Assignment 09

Author

Brady Guay

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)
library(ggplot2)

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 Sizes",
    x = "Carat",
    y = "Count"
  ) +
  theme_minimal()

Narrative: The distribution of diamond carat sizes is skewed right. In this case, that shows that most diamonds are small in carat weight. This histogram also shows that as carat weight increases the count of diamonds decreases very quickly.

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 Diamond Carat Sizes",
    x = "Carat",
    y = "Count"
  ) +
  theme_minimal()

Narrative: The distribution is still skewed right, but significantly less so. This histogram is more symmetrical and is closer to normal distribution while still showing that the higher the carat weight the lower the count.

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)

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

#linear regression model
lm_all_workflow <- workflow() |>
  add_model(lm_spec) |>
  add_recipe(lm_all_recipe)
#lasso model
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

#linear regression model
lm_all_fit <- lm_all_workflow |>
  fit(data = train_data)
#lasso model
lasso_all_fit <- lasso_all_workflow |>
  fit(data = train_data)

Exercise 8

Make predictions into two new tibbles: lm_all_predictions and lasso_all_predictions

#linear predictions
lm_all_predictions <- predict(lm_all_fit, new_data = test_data)|>
  bind_cols(test_data)
#lasso predictions
lasso_all_predictions <- predict(lasso_all_fit, new_data = test_data) |>
  bind_cols(test_data)

Exercise 9

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

#linear model
lm_rsme <- lm_all_predictions |>
  rmse(truth = carat, estimate = .pred)
#lasso model
lasso_rsme <- lasso_all_predictions |>
  rmse(truth = carat, estimate = .pred)
lm_rsme
# A tibble: 1 × 3
  .metric .estimator .estimate
  <chr>   <chr>          <dbl>
1 rmse    standard      0.0744
lasso_rsme
# A tibble: 1 × 3
  .metric .estimator .estimate
  <chr>   <chr>          <dbl>
1 rmse    standard      0.0812

Narrative: The linear model performed better than the lasso model since it had a lower RMSE. This is likely because of the extra regularization that was already written into the assignment. The lasso model tried to simplify an already clean data set which was likely why the linear model (not regularized) performed better.

Submission

To submit your assignment:

  • Change the author name to your name in the YAML portion at the top of this document
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  • Submit the link to your Rpubs document in the Brightspace comments section for this assignment.
  • 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.