Global CLI Project
Charles Miele
2022-01-19
Data Collection
# Load data
cli <- read.csv('cost-of-living_v2.csv')
# Remove any columns with NA values
cli <- cli[complete.cases(cli), ]
dim(cli)## [1] 1278 58varData <- setNames(stack(sapply(cli, class))[2:1], c('variable', 'class'))
descriptions <- read.csv('Descriptions.csv')
descriptions <- descriptions[, c('Column', 'Description')]
gt::gt(descriptions)| Column | Description |
|---|---|
| city | Name of the city |
| country | Name of the country |
| x1 | Meal, Inexpensive Restaurant (USD) |
| x2 | Meal for 2 People, Mid-range Restaurant, Three-course (USD) |
| x3 | McMeal at McDonalds (or Equivalent Combo Meal) (USD) |
| x4 | Domestic Beer (0.5 liter draught, in restaurants) (USD) |
| x5 | Imported Beer (0.33 liter bottle, in restaurants) (USD) |
| x6 | Cappuccino (regular, in restaurants) (USD) |
| x7 | Coke/Pepsi (0.33 liter bottle, in restaurants) (USD) |
| x8 | Water (0.33 liter bottle, in restaurants) (USD) |
| x9 | Milk (regular), (1 liter) (USD) |
| x10 | Loaf of Fresh White Bread (500g) (USD) |
| x11 | Rice (white), (1kg) (USD) |
| x12 | Eggs (regular) (12) (USD) |
| x13 | Local Cheese (1kg) (USD) |
| x14 | Chicken Fillets (1kg) (USD) |
| x15 | Beef Round (1kg) (or Equivalent Back Leg Red Meat) (USD) |
| x16 | Apples (1kg) (USD) |
| x17 | Banana (1kg) (USD) |
| x18 | Oranges (1kg) (USD) |
| x19 | Tomato (1kg) (USD) |
| x20 | Potato (1kg) (USD) |
| x21 | Onion (1kg) (USD) |
| x22 | Lettuce (1 head) (USD) |
| x23 | Water (1.5 liter bottle, at the market) (USD) |
| x24 | Bottle of Wine (Mid-Range, at the market) (USD) |
| x25 | Domestic Beer (0.5 liter bottle, at the market) (USD) |
| x26 | Imported Beer (0.33 liter bottle, at the market) (USD) |
| x27 | Cigarettes 20 Pack (Marlboro) (USD) |
| x28 | One-way Ticket (Local Transport) (USD) |
| x29 | Monthly Pass (Regular Price) (USD) |
| x30 | Taxi Start (Normal Tariff) (USD) |
| x31 | Taxi 1km (Normal Tariff) (USD) |
| x32 | Taxi 1hour Waiting (Normal Tariff) (USD) |
| x33 | Gasoline (1 liter) (USD) |
| x34 | Volkswagen Golf 1.4 90 KW Trendline (Or Equivalent New Car) (USD) |
| x35 | Toyota Corolla Sedan 1.6l 97kW Comfort (Or Equivalent New Car) (USD) |
| x36 | Basic (Electricity, Heating, Cooling, Water, Garbage) for 85m2 Apartment (USD) |
| x37 | 1 min. of Prepaid Mobile Tariff Local (No Discounts or Plans) (USD) |
| x38 | Internet (60 Mbps or More, Unlimited Data, Cable/ADSL) (USD) |
| x39 | Fitness Club, Monthly Fee for 1 Adult (USD) |
| x40 | Tennis Court Rent (1 Hour on Weekend) (USD) |
| x41 | Cinema, International Release, 1 Seat (USD) |
| x42 | Preschool (or Kindergarten), Full Day, Private, Monthly for 1 Child (USD) |
| x43 | International Primary School, Yearly for 1 Child (USD) |
| x44 | 1 Pair of Jeans (Levis 501 Or Similar) (USD) |
| x45 | 1 Summer Dress in a Chain Store (Zara, H&M, …) (USD) |
| x46 | 1 Pair of Nike Running Shoes (Mid-Range) (USD) |
| x47 | 1 Pair of Men Leather Business Shoes (USD) |
| x48 | Apartment (1 bedroom) in City Centre (USD) |
| x49 | Apartment (1 bedroom) Outside of Centre (USD) |
| x50 | Apartment (3 bedrooms) in City Centre (USD) |
| x51 | Apartment (3 bedrooms) Outside of Centre (USD) |
| x52 | Price per Square Meter to Buy Apartment in City Centre (USD) |
| x53 | Price per Square Meter to Buy Apartment Outside of Centre (USD) |
| x54 | Average Monthly Net Salary (After Tax) (USD) |
| x55 | Mortgage Interest Rate in Percentages (%), Yearly, for 20 Years Fixed-Rate |
| data_quality | 0 if Numbeo considers that more contributors are needed to increase data quality, else 1 |
Principal-Component Analysis
Setup
# Function for plotting on GG plot. Takes in data and PCs(int) to plot
pca.gg <- function(d, n1, n2) {
# Variation
p.var <- d$sdev^2
p.var.per <- round(p.var / sum(p.var)*100, 1)
ggD <- data.frame(Sample=rownames(d$x), X=d$x[,n1], Y=d$x[,n2])
ggplot(data=ggD, aes(x=X, y=Y, label=Sample)) +
geom_text() +
xlab(paste("PC", n1, p.var.per[n1], "%", sep = " ")) +
ylab(paste("PC", n2, p.var.per[n2], "%", sep=" ")) +
ggtitle("PCA Graph")
}
# Loading scores
load_scores <- function(d, n, onCols) {
loading_scores <- d$rotation[, n]
col_scores <- abs(loading_scores)
c_ranked <- sort(col_scores, decreasing = TRUE)
test <- data.frame(c_ranked[1:10])
colnames(test) <- "Loading Score"
test$Column <- row.names(test)
if (onCols) {
test <- left_join(test, descriptions, by="Column")
return(gt::gt(test))
} else {
return(gt::gt(test))
}
}
# Scree plot
s_plot <- function(d){
pca.var <- d$sdev^2
pca.var.per <- round(pca.var/sum(pca.var)*100, 1)
barplot(pca.var.per, main="Screeplot", xlab="Principal Component",
ylab="% variation")
}Which cities are most similar?
PCA.data <- cli
row.names(PCA.data) <- paste(PCA.data$city, PCA.data$country, sep = ", ")
PCA.data <- subset(PCA.data, select=-c(city, country))
PCA.1 <- prcomp(PCA.data, scale=TRUE, tol = 0.1)
s_plot(PCA.1)
pca.gg(PCA.1, 1, 2)
# Which variables were most influential on where the companies were plotted for PC1 (x-axis?)
load_scores(PCA.1, 1, TRUE)| Loading Score | Column | Description |
|---|---|---|
| 0.1787700 | x41 | Cinema, International Release, 1 Seat (USD) |
| 0.1778548 | x2 | Meal for 2 People, Mid-range Restaurant, Three-course (USD) |
| 0.1753416 | x54 | Average Monthly Net Salary (After Tax) (USD) |
| 0.1730512 | x1 | Meal, Inexpensive Restaurant (USD) |
| 0.1700596 | x14 | Chicken Fillets (1kg) (USD) |
| 0.1684964 | x12 | Eggs (regular) (12) (USD) |
| 0.1661474 | x6 | Cappuccino (regular, in restaurants) (USD) |
| 0.1656012 | x7 | Coke/Pepsi (0.33 liter bottle, in restaurants) (USD) |
| 0.1645299 | x3 | McMeal at McDonalds (or Equivalent Combo Meal) (USD) |
| 0.1635456 | x4 | Domestic Beer (0.5 liter draught, in restaurants) (USD) |
# Which variables were most influential on where the companies were plotted for PC2 (y-axis?)
load_scores(PCA.1, 2, TRUE)| Loading Score | Column | Description |
|---|---|---|
| 0.3234178 | x33 | Gasoline (1 liter) (USD) |
| 0.3014550 | x44 | 1 Pair of Jeans (Levis 501 Or Similar) (USD) |
| 0.2508365 | x16 | Apples (1kg) (USD) |
| 0.2166533 | x21 | Onion (1kg) (USD) |
| 0.2107541 | x24 | Bottle of Wine (Mid-Range, at the market) (USD) |
| 0.2101449 | x20 | Potato (1kg) (USD) |
| 0.2009413 | x18 | Oranges (1kg) (USD) |
| 0.1853395 | x7 | Coke/Pepsi (0.33 liter bottle, in restaurants) (USD) |
| 0.1845426 | x25 | Domestic Beer (0.5 liter bottle, at the market) (USD) |
| 0.1807534 | x26 | Imported Beer (0.33 liter bottle, at the market) (USD) |
load_scores(PCA.1, 3, TRUE)| Loading Score | Column | Description |
|---|---|---|
| 0.4072216 | x46 | 1 Pair of Nike Running Shoes (Mid-Range) (USD) |
| 0.3773023 | x35 | Toyota Corolla Sedan 1.6l 97kW Comfort (Or Equivalent New Car) (USD) |
| 0.3521002 | x34 | Volkswagen Golf 1.4 90 KW Trendline (Or Equivalent New Car) (USD) |
| 0.3183403 | x45 | 1 Summer Dress in a Chain Store (Zara, H&M, …) (USD) |
| 0.2455854 | x9 | Milk (regular), (1 liter) (USD) |
| 0.2289242 | x47 | 1 Pair of Men Leather Business Shoes (USD) |
| 0.2197251 | x17 | Banana (1kg) (USD) |
| 0.1804443 | x55 | Mortgage Interest Rate in Percentages (%), Yearly, for 20 Years Fixed-Rate |
| 0.1575918 | x28 | One-way Ticket (Local Transport) (USD) |
| 0.1553375 | x44 | 1 Pair of Jeans (Levis 501 Or Similar) (USD) |
Which metrics are most similar?
PCA.data2 <- t(data.matrix(PCA.data))
PCA.data2 <- t(apply(PCA.data2, 1, function(x)(x-min(x))/(max(x)-min(x))))
PCA.2 <- prcomp(PCA.data2)
s_plot(PCA.2)
# Graph
pca.gg(PCA.2, 1, 2)
# What companies were most influential on where the variables were plotted for PC1?
load_scores(PCA.2, 1, FALSE)| Loading Score | Column |
|---|---|
| 0.05501724 | Basel, Switzerland |
| 0.05468856 | Zurich, Switzerland |
| 0.05338798 | Bern, Switzerland |
| 0.05312936 | Lucerne, Switzerland |
| 0.05308558 | Lausanne, Switzerland |
| 0.05306766 | Winterthur, Switzerland |
| 0.05239151 | Zug, Switzerland |
| 0.05129129 | Geneva, Switzerland |
| 0.05064648 | Vejle, Denmark |
| 0.05026382 | Odense, Denmark |
# PC2?
load_scores(PCA.2, 2, FALSE)| Loading Score | Column |
|---|---|
| 0.09309229 | Baden, Switzerland |
| 0.09103455 | Schaffhausen, Switzerland |
| 0.08035352 | Vaduz, Liechtenstein |
| 0.07368335 | Drammen, Norway |
| 0.06942890 | Skien, Norway |
| 0.06881351 | Alesund, Norway |
| 0.06415414 | Santa Monica, United States |
| 0.06397552 | Esbjerg, Denmark |
| 0.06333390 | Svendborg, Denmark |
| 0.06254870 | Roskilde, Denmark |
Lasso Regression
y <- cli$x54
x <- cli %>% select(-c(x54, city, country, data_quality))
x <- data.matrix(x)
# Find lambda value
cross_val_model <- cv.glmnet(x, y, alpha = 1)
best_lamda <- cross_val_model$lambda.min
best_lamda## [1] 7.639528# Produce plot of test MSE by lambda value
plot(cross_val_model)
best_model <- glmnet(x, y, alpha = 1, lamda = best_lamda)
y_pred = predict(best_model, s = best_lamda, newx = x)
# Find SST and SSE
sst <- sum((y- mean(y))^2)
sse <- sum((y_pred - y)^2)
#find R-Squared
rsq <- 1 - sse/sst
# Best model explains {rsq * 100}% of the variation in the response values of the training data
rsq## [1] 0.8886567# Which metrics are most important?
# Extracts non-zero coefficients
predictors <- coef(best_model, s = best_lamda)
predictors <- data.matrix(predictors)
predictors <- data.frame(predictors)
predictors$Column <- row.names(predictors)
predictors <- left_join(predictors, descriptions, by="Column")
predictors <- filter(predictors, s1 > 0)
gt::gt(predictors)| s1 | Column | Description |
|---|---|---|
| 1.393020e+01 | (Intercept) | NA |
| 1.264219e+01 | x1 | Meal, Inexpensive Restaurant (USD) |
| 2.156619e+01 | x4 | Domestic Beer (0.5 liter draught, in restaurants) (USD) |
| 5.797697e+01 | x5 | Imported Beer (0.33 liter bottle, in restaurants) (USD) |
| 1.396463e+02 | x6 | Cappuccino (regular, in restaurants) (USD) |
| 3.864086e+01 | x7 | Coke/Pepsi (0.33 liter bottle, in restaurants) (USD) |
| 1.944209e+02 | x8 | Water (0.33 liter bottle, in restaurants) (USD) |
| 1.708005e+02 | x10 | Loaf of Fresh White Bread (500g) (USD) |
| 7.067897e+01 | x11 | Rice (white), (1kg) (USD) |
| 7.919745e+00 | x15 | Beef Round (1kg) (or Equivalent Back Leg Red Meat) (USD) |
| 6.546160e+01 | x18 | Oranges (1kg) (USD) |
| 9.387618e+01 | x22 | Lettuce (1 head) (USD) |
| 5.007859e+01 | x25 | Domestic Beer (0.5 liter bottle, at the market) (USD) |
| 1.407277e+01 | x27 | Cigarettes 20 Pack (Marlboro) (USD) |
| 1.275983e+02 | x28 | One-way Ticket (Local Transport) (USD) |
| 9.329867e-01 | x29 | Monthly Pass (Regular Price) (USD) |
| 2.866288e+00 | x31 | Taxi 1km (Normal Tariff) (USD) |
| 3.346334e+00 | x32 | Taxi 1hour Waiting (Normal Tariff) (USD) |
| 1.052438e+00 | x39 | Fitness Club, Monthly Fee for 1 Adult (USD) |
| 5.052342e+01 | x41 | Cinema, International Release, 1 Seat (USD) |
| 4.918712e-01 | x42 | Preschool (or Kindergarten), Full Day, Private, Monthly for 1 Child (USD) |
| 7.997152e-03 | x43 | International Primary School, Yearly for 1 Child (USD) |
| 6.299211e-01 | x47 | 1 Pair of Men Leather Business Shoes (USD) |
| 2.697215e-01 | x49 | Apartment (1 bedroom) Outside of Centre (USD) |
| 4.802380e-02 | x51 | Apartment (3 bedrooms) Outside of Centre (USD) |