# Ch 8: Regression & Correlation

### About This Chapter

## Regression & Correlation - Chapter Summary and Learning Objectives

Instructors in this chapter can introduce you to some of the methods used to create visual representations of research data. You can also find out how to draw a trendline demonstrating the relationships between two variables and learn to interpret these graphs. By the end of this chapter, you should be able to do the following:

- Create scatterplots and graph a regression line
- Interpret linear relationships between two variables
- Understand the difference between positive and negative correlations
- Find the correlation coefficient and the coefficient of determination

Video | Objectives |
---|---|

Creating & Interpreting Scatterplots: Process, Examples & Quiz | Create scatterplots and use them to interpret data. |

Problem Solving Using Linear Regression: Steps, Examples & Quiz | Analyze problems involving linear regression. |

Analyzing Residuals: Process, Examples & Quiz | Study residuals to find violations of regression assumptions. |

Interpreting the Slope & Intercept of a Linear Model: Lesson & Quiz | Interpret the slope and intercept of linear models. |

The Correlation Coefficient: Definition, Formula & Example | Find the correlation coefficient using formulas or software. |

How to Interpret Correlations in Research Results | Learn how to interpret negative and positive correlations. |

Correlation vs. Causation: Differences, Lesson & Quiz | Understand the difference between finding correlation and proving causation. |

Interpreting Linear Relationships Using Data: Practice Problems, Lesson & Quiz | Practice interpreting linear relationships. |

Transforming Nonlinear Data: Steps, Examples & Quiz | Transform nonlinear data so that linear models can be used. |

Coefficient of Determination: Definition, Formula & Example | Find the coefficient of determination and understand how it relates to variation. |

### 1. Creating & Interpreting Scatterplots: Process & Examples

Scatterplots are a great visual representation of two sets of data. In this lesson, you will learn how to interpret bivariate data to create scatterplots and understand the relationship between the two variables.

### 2. Problem Solving Using Linear Regression: Steps & Examples

Linear regression can be a powerful tool for predicting and interpreting information. Learn to use two common formulas for linear regression in this lesson.

### 3. 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.

### 4. 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!

### 5. 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.

### 6. The Correlation Coefficient: Practice Problems

The correlation coefficient is a long equation that can get confusing. This lesson will help you practice using the equation to find correlations and explore ways to check your answers.

### 7. How to Interpret Correlations in Research Results

Perhaps the most common statistic you'll see from psychology is a correlation. Do you know how to correctly interpret correlations when you see them? This lesson covers everything you need to know.

### 8. Correlation vs. Causation: Differences & Definition

When conducting experiments and analyzing data, many people often confuse the concepts of correlation and causation. In this lesson, you will learn the differences between the two and how to identify one over the other.

### 9. 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!

### 10. 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.

### 11. 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.

### 12. 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.

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### Other Chapters

Other chapters within the Statistics 101: Principles of Statistics course