The students have been introduced to creating a scatter plot, drawing the line of best fit, and writing the equation of the line of best fit by hand. This is the first lesson that the students are using the calculator for the linear regression.
The video below models how to write the equation of the line of best fit and interpret the correlation factor (r) on the TI- Nspire. The video first shows how a student can find the equation for the line of best fit using the Statistics capabilities of the calculator. The video also models creating the scatter plot, line of best fit, and prediction equation on the graph if desired.
On most standardized tests, the scatter plot and line of best fit are to be drawn by hand. So, it is important to approach this task using both pencil-and-paper and computer technology. However, the prediction equation, and the correlation factor are important in analyzing the strength of the correlation between the variables being compared.
In this section, I will provide Sample data of the femur length and height of students in one class. I model the line of best fit and the scatter plot using the TI-Nspire CX in the video below:
As you can see from the r-value, the correlation between femur length and height was weak for this class. The weak correlation resulted from measurement error. As a whole class we discussed the fact that if we used a different sample of people (e.g., measuring only adults) we might have found a stronger correlation (i.e., an r-value close to 1). We also discussed the size of our sample and how a more accurate predication equation can be produced by measuring a larger sample.
During class several students shared their predictions for the height of a criminal with a femur length of 36 cm:
There is almost a 9 cm difference between the 2 predictions. Expect more error when creating the prediction equation by hand from the scatter plot. Using a least squares regression, the calculator will offer a more precise approach. Students should learn that it is more efficient to use technology to calculate an accurate best fit line (Mathematical Practice 5).
In class, I also have students calculate the height as feet and inches to be consistent with the way that they normally represent height.
Extension: Anthropologists sometimes use a proportion to estimate height. Compare the use of a proportion with a linear model based on linear regression.