Plotting regression from its coefficients with ggplot

Question

I'm trying to plot some linear and polynomical regressions with ggplot . This is very straightforward when estimating the regression coefficients inside the geom_smoot function:

ggplot (mtcars, aes(x=wt, y=mpg, fill=factor(cyl), colour=factor(cyl))) + geom_smooth(method='lm', formula = y ~ poly(x,2)) + geom_point()

However, here I want to plot just a prediction (or more, as in the example above) based on previous knowledge about the regression parameters.

So here with my regression estimates can by printed by:

dlply(mtcars,.(cyl), lm, formula=mpg ~ poly(wt,2)) %>%
llply(summary) %>%
ldply(coefficients)

Now I want to build the plot in a reverse way, from the estimates to the plot. Or even better, to build a prediction from other values for these estimates (ej. Intercept=20 , poly(wt,2)1=-15 and poly(wt,2)2=4 for cyl=4 ), and then obtain a plot as the one above.

But here is where I dont know how to proceed. I guess I need to use a different geom_smooth , geom_line or similar for each level of cyl , including in each of these the corresponding values of the estimates, but cannot figure out how.

Answer 1

I usually do this by generating a dataframe of predictions.

mod <- lm(mpg ~ poly(wt,2), mtcars)
pred <- data.frame(wt = seq(0,6,0.01))
pred$mpg <- predict(mod, pred)
ggplot() +
  geom_line(data = pred, aes(x=wt, y=mpg)) +
  geom_point(data = mtcars, aes(x=wt, y=mpg, colour=factor(cyl)))

You can, of course, change the parameters to whatever you like.

pred$mpg <- 57 - pred$wt * 21 + pred$wt^2 * 3.3

Alternatively, you can use stat_function :

ggplot(pred, aes(x=wt)) +
  stat_function(fun = function(x) 57 - 21*x + 3.3*x^2) +
  geom_point(data = mtcars, aes(y=mpg, colour=factor(cyl)))

A final point: you can't interpret the coefficients of a poly() fit the way you think you would .

Answer 2

I thought this might be a good exercise to look at the broom package. I wasn't quite sure which way you wanted to go, so here's some examples of what I found:

Plotting regressions:

I don't know how you plot your polynomial function, so that's an exercise for you, but here's some code to get a polynomial regression into a data frame:

library(dplyr)
library(broom)
library(tidyr)

mtcars %>% group_by(cyl) %>% do(tidy(lm(mpg ~ poly(wt, 2), data=.))) %>%
     select(cyl, term, estimate) %>%
     spread(term, estimate)
# Source: local data frame [3 x 4]
# Groups: cyl [3]
# 
# cyl `(Intercept)` `poly(wt, 2)1` `poly(wt, 2)2`
# * <dbl>         <dbl>          <dbl>          <dbl>
# 1     4      26.66364     -10.170962       3.003872
# 2     6      19.74286      -2.426656      -1.589859
# 3     8      15.10000      -6.003055      -1.933630

But here's one for a linear regression:

fit <- mtcars %>% group_by(cyl) %>% do(tidy(lm(mpg ~ wt, data=.))) %>%
  select(cyl, term, estimate) %>%
  spread(term, estimate)
ggplot(mtcars, aes(x=wt, y=mpg, colour=cyl)) + geom_point() +
  geom_abline(data=fit, aes(slope=wt, intercept=`(Intercept)`, colour=cyl))

You can't just plot the fit, as you'll need to provide x- and y-values, so perhaps some predicted values:

wt <- c(2:5)
mtcars %>% group_by(cyl) %>% do(augment(lm(mpg ~ poly(wt, 2), data=.), newdata=data.frame(wt=wt))) %>%
  ggplot(aes(x=wt, y=.fitted, group=cyl, colour=cyl)) + geom_line()