Academic Context and Connections
Finer grained standards that are part of this one
Does a high correlation (close to ± 1) in the data of two quantitative variables mean that one causes a response in the other? Why or why not?
In what way(s) does a plot of the residuals help us consider the best model for a data set?
This expectation supports the major work of high school.
It is important that students understand the foundational concept that “correlation does not equal causation” within their study of curve/line-fitting and the associated numerical calculations. This presents a launching point for discussions about the design and analysis of randomized experiments, also included in high school statistics.
In Grade 8, students explore scatter plots with linear associations and create equations for informal “lines of best fit” in support of their in-depth study of linear equations. In high school, this statistical topic is formalized and includes fitting quadratic or exponential functions (where appropriate) in addition to linear. Additionally, students use graphing calculators or software to analyze the residuals and interpret the meaning of this analysis in terms of the correctness of fit.
The mathematics of summarizing, representing, and interpreting data on two categorical or quantitative variables lays the foundation for more advanced statistical topics, such as inference.
Look for and make use of structure.
Use appropriate tools strategically.