Module 3: Describing Bivariate Data & Regression

Module 3 includes a basic introduction to data relationships and regression.

Learning Objectives

These are the learning objectives for this portion of the class:

  1. Define “bivariate data”
  2. Define “scatter plot”
  3. Distinguish between a linear and a nonlinear relationship
  4. Identify positive and negative associations from a scatter plot
  5. Describe what Pearson’s correlation measures
  6. State the values that represent perfect linear relationships
  7. State the relationship between the correlation of Y with X and the correlation of X with Y
  8. State why \(\sum xy= 0\) when there is no relationship
  9. Calculate \(r\)
  10. State the variance sum law when X and Y are not assumed to be independent
  11. Compute the variance of the sum of two variables if the variance of each and their correlation is known
  12. Compute the variance of the difference between two variables if the variance of each and their correlation is known

These are the learning objectives for this portion of the class:

  1. Define linear regression
  2. Identify errors of prediction in a scatter plot with a regression line
  3. Compute the sum of squares Y
  4. Convert raw scores to deviation scores
  5. Compute predicted scores from a regression equation
  6. Partition sum of squares Y into sum of squares predicted and sum of squares error
  7. Define \(r^{2}\) in terms of sum of squares explained and sum of squares Y
  8. Make judgments about the size of the standard error of the estimate from a scatter plot
  9. Compute the standard error of the estimate based on errors of prediction
  10. Compute the standard error using Pearson’s correlation
  11. Estimate the standard error of the estimate based on a sample
  12. State the assumptions that inferential statistics in regression are based upon
  13. Identify heteroscedasticity in a scatter plot
  14. Compute the standard error of a slope
  15. Test a slope for significance
  16. Construct a confidence interval on a slope
  17. Test a correlation for significance
  18. State the regression equation
  19. Define “regression coefficient”
  20. Define “beta weight”
  21. Explain what R is and how it is related to r
  22. Explain why a regression weight is called a “partial slope”
  23. Explain why the sum of squares explained in a multiple regression model is usually less than the sum of the sums of squares in simple regression

Consumables

Each week there will be a number of items for you to consume, be it reading, watching, listening, or a combination thereof.

Consumable materials for module grouped by required or supplemental content.
Module Required? Text/Resource Chapter/Title Estimated time in minutes Type
3 Required Online Statistics Textbook Chapter 4: Describing Bivariate Data 120 Mathematics
3 Required Online Statistics Textbook Chapter 14: Prediction 180 Mathematics
3 Supplemental Introductory Statistics Regression 10 Mathematics
3 Supplemental thatRnerd How to make a scatter plot in R with Regression Line (ggplot2) 8 Programming
3 Supplemental Manga Guide to Statistics Chapter 6: Let's Look at the Relationship Between Two Variables 45 Mathematics

The total amount of time estimated on required texts and resources is 300 minutes, while you should expect to spend at most an additional 63 minutes on supplemental material.

The total amount of time estimated you should spend on these assignments depends on the amount of effort required, itself based on your previous experience with statistics, generally, and R, in particular. You can expect to spend somewhere between 94 and 248 minutes on this module beyond the readings. The estimated total number of words you’re likely to write in this module is 1,000.

Assignments for this module.
Module Due date Assignment type Short name Long name Points Effort (low) Effort (high) Expected word total
3 2024-02-02 Questions CH4M Chapter 4 questions 3 4 8 125
3 2024-02-02 Questions CH14M Chapter 14 questions 3 10 20 125
3 2024-02-02 Quiz CH4Q Chapter 4 quiz 15 20 40 0
3 2024-02-02 Quiz CH14Q Chapter 14 quiz 15 30 60 0
3 2024-02-02 Activity AB Activity B: Correlation 20 30 120 750

Module 3 Activity

This module’s activity covers correlations.

Quiz

Don’t forget about your chapter quizzes! Find them in the Quizzes menu in D2L.

Chapter Questions

Each week’s chapters follow the same basic process but may be slightly different in terms of which questions you can and cannot choose from. Be sure to read the instructions carefully!

Steps to completion

  1. (Setup: create your copy of the Chapter Questions Posit Cloud project once it’s available. Inside you will find a document template for creating your submitted responses.)
  2. From the end-of-chapter exercises for each chapter, choose three questions from the provided list.
  3. Do not choose from the “Questions from Case Studies” section.
  4. Create a Quarto HTML document using the provided template and answer the questions. This is an opportunity to practice your formatting and information presentation skills as many questions require varied approaches to response.
    1. Be absolutely certain that you leave the embed-resources: true YAML key present! Otherwise, the HTML file you submit will likely break anywhere other than your project.
  5. Submit your rendered HTML file (one per module) to the relevant module’s “Participation” dropbox.
    1. For example, in the Module 1 Exercises dropbox you should upload a single document for Chapter 1 questions and responses, and your Chapter 6 questions and responses.
    2. You will need to make sure your files are named appropriately by changing the output-file YAML key. Your template has instructions to remind you of this.

You are only required to do 3 questions in total.
Make sure to indicate the chapter and question that you are answering in your answer document.

Chapter 4, choose from: 4, 8-16

Chapter 14, choose from: 1, 3, 4, 7, 8, 10, 11