Introduction to Regression in R Cheat Sheet by patelivan

# Assume you have a real estate dataset and want to build a model predicting prices using n_convenience stores nearby within walking distance.

# Visualize the two variables. What is the relationship?
ggplot(taiwan_real_estate, aes(n_convenience, price_twd_msq)) +
  geom_point(alpha = 0.5) +
  geom_smooth(method='lm', se=FALSE)

# Run a linear regression of price_twd_msq vs. n_convenience
lm(price_twd_msq ~ n_convenience, data = taiwan_real_estate)

# Visualize prices v age_category using a histogram. What do you see?
ggplot(taiwan_real_estate, aes(price_twd_msq)) +
  # Make it a histogram with 10 bins
  geom_histogram(bins=10) +
  # Facet the plot so each house age group gets its own panel
  facet_wrap(vars(house_age_years))

# calculate means by each age category
taiwan_real_estate %>% 
  # Group by house age
  group_by(house_age_years) %>% 
  # Summarize to calculate the mean house price/area
  summarize(mean_by_group = mean(price_twd_msq))

# Run a linear regression of price_twd_msq vs. house_age_years
mdl_price_vs_age <- lm(data=taiwan_real_estate, price_twd_msq~house_age_years) #add +0 after house_age_years to get each category's mean.
 
# See the result
mdl_price_vs_age

# Model prices and n_convenience
mdl_price_vs_conv <- lm(formula = price_twd_msq ~ n_convenience, data = taiwan_real_estate)

# Create a tibble of integer values from 0 to 10.
explanatory_data <- tibble(n_convenience = 0:10)

# Make predictions and store them in prediction_data
prediction_data <- explanatory_data %>% 
  mutate(price_twd_msq = predict(mdl_price_vs_conv, explanatory_data))

# Plot the predictions along with all points
ggplot(taiwan_real_estate, aes(n_convenience, price_twd_msq)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) +
  # Add a point layer of prediction data, colored yellow
  geom_point(color='yellow', data=prediction_data)

# -------------- Regression to the mean example-------------

# Suppose you have data on annual returns from investing in companies in the SP500 index and you're interested in knowing if the invested performance stays the same from 2018 to 2019. 

# Using sp500_yearly_returns, plot return_2019 vs. return_2018
ggplot(data=sp500_yearly_returns, aes(x=return_2018, y=return_2019)) +
  # Make it a scatter plot
  geom_point() +
  # Add a line at y = x, colored green, size 1
  geom_abline(slope=1, color='green', size=1) +
  # Add a linear regression trend line, no std. error ribbon
  geom_smooth(method='lm', se=FALSE) +
  # Fix the coordinate ratio
  coord_fixed()

# Transforming variables and back-transforming the response---------------

# Assume you've facebook advertising data; how many people see the adds and how many people click on them.

mdl_click_vs_impression <- lm(
  I(n_clicks^0.25) ~ I(n_impressions^0.25),
  data = ad_conversion
)
explanatory_data <- tibble(
  n_impressions = seq(0, 3e6, 5e5)
)
prediction_data <- explanatory_data %>% 
  mutate(
    n_clicks_025 = predict(mdl_click_vs_impression, explanatory_data),
    n_clicks = n_clicks_025 ^ 4
  )

ggplot(ad_conversion, aes(n_impressions  0.25, n_clicks  0.25)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) +
  # Add points from prediction_data, colored green
  geom_point(data=prediction_data, color='green')

# Plot three diagnostics for mdl_price_vs_conv
library(ggplot2)
library(ggfortify)
autoplot(mdl_price_vs_conv, which=1:3, nrow=3, ncol=1)

# Plot the three outlier diagnostics for mdl_price_vs_conv
autoplot(mdl_price_vs_dist, which=4:6, nrow=3, ncol=1)

plt_churn_vs_relationship ggplot(churn, aes(time_since_first_purchase, has_churned)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE, color = "red") +
  # Add a glm trend line, no std error ribbon, binomial family
  geom_smooth(method='glm', se=FALSE, method.args=list(family=binomial))

# Fit a logistic regression of churn vs. 
# length of relationship using the churn dataset
mdl_churn_vs_relationship <- glm(has_churned ~ time_since_first_purchase, data=churn, family='binomial')

# See the result
mdl_churn_vs_relationship

# Make predictions. "response" type returns probabilities of churning. 
prediction_data <- explanatory_data %>% 
  mutate(   
    has_churned = predict(mdl_churn_vs_relationship, explanatory_data, type = "response"),
    most_likely_outcome = round(has_churned) # easier to interpret. 
  )

# Update the plot
plt_churn_vs_relationship +
  # Add most likely outcome points from prediction_data, colored yellow, size 2
  geom_point(data=prediction_data, size=2, color='yellow', aes(y=most_likely_outcome))

# Odds ratio------------------------------------------

# From previous step
prediction_data <- explanatory_data %>% 
  mutate(   
    has_churned = predict(mdl_churn_vs_relationship, explanatory_data, type = "response"),
    odds_ratio = has_churned / (1 - has_churned), 
    log_odds_ratio = log(odds_ratio)
  )

# Using prediction_data, plot odds_ratio vs. time_since_first_purchase
ggplot(data=prediction_data, aes(x=time_since_first_purchase, y=odds_ratio)) +
  # Make it a line plot
  geom_line() +
  # Add a dotted horizontal line at y = 1. Indicates where churning is just as likely as not churning. 
  geom_hline(yintercept=1, linetype='dotted')

# Get the confusion matrix.
library(yardstick)

# Get the actual and most likely responses from the dataset
actual_response <- churn$has_churned
predicted_response <- round(fitted(mdl_churn_vs_relationship))

# Create a table of counts
outcomes <- table(predicted_response, actual_response)

# Convert outcomes to a yardstick confusion matrix
confusion <- conf_mat(outcomes)

# Get performance metrics for the confusion matrix
summary(confusion, event_level = 'second')