Skip to ContentGo to accessibility page

Critical Thinking

1 .
Discuss how different ratios of training versus testing data can affect the model in terms of underfitting and overfitting. How does the testing set provide a means to identify issues with underfitting and overfitting?
2 .
A university admissions office would like to use a multiple linear regression model with students’ high school GPA and scores on both the SAT and ACT (standardized tests) as input variables to predict whether the student would eventually graduate university if admitted. Assuming the following statements are all accurate, which statement would be a reason not to use multiple linear regression?
  1. Students' SAT and ACT scores are often highly correlated with one another.
  2. GPA scores are measured on a different scale than either SAT or ACT scores.
  3. Scores of 0 are impossible to obtain on the SAT or ACT.
  4. Students can have high GPA but sometimes not do well on standardized tests like the SAT or ACT.
3 .
Using the data about words found in news articles from Example 6.12, classify an article that contains all three words, today, disaster, and police, as real or fake.
Citation/Attribution
Reuse and redistribution of this content in digital or print format:
  • This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's prior written permission.
  • This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License, which means that you can reuse and modify the material only for noncommercial purposes, must attribute OpenStax, and must distribute any derivative works under the same license.
  • Any commercial printing of this textbook, including using a local or custom printer, must be approved by OpenStax, and proper citation provided.
  • OpenStax-copyrighted images, activities, assessments, and similar components of this book are subject to the same licensing – CC-BY-NC-SA. They can be used for noncommercial purposes with attribution. Commercial use requires permission.
  • Permission requests: Anyone who intends to incorporate this content (including text, images, and other components) into large language models, use it in AI offerings, use it commercially (including in print), and/or has questions about another use case is welcome to complete our reuse request form.
Attribution information
  • If you are redistributing all or part of this book in a noncommercial print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/principles-data-science/pages/1-introduction

  • If you are redistributing all or part of this book in a noncommercial digital format, then for every page that includes OpenStax content, you must license the derivative work under the same CC-BY-NC-SA license as the original, and include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/principles-data-science/pages/1-introduction

Citation information

The information below includes the information needed to generate citations in most major styles (APA, MLA, etc.); you must reformat and organize the information as needed to fit the requirements of the style. Use the information below to generate a citation. We recommend using a citation tool such as this one.

© Apr 23, 2026 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo, and Rice University name, and Rice University logo trademarks, or wordmarks are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.