Reading a model's coefficients

A model’s coefficients are numbers in a table. gf_b() puts them on the plot, so you can see what each one measures.

Slope is rise over run

For a quantitative predictor, b1 is how much the prediction moves for a one-unit change in the predictor. gf_b() draws that as a triangle.

thumb_model <- lm(Thumb ~ Height, data = Fingers)
gf_point(Thumb ~ Height, data = Fingers, alpha = .4) %>%
  gf_model(thumb_model) %>%
  gf_b(thumb_model)

When one unit is too small to see, ask for a longer run. The label says which multiple it is showing.

gf_point(Thumb ~ Height, data = Fingers, alpha = .4) %>%
  gf_model(thumb_model) %>%
  gf_b(thumb_model, run = 10)

The intercept is a prediction, and it may sit outside the data

b0 is the prediction when the predictor is zero. Here that is a person of no height, which is why the intercept sits far below anything the data contains.

coef(thumb_model)
#> (Intercept)      Height 
#>  -3.3294866   0.9618834
range(Fingers$Height)
#> [1] 59.0 76.5

The plot makes the distance obvious: to show b0 at all, the panel has to stretch past every observation.

gf_point(Thumb ~ Height, data = Fingers, alpha = .4) %>%
  gf_model(thumb_model) %>%
  gf_b(thumb_model, show_b0 = TRUE)

Notice that the line stops well short of the dot. That is deliberate, and it is worth pausing on. Between the shortest and tallest people in this sample, every point on the line has observations on both sides of it. Out at zero there are none, so the line has nothing to stand on and does not go there. b0 is still a real number the model reports; the picture is just declining to pretend we watched it happen.

Centering the predictor moves zero into the data, and b0 becomes the prediction for someone of average height. The slope does not change.

Fingers$Height_c <- Fingers$Height - mean(Fingers$Height)
centered_model <- lm(Thumb ~ Height_c, data = Fingers)

gf_point(Thumb ~ Height_c, data = Fingers, alpha = .4) %>%
  gf_model(centered_model) %>%
  gf_b(centered_model, show_b0 = TRUE)

With groups, the coefficients are differences

For a categorical predictor, b0 is the first group’s mean and each other coefficient is a distance from it. The arrows measure those distances.

sex_model <- lm(Thumb ~ Sex, data = Fingers)
gf_jitter(Thumb ~ Sex, data = Fingers, width = .1, alpha = .4) %>%
  gf_model(sex_model) %>%
  gf_b(sex_model)

With three groups there are two arrows, both measured from the same reference.

three <- droplevels(subset(Fingers, Year %in% c("1", "2", "3")))
year_model <- lm(Thumb ~ Year, data = three)
gf_jitter(Thumb ~ Year, data = three, width = .1, alpha = .4) %>%
  gf_model(year_model) %>%
  gf_b(year_model)

The arrows start where the reference group’s prediction is, so a coefficient that reads as a small number is a short arrow, whatever the outcome’s scale.