Lesson Plan: Lesson plans were written by Maryland mathematics educators and could be used when teaching the concepts.
 Goal 3 Data Analysis And Probability Expectation 3.2 The student will apply the basic concepts of statistics and probability to predict possible outcomes of real-world situations. Indicator 3.2.2 The student will interpret data and/or make predictions by finding and using a line of best fit and by using a given curve of best fit.

### Lesson Content

Lines of Best Fit

### Objectives

• The student will determine if there is an association in a scatter plot of data.
• The student will display data in charts and graphs and approximate the line of best fit.
• The student will calculate the line of best fit using a graphing calculator.
• The student will analyze data through predictions, comparisons, and applications.

### Calculator Skills

• Enter data into lists.
• Graph a scatter plot.
• Calculate a linear regression.
• Graph a linear equation.

### Assessment

• Drill
• Class discussion
• Group work

### Introduction

Analyzing Scatter plots - Students should follow the instructions on the worksheet and compare their lines of best fit with a partner. One method to determine an association is to draw an oval that includes all the data points. The thinner and more oblong the oval, the stranger the association. Students may disagree on graph #4. Discuss the impact of the outlier (22,5).

### Warm-Up/Opening Activity

The drill is a review of the concept of slope and y-intercept in relation to a real-world situation. In this problem the slope represents the change in monthly charges for each additional video that is rented. The y-intercept represents the charge when zero videos are rented.
If C represents total monthly charges and v represents the number of videos rented per month, where C=1.25v + 3.25.
1. What is the slope of this equation? What does the slope mean in the context of the problem?
2. What is the y-intercept of this equation? What does the y-intercept mean in the context of the problem?

### Exploration

Students may be introduced to finding equations for lines of best fit by using two data points to determine their equation. If they are reading data points from a graph, be sure to emphasize the importance of reading the scales on the x- and y-axis. Students should also be instructed to find a line of best fit using the graphing calculator. Have students work with a partner to answer questions on "Biking Home". Discuss the limits of using a line of best fit. Complete "Dentists for the Future". Be sure to review window settings appropriate for the data and how to graph scatter plots and equation on the same graph. Demonstrate how to calculate the line of best fit in the stat menu.

### Class Discussion

Ask students to explain the equation form (ax +b) and how it relates to (mx +b). Discuss the differences between students' estimates and the calculated lines of best fit.