Lab 07: Review

Due date

This lab is not due for grade.

Conceptual Practice

Exercise

Review ridge regression notes, GLS notes, and logistic regression notes.

Summarize the main ideas, including (1) when the idea is appropriate, (2) the mathematical formulation, (3) how to fit the model to data.

Additional applied practice

You will use the following packages in today’s lab. Add other packages as needed.

library(tidyverse)
library(tidymodels)
library(knitr)
library(pROC)

Data

rice <- readr::read_csv("https://sta221-fa25.github.io/labs/data/rice.csv")

The data in this lab contains measures describing the shape and structure of two rice varieties - Cammeo and Osmancik. To curate the data set, researchers used images from over 3,000 grains a rice in these two varieties. They then used automated methods to process the image data and extract 7 morphological features (features related to the structure) from each image. The data were originally presented and analyzed in Cinar and Koklu (2019) and was obtained from the UCI Machine Learning Repository.

This analysis will focus on the following variables:

  • Class: Cammeo or Osmancik

  • Area: Size of the rice grain measured in pixels

  • Eccentricity: A measure of how round the ellipse is, i.e., how close the shape of the grain is to a circle.

Click here for the full data dictionary.

rice <- read_csv("data/rice.csv")

Exercises

Goal: The goal of the analysis is to use Area and Eccentricity to identify grains from the Cammeo variety versus those from the Osmancik variety.

Exercise 1

We’ll begin by exploring the data. Create a scatterplot of Area versus Eccentricity with the color and shape of the points by Class.

Exercise 2

Based on the plot from the previous exercise, do you think the two types of rice can be distinguished based on Area and Eccentricity. Briefly explain.

Exercise 3

With this type of classification problem, it is common to test the performance of a logistic regression model by splitting the data into a training and a test set. This means that we will choose a random subset of the data to estimate the regression coefficient (training), and we will then test the predictions on the remaining observations (test).

  • Randomly select 75% of the rows of the data to create the training set rice_train . Use set.seed(221).

  • Put the remaining 25% of the observations in the testing set called rice_test.

Exercise 4

In a logistic regression model, the log-odds of the response being “1” (or a “success”) is given by \[\log\Big(\frac{\pi_i}{1-\pi_i}\Big) = \mathbf{x}_i^\mathsf{T} \boldsymbol{\beta}\]

In this analysis a “success” is the Class “Osmancik”.

  • What does each \(\pi_i\) represent in the context of this analysis?

  • How is the probability of the response variable being “1” calculated from the log-odds? Show the mathematical steps to go from the log-odds to the probability in your response.

Exercise 5

Use rice_train to fit the logistic regression model for the response variable Class on the predictors Area and Eccentricity .

  • Neatly display the output using 3 digits.
  • Does the intercept have any reasonable interpretation? If so, interpret the intercept. Otherwise explain why not.

Exercise 6

  • Interpret the coefficients on Area and Eccentricity in the context of the data in terms of the odds and comment on whether they are useful predictors of Class in the model.

Exercise 7

  • How would you expect the log-odds of the rice grain being of the Osmancik variety to change if the measures eccentricity changes from 0.85 to 0.9?

  • How would you expect the odds of the rice grain being of the Osmancik variety to change if the measures eccentricity changes from 0.85 to 0.9?

Exercise 8

Now let’s test our model on the test set. Use the predict() function to obtain the predicted probabilities of the rice being Osmancik for the observations in rice_test.

Exercise 9

With these estimated probabilities, we can now try to classify the rice in the test set. Choose a threshold for assigning a class to each observation based on the estimated probability. Briefly explain your reasoning for selecting the threshold, including any analysis used to make your decision.

Exercise 10

Compare the estimated class assignments you constructed with the actual classes. Comment on the result and thus the model performance.

References

Cinar, Ilkay, and Murat Koklu. 2019. “Classification of Rice Varieties Using Artificial Intelligence Methods.” International Journal of Intelligent Systems and Applications in Engineering 7 (3): 188–94.