Introductory Statistics in R Cheat Sheet by patelivan

# Using food consumption data to show how to use dplyr verbs and calculate a column's summary stats.

# Calculate Belgium's and USA's "typical" food consumption and its spread. 
food_consumption %>%
  filter(country %in% c('Belgium', 'USA')) %>%
  group_by(country) %>%
  summarize(mean_consumption = mean(consumption), 
            median_consumption = median(consumption)
            sd_consumption = sd(consumption))

# Make a histogram to compare the distribution of rice's carbon footprint. A great way to understand how skewed is the variable. 

food_consumption %>%
  # Filter for rice food category
  filter(food_category == "rice") %>%
  # Create histogram of co2_emission
  ggplot(aes(co2_emission)) +
    geom_histogram()

# Calculate the quartiles of co2 emission
quantile(food_consumption$co2_emission)

# If you want to split the data into n pieces. This is equivalent of splitting the data into n+1 quantiles. 
quantile(food_consumption$co2_emission, probs = seq(0, 1, 1/n). 

# Calculate variance and sd of co2_emission for each food_category
food_consumption %>% 
  group_by(food_category) %>% 
  summarize(var_co2 = var(co2_emission),
     sd_co2 = sd(co2_emission))

# Plot food_consumption with co2_emission on x-axis
ggplot(data = food_consumption, aes(co2_emission)) +
  # Create a histogram
  geom_histogram() +
  # Create a separate sub-graph for each food_category
  facet_wrap(~ food_category)

# Randomly select n observations with or without replacement
df %>% sample_n(# of obvs to sample, replace=TRUE or FALSE). 

# Say you assume that the probability distribution of a random variable (wait time for ex.) is uniform, where it takes a min value and a max value. Then, the probability that this variable will take on a value less than x can be calculated as:
punif(x, min, max)

# To generate 1000 wait times between min and max. 
runif(1000, min, max). 

# Binomial distribution -------------------------------------
rbinom(# of trials, # of coins, pr(success))

rbinom(1, 1, 0.5) # To simulate a single coin flip
rbinom(8, 1, 0.5) # Eight flips of one coin. 
rbinom(1, 8, 0.5) # 1 flip of eight coins. Gives us the total # of successes. 

dbinom(# of successes, # of trial, pr(success)).
dbinom(7, 10, 0.5) # The chances of getting 7 successes when you flip 10 coins. 
pbinom(7, 10, 0.5) # Chances of getting 7 successes or less when you flip 10 coins. 
pbinom(7, 10, 0.5, lower.tail = FALSE) # Chances of getting more than 7 successes when you flip 10 coins.

# Say you're a salesman and each deal you worked on was worth different amount of money. You tracked every deal you worked on, and the amount column follows a normal distribution with a mean of $5000 and sd of $2000.

# Pr(deal < $7500):
pnorm(7500, mean=5000, sd=2000)

# Pr(deal > 1000)
pnorm(1000, mean=5000, sd=2000, lower.tail=FALSE)

# Pr(deal between 3000 and 7000)
pnorm(7000, mean=5000, sd=2000) - pnorm(3000, mean=5000, sd=2000)

# How much money will 75% of your deals will be worth more than?
qnorm(0.75, mean=5000, sd=2000)

# Simulate 36 deals.
rnorm(36, mean=5000, sd=2000)


CLT in action----------------------------------------
# Say you also tracked how many users used the product you sold in num_users column. The CLT, in this case, says that the sampling distribution of the average number of users approaches the normal distribution as you take more samples. 

# Set seed to 104
set.seed(104)

# Sample 20 num_users from amir_deals and take mean
sample(amir_deals$num_users, size = 20, replace = TRUE) %>%
  mean()

# Repeat the above 100 times
sample_means <- replicate(100, sample(amir_deals$num_users, size = 20, replace = TRUE) %>% mean())

# Create data frame for plotting
samples <- data.frame(mean = sample_means)

# Histogram of sample means
samples %>% ggplot(aes(x=mean)) + geom_histogram(bins=10)

# Make a scatter plot to view a bi-variate relationship
df %>% ggplot(aes(x=col_1, y=col_2)) + geom_point() +
 geom_smooth(method='lm', se=FALSE (usually)). 

# Measure the correlation between two data frame columns
cor(df$col_1, df$col_2)

# Transform the x variable to log. 
df %>% mutate(log_x = log(col_x)) %>%  # Natural log by default
 ggplot(aes(x=log_x, y=col_y)) + geom_point() + 
 geom_smooth(method='lm', se=FALSE).