Module 9 Lab

library(tidymodels)
library(tidyverse)

Part 1: Simple linear regression

1. Import data set

boston <- readr::read_csv('data/boston.csv')

2. Split the data

set.seed(123)
split <- initial_split(boston, prop = .7, strata = cmedv)
train <- training(split)
test <- testing(split)

3.Assess the correlation between cmedv and predictor variables

cor(train) %>%
  as_tibble(rownames = 'predictor_vars') %>%
  select(predictor_vars, cmedv) %>%
  arrange(desc(cmedv))

predictor variable with the strongest positive correlation is rm, and the strongest negative correlation is lstat.

4. Plot relationship between cmedv and rm

train %>%
  ggplot(aes(x = rm, y = cmedv)) +
  geom_point(alpha = .2) +
  geom_smooth(method = "lm")

accurate capture of relationship

5. Train a simple regression model with rm

model_rm <- linear_reg() %>%
  fit(cmedv ~ rm, data = train)
tidy(model_rm)

our intercept value is -35.429 this means that if a house has 0 rooms, we predict that its median sale price would be -35,429. Our coefficient for rm is 9.217, this means that if our number of rooms increase by 1, the predicted cmedv increases by 9,217. Both of our values are statistically different than 0, as their p values are both less than 0.05.

confint(model_rm$fit)

                 2.5 %    97.5 %
(Intercept) -41.546106 -29.31285
rm            8.250909  10.18311

The confidence interval also confirms that these are statistically different than 0.

6. compute the generalization RMSE for the model and interpret the results.

model_rm %>%
  predict(test) %>%
  bind_cols(test %>% select(cmedv)) %>%
  rmse(truth = cmedv, estimate = .pred)

The generalization RMSE for this model is 6.83, This means that, on average, our model is off by 6,831.41.

7. Create a multiple linear regression model using all variables

model_all <- linear_reg() %>%
  fit(cmedv ~ ., data = train)

tidy(model_all)

8. Compute RMSE

model_all %>%
  predict(test) %>% 
  bind_cols(test %>% select(cmedv)) %>%
  rmse(truth = cmedv, estimate = .pred)

This RMSE is Better.

9.

top_predictors <- tidy(model_all) %>%
  arrange(desc(abs(statistic)))

top_predictors

rm, lstat, ptratio, dis, b