Module 11: Linear Regression and Correlation (Chapter 10)
Section outline
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Professionals often want to know how two or more numeric variables are related. For example, is there a relationship between the grade on the second math exam a student takes and the grade on the final exam? If there is a relationship, what is the relationship and how strong is it?In another example, your income may be determined by your education, your profession, your years of experience, and your ability. The amount you pay a repair person for labor is often determined by an initial amount plus an hourly fee.
The type of data described in the examples is bivariate data — "bi" for two variables. In reality, statisticians use multivariate data, meaning many variables.
In this chapter, you will be studying the simplest form of regression, "linear regression" with one independent variable (x). This involves data that fits a line in two dimensions. You will also study correlation which measures how strong the relationship is.
Image Caption: Linear regression and correlation can help you determine if an auto mechanic’s salary is related to his work experience. (credit: Joshua Rothhaas)
(Content & Image Source: Chapter 12 Introduction, Introductory Statistics, Barbara Illowsky and Susan Dean, OpenStax, CC BY 4.0 License)
Upon completion of this module, you will be able to:10.1 Linear Equations- Interpret the independent and dependent variable
- Calculate and interpret the slope and y intercept of a linear equation
10.2 Scatter Plots- Construct and interpret scatter plots.
10.3 The Regression Equation- Create and interpret the line of best fit.
- Calculate and interpret the correlation coefficient.
- Calculate and interpret the coefficient of determination.
10.4 Testing the Significance of the Correlation Coefficient- Test the significance of the correlation coefficient.
10.5 Prediction- Use the line of best fit for prediction.
10.6 Outliers- Find and interpret outliers between two quantitative variables.
To achieve these objectives:- Read the Module 11 Introduction (see above).
- Read Sections 10.1 - 10.6 of Chapter 10: Linear Regression and Correlation in Introductory Statistics (links to each Section provided below)
- Complete the MyOpenMath Homework Assignments for the topics in the Chapter (links provided below) - These are graded!
- View the Chapter 10 Review (link provided below)
- Practice the problems in the Chapter 10 Practice and Homework, checking the solutions provided (links to each provided below)
- Submit the Chapter 10 Project I: Distance from School, Chapter 10 Project II: Textbook Cost, or Chapter 10 Project III: Fuel Efficiency (links to project and submission link provided below)
- Complete the MyOpenMath Quiz for Chapter 10 (link provided below) - This is graded!
- Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
- Post in the Chapter 10 Q&A Discussion Forum - link provided below.
Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.Module Pressbooks Resources and Activities
You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.
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