Ch 7: Linear Relationships

About This Chapter

Further develop your understanding of linear relationships and models in math by referring to the video and text lessons in this chapter. Use this resource to support your math class studies or to help you prepare for year-end assessment or a college entrance exams.

Linear Relationships - Chapter Summary

From coefficients to residuals, this chapter covers everything about linear relationships that you would need to know at the secondary or college level. You will have the opportunity to review definitions and formulas used in this area of statistics and mathematics.

How do you interpret slope? What is linear regression? Why is understanding linear relationships important in statistics? These are some of the topics you can expect to explore in this chapter. Once you are finished with these lessons, you should be able to:

  • Differentiate between linear and nonlinear relationships and transform nonlinear data
  • Evaluate linear models and calculate linear regression
  • Define line of best fit
  • Analyze residuals and interpret slope and intercept
  • Determine the relationship between two variables
  • Describe how to compute coefficient of determination
  • Understand the formula to determine the Pearson correlation coefficient
  • Use data to interpret linear relationships

Complex data is explained in simple terms by expert instructors in this field and students can easily contact instructors if they are having difficulty with any topic. Lessons are accessible 24/7 and video lesson transcripts are printable for quick reference. Self-assessment quizzes measure how much has been retained from each lesson and one's readiness in moving from one topic to the next.

12 Lessons in Chapter 7: Linear Relationships
Test your knowledge with a 30-question chapter practice test
Linear & Nonlinear Relationships in Data Graphs

1. Linear & Nonlinear Relationships in Data Graphs

After watching this video, you will be able to explain the difference between linear and nonlinear relationships when plotting graphs. A short quiz will follow.

Transforming Nonlinear Data: Steps & Examples

2. Transforming Nonlinear Data: Steps & Examples

Sometimes we have data sets that we need to analyze and interpret, but it's difficult because the data is nonlinear. This lesson will teach you how to transform nonlinear data sets into more linear graphs.

Writing & Evaluating Real-Life Linear Models: Process & Examples

3. Writing & Evaluating Real-Life Linear Models: Process & Examples

You make decisions about budgeting and other financial issues using linear models without even realizing it. Learn how to write and evaluate linear models.

Linear Regression Model: Definition, Equation & Example

4. Linear Regression Model: Definition, Equation & Example

Ever hear of the linear regression model? If you are confused about what linear regression is, come inside this less for an explanation, how it is used and calculated. Then test your new skills with a short quiz.

Simple Linear Regression: Definition, Formula & Examples

5. Simple Linear Regression: Definition, Formula & Examples

Simple linear regression is a great way to make observations and interpret data. In this lesson, you will learn to find the regression line of a set of data using a ruler and a graphing calculator.

Line of Best Fit: Definition, Equation & Examples

6. Line of Best Fit: Definition, Equation & Examples

Linear graphs are a terrific way to see a trend when comparing any two factors. A line of best fit is the trendline that best fits the data set. In this lesson, we will see how the line of best fit helps to predict future events.

Analyzing Residuals: Process & Examples

7. Analyzing Residuals: Process & Examples

Can you tell what's normal or independent and what's not? Sometimes, we need to figure this out in the world of statistics. This lesson shows you how as it explains residuals and regression assumptions in the context of linear regression analysis.

Interpreting the Slope & Intercept of a Linear Model

8. Interpreting the Slope & Intercept of a Linear Model

You've probably seen slope and intercept in algebra. These concepts can also be used to predict and understand information in statistics. Take a look at this lesson!

The Correlation Coefficient: Definition, Formula & Example

9. The Correlation Coefficient: Definition, Formula & Example

The correlation coefficient is an equation that is used to determine the strength of the relationship between two variables. This lesson helps you understand it by breaking the equation down.

Coefficient of Determination: Definition, Formula & Example

10. Coefficient of Determination: Definition, Formula & Example

The coefficient of determination is an important quantity obtained from regression analysis. In this lesson, we will show how this quantity is derived from linear regression analysis, and subsequently demonstrate how to compute it in an example.

Pearson Correlation Coefficient: Formula, Example & Significance

11. Pearson Correlation Coefficient: Formula, Example & Significance

The Pearson correlation coefficient is just one of many types of coefficients in the field of statistics. The following lesson provides the formula, examples of when the coefficient is used, its significance, and a quiz to assess your knowledge of the topic.

Interpreting Linear Relationships Using Data: Practice Problems

12. Interpreting Linear Relationships Using Data: Practice Problems

Understanding linear relationships is an important part of understanding statistics. This lesson will help you review linear relationships and will go through three practice problems to help you retain your knowledge. When you are finished, test out your knowledge with a short quiz!

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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