About This Chapter
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.
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.
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.
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.
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.
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.
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.
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.
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!
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.
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.
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.
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!
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Other chapters within the VCE Further Mathematics: Exam Prep & Study Guide course
- Population & Samples
- Categorical Data Representation
- Numerical Data Representation
- Data Distribution
- Correlation & Causation in Math
- Non-Causal Relationships in Statistics
- Time Series Data
- Recursion & Financial Modeling
- Concepts of Financial Mathematics
- Matrices Overview
- Graphs & Networks
- Paths & Circuits
- Problem Solving With Networks
- Geometric Solids
- Measurement & Trigonometry
- Spherical Geometry
- Applications of Spherical Geometry
- Graphs & Relations
- Linear Programming Overview
- VCE Further Mathematics Flashcards