Types of variables

Variable types

• There are two major classes of variables
  • numeric (quantitative)
  • categorical

Variable types

• Recall from the first week of class, you can use the glimpse() function to see all of your variables and their types

data("Diamonds")
glimpse(Diamonds)

Rows: 351
Columns: 6
$ Carat      <dbl> 1.08, 0.31, 0.31, 0.32, 0.33, 0.33, 0.35, 0.35, 0.37, 0.38,…
$ Color      <fct> E, F, H, F, D, G, F, F, F, D, E, F, D, D, F, F, D, D, E, F,…
$ Clarity    <fct> VS1, VVS1, VS1, VVS1, IF, VVS1, VS1, VS1, VVS1, IF, VVS2, I…
$ Depth      <dbl> 68.6, 61.9, 62.1, 60.8, 60.8, 61.5, 62.5, 62.3, 61.4, 60.0,…
$ PricePerCt <dbl> 6693.3, 3159.0, 1755.0, 3159.0, 4758.8, 2895.8, 2457.0, 245…
$ TotalPrice <dbl> 7228.8, 979.3, 544.1, 1010.9, 1570.4, 955.6, 860.0, 860.0, …

• What are the variables here?
• fct: “factor” this is a type of categorical variable

Variable types

• Recall from the first week of class, you can use the glimpse() function to see all of your variables and their types

glimpse(starwars)

Rows: 87
Columns: 5
$ name       <chr> "Luke Skywalker", "C-3PO", "R2-D2", "Darth Vader", "Leia Or…
$ height     <int> 172, 167, 96, 202, 150, 178, 165, 97, 183, 182, 188, 180, 2…
$ mass       <dbl> 77.0, 75.0, 32.0, 136.0, 49.0, 120.0, 75.0, 32.0, 84.0, 77.…
$ hair_color <chr> "blond", NA, NA, "none", "brown", "brown, grey", "brown", N…
$ skin_color <chr> "fair", "gold", "white, blue", "white", "light", "light", "…

• chr: “character” this is a type of categorical variable

Variable types

• So far, our models have only included numeric (quantitative) variables
• What would the equation be for predicting \(y\) from \(x\) when \(x\) is numeric?
• What would happen if \(x\) is categorical?
  • What would the equation be for predicting \(y\) from \(x\) if \(x\) is categorical with 2 levels?
  • What would the equation be for predicting \(y\) from \(x\) if \(x\) is categorical with 3 levels?

Indicator variable

Indicator variables

Diamonds <- Diamonds |>
  mutate(
    ColorD = ifelse(Color == "D", 1, 0), 
    ColorE = ifelse(Color == "E", 1, 0),
    ColorF = ifelse(Color == "F", 1, 0),
    ColorG = ifelse(Color == "G", 1, 0),
    ColorH = ifelse(Color == "H", 1, 0),
    ColorI = ifelse(Color == "I", 1, 0),
    ColorJ = ifelse(Color == "J", 1, 0)
  )

Indicator variables

Diamonds <- Diamonds |>
  mutate(
    ColorD = ifelse(Color == "D", 1, 0), 
    ColorE = ifelse(Color == "E", 1, 0), 
    ColorF = ifelse(Color == "F", 1, 0),
    ColorG = ifelse(Color == "G", 1, 0),
    ColorH = ifelse(Color == "H", 1, 0),
    ColorI = ifelse(Color == "I", 1, 0),
    ColorJ = ifelse(Color == "J", 1, 0)
  )

Indicator variables

Indicator variables

R is smart

lm(TotalPrice ~ Color, data = Diamonds)

Call:
lm(formula = TotalPrice ~ Color, data = Diamonds)

Coefficients:
(Intercept)       ColorE       ColorF       ColorG       ColorH       ColorI  
       5569        -1209         3592         3990         3100         2071  
     ColorJ  
      -3632  

Relevel

levels(Diamonds$Color)

[1] "D" "E" "F" "G" "H" "I" "J"

new_levels <- c("J", "D", "E", "F", "G", "H", "I")
Diamonds <- Diamonds |>
  mutate(Color = fct_relevel(Color, new_levels))

levels(Diamonds$Color)

[1] "J" "D" "E" "F" "G" "H" "I"

Diamonds <- Diamonds |>
  mutate(Color = fct_relevel(Color, "J"))

levels(Diamonds$Color)

[1] "J" "D" "E" "F" "G" "H" "I"

R is smart

lm(TotalPrice ~ Color, data = Diamonds)

Call:
lm(formula = TotalPrice ~ Color, data = Diamonds)

Coefficients:
(Intercept)       ColorD       ColorE       ColorF       ColorG       ColorH  
       1936         3632         2423         7224         7623         6732  
     ColorI  
       5704  

What if the variable is binary

• A binary variable is a special type of categorical variable with two levels

ICU example

• A sample of 200 patients in an ICU unit
• Want to see if the patient’s heart rate is related to whether they were admitted via the emergency room
  • y: Heart rate (beats per minute)
  • x: indicator for emergency room admission
• Aside: Is this inference or prediction?

Binary x variable

data("ICU")
lm(Pulse ~ Emergency, data = ICU)

Call:
lm(formula = Pulse ~ Emergency, data = ICU)

Coefficients:
(Intercept)    Emergency  
      91.11        10.63  

• How can we interpret \(\hat{\beta}_0\) now?
• How can we interpret \(\hat{\beta}_1\)?