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Statistics in Schools is a free Census Bureau program that uses the data to create resources for K-12 students in a variety of subjects.

# Analyzing Relationships: Marriage, Divorce, and Linear Regression

### Activity Description

Students will examine census data on marriage and divorce rates for women and men in each state and the District of Columbia. From these data, they will create a scatter plot, find a line of best fit, and analyze the relationship between the two variables (i.e., sex and marriage/ divorce rates). They will also use a residual plot, explain the meaning of the slope and of the y-intercept of the line of best fit, and investigate the effect of outliers on this line.

9

45-60 Minutes

### Learning Objectives

• Students will be able to assess how well a linear model fits the data by plotting and analyzing the residuals.
• Students will be able to determine the impact of outliers on the linear model.
• Students will be able to explain the meaning of the slope and y-intercept of the linear model in the context of the data.

### Materials Required

• The student version of this activity, 13 pages
• Graphing calculators

### Activity Items

The following item is part of this activity.

• Table of Marriage and Divorce Rates per 1,000 Women and Men Aged 15 or Older in Each U.S. State and the District of Columbia

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## Teacher Notes

#### Blooms Taxonomy

Analyzing

Students will analyze data in a linear model, apply the model to make predictions, and evaluate the effectiveness
of the model.

High School Math

#### Topics

• Linear model
• Linear regression
• Residuals and residual plots
• Scatter plots
• Slope
• Y-intercept

#### Skills Taught

• Analyzing a scatter plot and a residual plot
• Interpreting slope and y-intercept
• Making predictions using a linear model
Page Last Revised - October 8, 2021