line through all of the data, ignoring how they are clustered.
As you say in your edit, what you need is a model that can account for the fact that you have an Area ~ X relationship in each group:
EDIT: My guess is that it's not enough to simply disregard the group variable by running a model over all Area and all x values and excluding the groupvariable. This would treat the different groups as irrelevant. In actual fact each group represents a distribution in its own right. Consider each group as collecting the values of an independent event . What I need is a model that incorporates the distinction between the groups/events while at the same time summarizing over them.
Without knowing more about your design, my first recommendation would be a mixed-effects model (e.g., using lme4).
You can fit the model, accounting for the fact that you have unique relationships in each group:
example_mod<- lmer(Area~
# Fixed Effects
1+X+
# Random Effects
(1+X|Group),
data=df,
REML=TRUE,
control=lmerControl(optimizer="bobyqa",optCtrl=list(maxfun=5e5)))
You can then extract the predicted values from this model to plot those, or calculate your own predicted values from the fixed-effects.
fitted(example_mod)
fixef(example_mod)

Answer 2

use two geom_smooth and put the grouping aesthetic into each geom separately
set.seed(123)
df <- data.frame(
Group = c(rep("A",8), rep("B",10), rep("C",7)),
Area = c(1,3,2,4,3,5,7,9, rnorm(10), sample(7)),
x = c(1:8,1:10,1:7)
)
library(ggplot2)
ggplot(df, aes(x = x, y = Area)) +
geom_smooth(aes(group = factor(Group)), method = "lm", se = FALSE) +
geom_smooth()
#> `geom_smooth()` using formula 'y ~ x'
#> `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Created on 2022-06-29 by the reprex package (v2.0.1)

Answer 3

ggplot(df,
aes(x = x, y = Area)) +
geom_smooth(method = "lm", se = FALSE, colour="red") +
geom_smooth(method="lm", se = FALSE, aes(group=factor(Group)))
Edit: Since I'd been called out to provide more details, here is what is going on behind the scene for when you run geom_smooth(aes(group=factor(Group))
library(nlme)
fit1 <- lmList(Area ~ x|Group, data=df)
df$fit1 <- fitted(fit1)
ggplot(df, aes(x, fit1, colour=Group)) + geom_line()
When you add a second geom_smooth without the group factor, you are running a linear regression (method lm) for the whole data set. i.e.
fit2 <- lm(Area ~ x, data=df)
df$fit2 <- fitted(fit2)
ggplot(df, aes(x, fit2)) + geom_line()