IM 8.6.8 Lesson: Analyzing Bivariate Data
A researcher found an association between a dog’s stride length and its speed: the longer a dog’s steps, the faster it goes. The predicted speed in meters per second, , as a function of step length in meters, , is What does the rate of change of the function tell you about the association between stride length and speed?
Is there an association between the weight of an animal’s body and the weight of the animal’s brain?
Use the data to make a scatter plot.
Are there any outliers?
Experiment with the line to fit the data. Drag the points to move the line.
Without including any outliers, does there appear to be an association between body weight and brain weight? Describe the association in a sentence.
Adjust the line by moving the green points, fitting the line to your scatter plot, and estimate its slope. What does this slope mean in the context of brain and body weight?
Does the fitted line help you identify any other outliers?
Use one of the suggestions or find another set of data that interested you to look for associations between the variables.
- Number of wins vs number of points per game for your favorite sports team in different seasons
- Amount of money grossed vs critic rating for your favorite movies
- Price of a ticket vs stadium capacity for popular bands on tour
Are any of the points very far away from the rest of the data?
Would a linear model fit the data in your scatter plot? If so, draw it. If not, explain why a line would be a bad fit.
Is there an association between the two variables? Explain your reasoning.
Earlier, your class gathered data on height and arm span.
Sometimes a person’s arm span is the same as their height. Is this true for anyone in the class?
Make a scatter plot for the arm span and height data, and describe any association.
Is the line a good fit for the data? If so, explain why. If not, find the equation of a line that fits the data better.
Examine the scatter plot. Which person in your class has the largest ratio between their arm span and their height? Explain or show your reasoning.