library(tidyverse)
library(tidymodels)
library(scatterplot3d)

Bulletin

Upcoming
- prep quiz due Thursday
- lab 08 due Friday
- Exam 02 next Friday through Tuesday. Exam 02 will cover topics up until Tues Nov. 9th.

Learning goals

Understand the language and notation of linear modeling.
Use tidymodels to make inference under a linear regression model

To begin, let’s load the data. Again, we’ll work with the pokemon data from last week.

pokemon <- read_csv("data/pokemon.csv")

## 
## ── Column specification ────────────────────────────────────────────────────────
## cols(
##   pokedex_number = col_double(),
##   name = col_character(),
##   generation = col_double(),
##   leg_status = col_character(),
##   type_1 = col_character(),
##   type_2 = col_character(),
##   height_m = col_double(),
##   weight_kg = col_double(),
##   bst = col_double(),
##   hp = col_double(),
##   atk = col_double(),
##   def = col_double(),
##   spa = col_double(),
##   spd = col_double(),
##   spe = col_double()
## )

The language of linear modeling

What is a linear model?

A linear model is a simple way to mathematically model the relationship between two or more observed phenomena.

Exercise 1)

Is there a relationship between a pokemon’s size and their hit points (hp)? Specifically, does a pokemon’s height/weight tell us something about how many hit points they have?

Create two scatterplots, one for hp vs height and another illustrating hp vs weight.

# code here

Describe the relationship you see here.

Label the following:

Response variable:

Explanatory variable(s):

Exercise 2)

For now, let’s focus on just two of these variables, namely hp and height.

Write down a model (using \(x\), \(y\), \(\beta\) notation) that describes a linear relationship between hp and height. Define each variable.

[write here]

Exercise 3)

Click here to interact with an ordinary least squares (OLS) linear regression model.

Select I and move the data points around.

Describe what you see.

Exercise 4)

Now let’s fit a ordinary least squares lm.

Use functions from the preparation video/slides to fit a linear model to hp and height as described in exercise 2. Save the model in a variable entitled hp_height_fit.

# code here

Write out the equation of the fitted model.

Uncomment and fill in blanks below to visualize the linear model on top of the scatterplot from Exercise 1.

#hp_height_fit_aug <- augment(hp_height_fit$fit) # need $fit for plotting

# hp_height_fit_aug %>%
#   ggplot() +
#   geom_point(aes(___, ___)) +
#   geom_line(aes(x = ___, y = .fitted), size = 0.75, color = "darkred") +
#   theme_minimal()

Exercise 5)

Use the equation of the fitted model to predict the hp of an unknown pokemon with a height of 1.1 meters.

# code here

If you were asked to predict the hp of a pokemon that is 2.5 meters tall, is this model appropriate? Why or why not?

Exercise 6)

What about a linear model with multiple explanatory variables?

scatterplot3d(pokemon[,c("weight_kg", "height_m", "hp")], pch = 19, color="steelblue")