R print equation of linear regression on the plot itself - r

Question

How do we print the equation of a line on a plot?
I have 2 independent variables and would like an equation like this:
y=mx1+bx2+c
where x1=cost, x2 =targeting
I can plot the best fit line but how do i print the equation on the plot?
Maybe i cant print the 2 independent variables in one equation but how do i do it for say
y=mx1+c at least?
Here is my code:
fit=lm(Signups ~ cost + targeting)
plot(cost, Signups, xlab="cost", ylab="Signups", main="Signups")
abline(lm(Signups ~ cost))

Answer 1

I tried to automate the output a bit:
fit <- lm(mpg ~ cyl + hp, data = mtcars)
summary(fit)
##Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.90833 2.19080 16.847 < 2e-16 ***
## cyl -2.26469 0.57589 -3.933 0.00048 ***
## hp -0.01912 0.01500 -1.275 0.21253
plot(mpg ~ cyl, data = mtcars, xlab = "Cylinders", ylab = "Miles per gallon")
abline(coef(fit)[1:2])
## rounded coefficients for better output
cf <- round(coef(fit), 2)
## sign check to avoid having plus followed by minus for negative coefficients
eq <- paste0("mpg = ", cf[1],
ifelse(sign(cf[2])==1, " + ", " - "), abs(cf[2]), " cyl ",
ifelse(sign(cf[3])==1, " + ", " - "), abs(cf[3]), " hp")
## printing of the equation
mtext(eq, 3, line=-2)
Hope it helps,
alex

Answer 2

You use ?text. In addition, you should not use abline(lm(Signups ~ cost)), as this is a different model (see my answer on CV here: Is there a difference between 'controling for' and 'ignoring' other variables in multiple regression). At any rate, consider:
set.seed(1)
Signups <- rnorm(20)
cost <- rnorm(20)
targeting <- rnorm(20)
fit <- lm(Signups ~ cost + targeting)
summary(fit)
# ...
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 0.1494 0.2072 0.721 0.481
# cost -0.1516 0.2504 -0.605 0.553
# targeting 0.2894 0.2695 1.074 0.298
# ...
windows();{
plot(cost, Signups, xlab="cost", ylab="Signups", main="Signups")
abline(coef(fit)[1:2])
text(-2, -2, adj=c(0,0), labels="Signups = .15 -.15cost + .29targeting")
}

Answer 3

Here's a solution using tidyverse packages.
The key is the broom package, whcih simplifies the process of extracting model data. For example:
fit1 <- lm(mpg ~ cyl, data = mtcars)
summary(fit1)
fit1 %>%
tidy() %>%
select(estimate, term)
Result
# A tibble: 2 x 2
estimate term
<dbl> <chr>
1 37.9 (Intercept)
2 -2.88 cyl
I wrote a function to extract and format the information using dplyr:
get_formula <- function(object) {
object %>%
tidy() %>%
mutate(
term = if_else(term == "(Intercept)", "", term),
sign = case_when(
term == "" ~ "",
estimate < 0 ~ "-",
estimate >= 0 ~ "+"
),
estimate = as.character(round(abs(estimate), digits = 2)),
term = if_else(term == "", paste(sign, estimate), paste(sign, estimate, term))
) %>%
summarize(terms = paste(term, collapse = " ")) %>%
pull(terms)
}
get_formula(fit1)
Result
[1] " 37.88 - 2.88 cyl"
Then use ggplot2 to plot the line and add a caption
mtcars %>%
ggplot(mapping = aes(x = cyl, y = mpg)) +
geom_point() +
geom_smooth(formula = y ~ x, method = "lm", se = FALSE) +
labs(
x = "Cylinders", y = "Miles per Gallon",
caption = paste("mpg =", get_formula(fit1))
)
Plot using geom_smooth()
This approach of plotting a line really only makes sense to visualize the relationship between two variables. As #Glen_b pointed out in the comment, the slope we get from modelling mpg as a function of cyl (-2.88) doesn't match the slope we get from modelling mpg as a function of cyl and other variables (-1.29). For example:
fit2 <- lm(mpg ~ cyl + disp + wt + hp, data = mtcars)
summary(fit2)
fit2 %>%
tidy() %>%
select(estimate, term)
Result
# A tibble: 5 x 2
estimate term
<dbl> <chr>
1 40.8 (Intercept)
2 -1.29 cyl
3 0.0116 disp
4 -3.85 wt
5 -0.0205 hp
That said, if you want to accurately plot the regression line for a model that includes variables that don't appear included in the plot, use geom_abline() instead and get the slope and intercept using broom package functions. As far as I know geom_smooth() formulas can't reference variables that aren't already mapped as aesthetics.
mtcars %>%
ggplot(mapping = aes(x = cyl, y = mpg)) +
geom_point() +
geom_abline(
slope = fit2 %>% tidy() %>% filter(term == "cyl") %>% pull(estimate),
intercept = fit2 %>% tidy() %>% filter(term == "(Intercept)") %>% pull(estimate),
color = "blue"
) +
labs(
x = "Cylinders", y = "Miles per Gallon",
caption = paste("mpg =", get_formula(fit2))
)
Plot using geom_abline()