Carbohydrates in Starbucks food

• Starbucks often displays the total calories in their food items but not the other nutritional information.

• Our goal is to analyze the relationship between the calories and total carbohydrates (carbs) in Starbucks food items, and assess if it differs based on the type of food item (bakery, salad, sandwich, etc.)

• We can use our analysis to estimate the total carbs using information about the total calories and type for a given food time

Starbucks data

• Observations: 77 Starbucks food items

• Variables:

  • carb: Total carbohydrates (in grams)
  • calories: Total calories
  • bakery: 1: bakery food item, 0: other food type

Terminology

• carb is the response variable
  • variable whose variation we want to understand / variable we wish to predict
  • also known as outcome or dependent variable

• calories, bakery are the predictor variables
  • variables used to account for variation in the outcome
  • also known as explanatory, independent, or input variables

Let's look at the data

starbucks <- openintro::starbucks %>%
  mutate(bakery = factor(if_else(type == "bakery", 1, 0)))

p1 <- ggplot(data = starbucks, aes(x = carb))  + 
  geom_histogram(fill = "steelblue", color = "black") + 
  labs(x = "Carbohydrates (in grams)", 
       y = "Count")
p2 <- ggplot(data = starbucks, aes(x = calories))  + 
  geom_histogram(fill = "steelblue", color = "black") + 
  labs(x = "Calories", 
       y = "Count")
p3 <- ggplot(data = starbucks, aes(x = bakery))  + 
  geom_bar(fill = "steelblue", color = "black") + 
  labs(x = "Bakery Item", 
       y = "Count")
p1 + (p2 / p3)

Response vs. Predictors

p1 <- ggplot(data = starbucks, aes(x = calories, y = carb)) + 
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", se = FALSE, color = "steelblue") +
  labs(x = "Calories", 
      y  = "Carbohydrates (grams)")
p2 <- ggplot(data = starbucks, aes(x = bakery, y = carb)) + 
  geom_boxplot(fill = "steelblue", color = "black") +
  labs(x = "Bakery", 
      y  = "Carbohydrates (grams)")
p1 + p2

Model

• Goal: Determine f

• How do we determine f?

  • Make an assumption about the functional form f
  • Use the data to fit a model based on that form

Determine f

In general,

1) Choose the functional form of f, i.e. choose the appropriate model given the response variable

• Suppose f is a linear model y=f(X)=β0+β1x1+⋯+βpxp+ϵ

2) Use the data to fit (or train) the model, i.e estimate the model parameters

• Estimate β0,β1,…,βp

Carbs vs. Calories

Carbs vs. Calories + Bakery

Carbs vs. Calories + Bakery (with interaction)

Code for plot on previous slide

ggplot(data = starbucks, aes(x = calories, y = carb, color = bakery)) + 
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "Calories", 
      y  = "Carbohydrates (grams)",
      color = "Bakery", 
      title = "Total Carbohydrates vs. Calories", 
      subtitle = "With Interaction") + 
  scale_color_manual(values=c("#1B9E77", "#7570B3"))

Why?

Prediction:

What do we expect the total carbohydrates to be in a piece of Starbucks pumpkin bread, a bakery item that is 410 calories?

Inference:

What is the relationship between the calories and total carbohydrates for bakery items at Starbucks? For non-bakery items?

Course Outline