Course Notes: Introduction to Regression in R

# Import any packages you want to use here

# Add your code snippets here
# Add a linear trend line without a confidence ribbon
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)

# Using taiwan_real_estate, plot price_twd_msq
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(~house_age_years)

summary_stats <- 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))

# See the result
summary_stats

# Update the model formula to remove the intercept
mdl_price_vs_age_no_intercept <- lm(
  price_twd_msq ~ house_age_years + 0, 
  data = taiwan_real_estate
)

# See the result
mdl_price_vs_age_no_intercept

# Create a tibble with n_convenience column from zero to ten
explanatory_data <- tibble(
  n_convenience = 0:10
)

# Edit this, so predictions are stored in prediction_data
prediction_data <- explanatory_data %>%
  mutate( price_twd_msq = predict(mdl_price_vs_conv, explanatory_data))
# See the result
prediction_data

# Add to the plot
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(
    data = prediction_data,
    color = "yellow"
  )

# Get the coefficients of mdl_price_vs_conv
coeffs <- coefficients(mdl_price_vs_conv)

# Get the intercept
intercept <- coeffs[1]

# Get the slope
slope <- coeffs[2]

explanatory_data %>% 
  mutate(
    # Manually calculate the predictions
    price_twd_msq = intercept + slope*n_convenience
  )

# Compare to the results from predict()
predict(mdl_price_vs_conv, explanatory_data)

# Using sp500_yearly_returns, plot return_2019 vs. return_2018
ggplot(sp500_yearly_returns, aes(return_2018, return_2019)) +
  # Make it a scatter plot
  geom_point() +
  # Add a line at y = x, colored green, size 1
  geom_abline(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()

# From previous steps
mdl_price_vs_dist <- lm(
  price_twd_msq ~ sqrt(dist_to_mrt_m), 
  data = taiwan_real_estate
)
explanatory_data <- tibble(
  dist_to_mrt_m = seq(0, 80, 10) ^ 2
)
prediction_data <- explanatory_data %>% 
  mutate(
    price_twd_msq = predict(mdl_price_vs_dist, explanatory_data)
  )

ggplot(taiwan_real_estate, aes(sqrt(dist_to_mrt_m), price_twd_msq)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) +
  # Add points from prediction_data, colored green, size 5
  geom_point(data = prediction_data,
  color = "green", size = 5)              

# From previous steps
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")

# Get coeff of determination for mdl_click_vs_impression_orig
mdl_click_vs_impression_orig %>% 
  # Get the model-level details
  glance() %>% 
  # Pull out r.squared
  pull(r.squared)

# Do the same for the transformed model
mdl_click_vs_impression_trans %>%
  glance() %>%
    pull(r.squared)

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

mdl_price_vs_dist %>% 
  # Augment the model
  augment() %>% 
  # Arrange rows by descending leverage
  arrange(desc(.hat)) %>% 
  # Get the head of the dataset
  head()

mdl_price_vs_dist %>% 
  # Augment the model
  augment() %>% 
  # Arrange rows by descending Cook's distance
  arrange(desc(.cooksd)) %>% 
  # Get the head of the dataset
  head()
  

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

# Using churn, plot time_since_last_purchase
ggplot(churn, aes(time_since_last_purchase)) +
  # as a histogram with binwidth 0.25
  geom_histogram(binwidth = 0.25) +
  # faceted in a grid with has_churned on each row
  facet_grid(has_churned~.)

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))

# Update the data frame
prediction_data <- explanatory_data %>% 
  mutate(   
    has_churned = predict(mdl_churn_vs_relationship, explanatory_data, type = "response"),
    most_likely_outcome = round(has_churned)
  )

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