Common Core Standards: Math
6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
Even if they don't seem like it sometimes, people are complex and endlessly interesting. Every person is the combination of so many different traits—hair color, eye color, weight, height, nationality, sex, gender, age—that it's practically impossible for any two to be identical.
Students should already know that these different traits are called variables because... well, they vary. Some variables have nothing to do with one another (your age doesn't affect your eye color, does it?), but others, like height and weight, are related in some way. An excellent way to plot out the relationship between two variables is to use a scatter plot.
Students should know to first assign variables to axes. Usually, the dependent variable is on the vertical (y) axis and the independent variable is on the horizontal (x) axis. So if we want to figure out if a person's weight depends on their height, the height will go on the horizontal axis and weight will go on the vertical axis. It should look something like this.
Then, one by one, we can plot points from the data table onto the graph, just like on the x-y coordinate plane. Here, the x coordinate is the height and the y coordinate is the weight. After we've plotted all our points, we should have our completed scatter plot.
Now what? We've plotted the points, but we still haven't answered how a person's height affects his or her weight. Well, we can see that as a person's height increases, their weight has a tendency to increase, too. While we can't prove any concrete relationship just yet, we can say that they're correlated. Weight does depend on height and while we aren't exactly sure how, we can use functions to fit to the data.
- Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
- Informally assess the fit of a function by plotting and analyzing residuals.
- Fit a linear function for a scatter plot that suggests a linear association.