Assignment 09

Author

Annalise

Open the assign09.qmd file and complete the exercises.

We will be working the the diamonds dataset and tidymodels to predict the carat of a diamond based on other variables.

The Grading Rubric is available at the end of this document.

Exercises

We will start by loading our required packages.

library(tidymodels)
library(glmnet)

Exercise 1

Create a histogram using geom_histogram(binwidth = 0.1), showing the distribution of carat in the diamonds dataset. Set the fill to “blue” and the color to “black”. In the narrative below describe what the distribution looks like.

ggplot(diamonds, aes(x = carat)) +
  geom_histogram(binwidth = 0.1, fill = "blue", color = "black") +
  labs(title = "Distribution of Diamond Carat", x = "Carat", y = "Count")

The distribution is right skewed with most diamonds under 1 carat.

Exercise 2

Repeat the histogram, but this time plot sqrt(carat) instead of carat. Describe if and how the distribution changed.

ggplot(diamonds, aes(x = sqrt(carat))) +
  geom_histogram(binwidth = 0.1, fill = "blue", color = "black") +
  labs(title = "Distribution of sqrt(Carat)", x = "sqrt(Carat)", y = "Count")

The square root reduced the skew in he distribution.

Exercise 3

Below set.seed(), split the data into two datasets: train_data will contain 80% of the data using stratified sampling on carat, test_data will contain the remaining 20% of the data.

# set a seed for reproducibility
set.seed(1234)

data_split <- initial_split(diamonds, prop = 0.8, strata = carat)
train_data <- training(data_split)
test_data <- testing(data_split)

Exercise 4

Exercise 4 is already completed for you. It creates a recipe called lm_all_recipe that uses carat as the target variable and all other variables as predictors. It creates dummy variables for all nominal predictors so we can use the recipe for reguralized regression.

# recipe using all predictors
lm_all_recipe <- recipe(carat ~ ., data = train_data) |> 
  step_dummy(all_nominal_predictors())

Exercise 5

Below is a model specified for reguralized regression model called lasso_spec. Add a second specification called lm_spec for just plain old linear regression using the “lm” engine.

# Define the lasso model specification
lasso_spec <- linear_reg(penalty = 0.01, mixture = 1) |> 
  set_engine("glmnet")

# Define the linear regression model specification.
lm_spec <- linear_reg() |> 
  set_engine("lm")

Exercise 6

Create two workflows. lm_all_workflow should use the lm_spec model specification and lm_all_recipe. lasso_all_workflow should use the lasso_spec model and lm_all_recipe.

lm_all_workflow <- workflow() |> 
  add_model(lm_spec) |> 
  add_recipe(lm_all_recipe)

lasso_all_workflow <- workflow() |> 
  add_model(lasso_spec) |> 
  add_recipe(lm_all_recipe)

Exercise 7

Fit two models. lm_all_fit should use the lm_all_workflow, and lasso_all_fit should use the lasso_all_workflow

lm_all_fit <- fit(lm_all_workflow, data = train_data)
lasso_all_fit <- fit(lasso_all_workflow, data = train_data)

Exercise 8

Make predictions into two new tibbles: lm_all_predictions and lasso_all_predictions

lm_all_predictions <- predict(lm_all_fit, test_data) |> 
  bind_cols(test_data |> select(carat))

lasso_all_predictions <- predict(lasso_all_fit, test_data) |> 
  bind_cols(test_data |> select(carat))

Exercise 9

Compute and display the rmse for each model. Discuss which one performed better and why in the narrative below.

lm_rmse <- lm_all_predictions |> 
  metrics(truth = carat, estimate = .pred) |> 
  filter(.metric == "rmse")

lasso_rmse <- lasso_all_predictions |> 
  metrics(truth = carat, estimate = .pred) |> 
  filter(.metric == "rmse")

bind_rows(
  lm_rmse |> mutate(model = "Linear Regression"),
  lasso_rmse |> mutate(model = "Lasso Regression")
)
# A tibble: 2 × 4
  .metric .estimator .estimate model            
  <chr>   <chr>          <dbl> <chr>            
1 rmse    standard      0.0744 Linear Regression
2 rmse    standard      0.0812 Lasso Regression

Both models performed similarly, but the linear regression model performed slightly better. This suggests that the simple linear model made more accurate predictions.

Submission

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  • Change the author name to your name in the YAML portion at the top of this document
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  • Click on the “Add a File” button and upload your .qmd file for this assignment to Brightspace.

Grading Rubric

Item
(percent overall)		 100% - flawless 67% - minor issues 33% - moderate issues 0% - major issues or not attempted
Document formatting: correctly implemented instructions
(9%)
Exercises - 9% each
(81% )
Submitted properly to Brightspace
(10%)		 NA NA You must submit according to instructions to receive any credit for this portion.