Project 2

Enter your name and EID here

This is the dataset you will be working with:

wine_features <- 
  read_csv("https://wilkelab.org/classes/SDS348/data_sets/wine_features.csv") %>%
  mutate(type = as.factor(type))

## Parsed with column specification:
## cols(
##   type = col_character(),
##   quality = col_double(),
##   quality_grade = col_character(),
##   alcohol = col_double(),
##   alcohol_grade = col_character(),
##   pH = col_double(),
##   acidity_grade = col_character(),
##   fixed_acidity = col_double(),
##   volatile_acidity = col_double(),
##   citric_acid = col_double(),
##   residual_sugar = col_double(),
##   chlorides = col_double(),
##   free_sulfur_dioxide = col_double(),
##   total_sulfur_dioxide = col_double(),
##   density = col_double(),
##   sulphates = col_double()
## )

Part 1

Question: Can red and white wines be distinguished based on their physicochemical composition?

To answer this question, perform a principal component analysis. Make a scatterplot of PC2 vs. PC1, and a rotation matrix visualizing the influence of the input variables. Hint: You must remove all categorical variables before creating the PCA object.

Introduction: The dataset wine_features contains 6497 rows describing various chemical attributes of red and white wine (indicated by the type column) and each wine’s relative quality (indicated by the quality/quality_grade column) on a scale of 3 to 9 as graded by experts performing a blind taste test. Chemical attributes recorded for each wine include fixed_acidity, volatile_acidity, citric_acid, residual_sugar, chlorides, free_sulfur_dioxide, total_sulfur_dioxide, density, pH, sulphates, alcohol. Categorical descriptions of alcohol content and acidity are given by alcohol_grade and acidity_grade.

Approach: First, I will remove all non-numerical columns from the dataset (type, quality_grade, alcohol_grade, and acidity_grade). Then, I will perform a PCA on the remaining numerical columns using the functions scale() and prcomp(), and save the results in a new dataframe called pca_data. To evaluate whether the physicochemical properties describe the type of wine, I’ll make a scatterplot (using geom_point()) comparing the first and second principal components, coloring each point by type of wine. Then, I’ll make a new dataframe containing the rotation matrix and visualize the rotation matrix using geom_segment() and geom_text_repel().

Analysis:

# perform PCA on `wine_features` dataset
pca <- wine_features %>%
  select(-type, -quality_grade,
         -alcohol_grade, -acidity_grade) %>%
  scale() %>%
  prcomp()

# get transformation data from PCA object for further analysis
pca_data <- data.frame(pca$x, wine_features)

# color PC2 vs. PC1 scatterplot by type of wine
ggplot(pca_data, aes(x = PC1, y = PC2, color = type)) + 
  geom_point(alpha = 0.75, size = 2) + 
  scale_color_manual(values = c(wine_palette[5], wine_palette[1]))

# capture the rotation matrix in a data frame
rotation_data <- data.frame(pca$rotation, 
                            variable = row.names(pca$rotation))

# define a pleasing arrow style
arrow_style <- arrow(length = unit(0.075, "inches"),
                     type = "closed")

# now plot, using geom_segment() for arrows and geom_text for labels
ggplot(rotation_data) +
  geom_segment(aes(xend = PC1, yend = PC2), 
               x = 0, y = 0, 
               arrow = arrow_style) +
  geom_text_repel(aes(x = PC1, y = PC2, label = variable), 
                  size = 3, 
                  color = wine_palette[5],
                  #vjust = 0,
                  segment.size = 0,
                  set.seed(13)) +
  xlim(-1., 1.) +
  ylim(-1., 1.) +
  coord_fixed() # fix aspect ratio to 1:1