About This Chapter
Standard: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. (CCSS.Math.Content.HSS-ID.B.5)
Standard: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. (CCSS.Math.Content.HSS-ID.B.6a)
Standard: Informally assess the fit of a function by plotting and analyzing residuals. (CCSS.Math.Content.HSS-ID.B.6b)
Standard: Fit a linear function for a scatter plot that suggests a linear association. (CCSS.Math.Content.HSS-ID.B.6c)
Standard: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (CCSS.Math.Content.HSS-ID.C.7)
Standard: Compute (using technology) and interpret the correlation coefficient of a linear fit. (CCSS.Math.Content.HSS-ID.C.8)
Standard: Distinguish between correlation and causation. (CCSS.Math.Content.HSS-ID.C.9)
About This Chapter
Students who exhibit mastery of these standards are able to perform statistical analyses using bivariate data. While completing those analyses, students will make use of two-way tables, scatter plots and linear regression models.
Lessons in these standards address concepts such as:
- Two-way tables
- Joint, marginal and conditional frequencies
- Scatter plots
- Linear regression
- Slope and intercept
- Correlation coefficient
- Correlation vs. causation
Students who have mastered these standards are able to create two-way tables and scatter plots with bivariate data, in addition to performing simple linear regressions to solve various types of problems. They will also demonstrate an understanding of correlation vs. causation, enabling them to interpret correlations in research being completed in their major areas of college study.
How to Use These Lessons in Your Classroom
The following are some tips on how you can incorporate these lessons on bivariate data into your curriculum to help meet the common core standards:
Pre- and Post-Quiz Lessons
Have students complete the quizzes for the What is a Two-Way Table? and How to Interpret Correlations in Research Results lessons to introduce the concepts and make them aware of what to look for during the videos. After watching the video lessons, have students re-take the quizzes to assess understanding.
Scatter Plots Lesson
After viewing the scatter plots video lesson, supply your class with data concerning the major species of dogs' maximum longevity and typical adult weight. As a class, construct a scatter plot to find a possible correlation between longevity and adult weight in dogs.
Scatter Plots, Linear Regressions, Slope/Intercept, Residuals and Correlations Lessons
Share the video lessons on the topics listed above. Assign each student one or two states in the U.S. to research the number of area codes and the population in a given year. As a group, plot a scatter plot to predict the number of area codes from the population. Incorporate regression equations, computation of residuals and estimation of correlation.
1. What is a Two-Way Table?
Do you believe in Martians? Do you watch football on television? A Two-Way Table or Contingency Table is a great way to show the results of all kinds of survey questions. In this video we will learn how to read a two-way table.
2. Joint, Marginal & Conditional Frequencies: Definitions, Differences & Examples
Joint, marginal, and conditional frequencies are all part of analyzing categorical data and two-way tables. This lesson will help you learn the definitions and differences between each concept.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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!
8. 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.
9. 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.
10. 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.
11. 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 Common Core Math - Statistics & Probability: High School Standards course