15.4 Complete Pooling

• Complete pooling just combines all the observations, ignoring which runner they came from

• No clear trend appears, book performs linear regression and finds slope consistent with zero.

• This seems strange: dont we get slower as we age?

• Zoom in on three runners:

# Select an example subset
examples <- running %>% 
  filter(runner %in% c("1", "20", "22"))

ggplot(examples, aes(x = age, y = net)) + 
  geom_point() + 
  facet_wrap(~ runner) + 
  geom_abline(aes(intercept = 75.2242, slope = 0.2678), 
              color = "blue")

15.4.1 Drawbacks of complete pooling

• Violates assumption of independence! Observations within a runner are correlated.

• Ignores information about individual runners: people age differently!

• Produce misleading conclusions of the relationship between predictor and response