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lecture11.md

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Lecture 11 (Week 6, Monday)

Vegemite

  • why do some people eat more vegemite than others?
  • explore variation: make a scatterplot to see whether respect_condition explains variation in veg_eaten
    • veg_eaten = respect + error
library(readr)
vegemite_clean <- read_csv("http://bit.ly/vegemite_clean")
gf_point(veg_eaten ~ respect_condition, data = vegemite_clean)
gf_jitter(veg_eaten ~ respect_condition, data = vegemite_clean, width=.1, height=0, size=5, alpha=.3, color="darkolivegreen4")

Model Variation

2) Draw the models onto the jitter plot.

  • draw in the empty model
    • straight line at 0.1836
    • predicts the same for everybody
  • draw respect model
    • thinks there are two different groups
    • predicts something different for different people
    • for the no respect group, predict 0.14
    • for the respect group, predict 0.14 + 0.09
  • why jitter plots come in handy:
    • veg_eaten = respect + model
  • let's draw the models onto the jitter plots in R
empty.model <- lm(veg_eaten ~ NULL, data = vegemite_clean)
respect.model <- lm(veg_eaten ~ respect_condition, data = vegemite_clean)

vegemite_clean$empty.pred <- predict(empty.model)
vegemite_clean$empty.pred <- predict(respect.model)

gf_jitter(veg_eaten ~ respect_condition, data = vegemite_clean, width=.1, height=0, size=5, alpha=.3, color="darkolivegreen4") %>%
gf_jitter(empty.pred ~ respect_condition, color="blue", height=0) %>%
gf_jitter(respect.pred ~ respect_condition, color="orange", height=0)

3) Just by looking, is there left over variation from the respect model?

  • we've predicted very little

4) What would the data look like if the respect model explained 100% of variation?

  • that's never how data looks

Draw the Residuals

5) empty model's residuals vs. respect model's residuals

  • residuals balance each other out

7) Isn't the error from the empty model always bigger than error from the complex model?

  • yes, always
  • true at the aggregate level
  • not true at the level of individual data points

Error at Two Levels

  • individual data points: residuals
  • aggregated (the whole distribution): SS
    • always bigger for the empty model

8) Draw a few squared residuals that go with each SS.

  • green boxes + orange boxes = blue boxes

Run supernova( ) on both the empty.model and the respect.model.

supernova(empty.model)
  • sum of squares: empty model
supernova(respect.model)
  • no matter what the complex model is, SS total stays the same
  • is 0.311 a lot of error reduced? difficult for us to tell

PRE: Converting Squared Error Units into Proportion

  • how would you calculate PRE from these three sums of squares?
  • (SS Total - SS Error) / SS Total