## Least Squares Regression

This Unit Plan consists of lessons
in which students interpret the slope and *y*-intercept of least squares
regression lines in the context of real-life data. Students use an e-example
applet to plot the data and calculate the correlation coefficient and equation
of the least squares regression line. These lessons develop skills in
connecting, communicating, reasoning, and problem solving as well as representing
fundamental ideas about data.

**Math
Content**

Students will:

- Build skills necessary for interpreting the slope and y-intercept of linear equations.
- Be provided with a real-life context in which to relate both concepts.
- Be given multiple opportunities to explore slope as a rate of change and to view the y-intercept of a graph as having real meaning.
- Be given the opportunity to view data in tabular, graphic, and algebraic form.
- Have opportunities to discuss and display their work.

**Prerequisite
Knowledge**

It is strongly recommended that teachers go online and become familiar with the program before conducting any of the lessons in this Unit Plan.

### Traveling Distances

*y*-intercept of the graph of real-life data. By examining the graphical representation of the data, students relate the slope and

*y*-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the resulting least squares regression line.

### Bathtub Water Levels

*y*-intercept of the graph of the real-life data. By examining the graphical representation of the data, students relate the slope and

*y*-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the least squares regression line.

### My Graph Is…

*y*-intercept of their least squares regression lines will help reinforce the concepts introduced in Lessons One and Two of this Unit Plan. The students are then given the opportunity to display their work.

### Gallery Walk

### Automobile Mileage: Year vs. Mileage

*y*-intercept in the resulting equation for the least squares regression line. By examining the graphical representation of the data, students analyze the meaning of the slope and

*y*-intercept of the line and interpret them in the context of the real-life application. Students also make decisions about the age and mileage of automobiles based on the equation of the least squares regression line.

### Automobile Mileage: Age vs. Mileage

In this lesson, students plot data about automobile mileage and interpret the meaning of the slope and *y*-intercept
of the least squares regression line. By examining the graphical
representation of the data, students analyze the meaning of the slope
and *y*-intercept of the line and put those meanings in the context of the real-life application.

The activity is very similar to that in Lesson Five of this Unit Plan. However, by graphing the data in a different format, the students will produce a line with a positive slope in this activity, while the line in Lesson Five had a negative slope. Doing both lessons allows students to investigate how changing the independent variable affects the resulting graph and equation.

### Automobile Mileage: Years Since 1990 vs. Mileage

Five and Six.

### Automobile Mileage: Comparing and Contrasting

### Looking Back and Moving Forward

*Principles and Standards for School Mathematics*.