Linear Data, Equations and Least Squares Regression

Overview

Continues with linear regression line analysis, but with data producing
a negative slope and a y-intercept other than at the origin.

Materials and Equipment

- Bathtub
- Meter stick
- TI-83 Graphing Calculator
- TI-83 Timer and Data Collection Programs
- Computer Lab
- Microsoft Excel
- File Storage (floppy disks or networked file server)

Learning Objectives

- Collect real-life data
- Plot data using Excel
- Create a chart in Excel
- Interpret the negative slope of a line as a rate of change in the context of real-life data
- Interpret the y-intercept of a line in the context of real-life data
- Interpret the meaning of the correlation coefficient of the least squares regression line

Guiding Questions

- What is the slope of a line? How does the slope relate to the graph of a line?
- What is the relationship between the slope of a line and the rate of change?
- How do the values and labels on the axes of a graph help determine the rate of change?
- What do we know about the y-intercept of a graph?
- What does the y-intercept tell us about a real-life application?
- What is a correlation coefficient (r)? What does the correlation coefficient tell us about the data (points being plotted) and the resulting least squares regression line?
- Can the least squares regression line be extrapolated to negative x values? Why or why not?

Lesson Outline

- Have students collect data in the homework assignment from Lesson One: Fill the bathtub. Use a meter stick to record the depth in centimeters. Use the TI-83 timer and data collection programs to record the depth of the bathtub every 1 minute. Repeat until bathtub is empty.
- Have students enter the data into a new Excel spreadsheet and create a Scatter chart similar to Lesson One. Have students save their spreadsheet.
- Use the chart and data to facilitate answers to the Guiding Questions. Pay particular attention to the slope, y-intercept and correlation coefficient analysis.

Assessment

- Homework or Quiz based on Guiding Questions
- Lab Report (Lab Report Worksheet)
- Excel Spreadsheet (Spreadsheet Rubric)