# Illuminations: Least Squares Regression

This is an entire unit reviewing slope, y-intercept and moving into linear regression, but I’m most interested in an activity that they provide involving graphing mileage against the age of a car:

Today’s activity should begin with a general discussion of what students know about the year in which an automobile was produced and the mileage they would expect to be on the automobile. The teacher should consistently refer to the year in which the car was produced and not the age of the automobile.

Students should be divided into teams of two to work at the computer and given a copy of the handout Automobile Mileage—Year vs. Mileage (or a similar handout of student-produced data). They should visit the Web site: http://illuminations.nctm.org/index_d.aspx?id=454.

Working together, the partners can share the responsibility of making sure the data is plotted correctly. One student should plot the data, while the second reads out the data and makes sure it is plotted correctly. This is a good time to bring independent and dependent variables. Explain to students that x is the independent variable and y is the dependent variable and ask them to differentiate which is which for our year vs. mileage situation. Are students clear on the fact that the year is associated with the x-axis and is the independent variable and the mileage is on the y-axis and is the dependent variable?

Incidentally, there’s no need to work on the computer for plotting points on a scatter plot, because all of that can be done using the TI-83.