Lesson 8Analyzing Bivariate Data
Learning Goal
Let’s analyze data like a pro.
Learning Targets
I can analyze a set of data to determine associations between two variables.
Lesson Terms
- negative association
- positive association
Warm Up: Speed vs. Step Length
Problem 1
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,
What does the rate of change of the function tell you about the association between stride length and speed?
Activity 1: Animal Brains
Problem 1
Is there an association between the weight of an animal’s body and the weight of the animal’s brain?
animal | body weight (kg) | brain weight (g) |
|---|---|---|
cow | ||
grey wolf | ||
goat | ||
donkey | ||
horse | ||
potar monkey | ||
cat | ||
giraffe |
animal | body weight (kg) | brain weight (g) |
|---|---|---|
gorilla | ||
human | ||
rhesus monkey | ||
kangaroo | ||
sheep | ||
jaguar | ||
chimpanzee | ||
pig |
What do you notice in the table of data?
Consider the scatter plot of the data. Are there any outliers?
Experiment with the line to fit the data. Drag the points to move the line. You can close the expressions list by clicking on the double arrow.
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 more outliers?
Print Version
Is there an association between the weight of an animal’s body and the weight of the animal’s brain?
animal | body weight (kg) | brain weight (g) |
|---|---|---|
cow | ||
grey wolf | ||
goat | ||
donkey | ||
horse | ||
potar monkey | ||
cat | ||
giraffe |
animal | body weight (kg) | brain weight (g) |
|---|---|---|
gorilla | ||
human | ||
rhesus monkey | ||
kangaroo | ||
sheep | ||
jaguar | ||
chimpanzee | ||
pig |
Use the data in the table to make a scatter plot. Are there any outliers?
After removing the outliers, does there appear to be an association between body weight and brain weight? Describe the association in a sentence.
Using a piece of pasta and a straightedge, fit a 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 more outliers?
Are you ready for more?
Problem 1
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
After you have collected the data:
Create a scatter plot for the data.
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.
Activity 2: Equal Body Dimensions
Problem 1
Earlier, your class gathered data on height and arm span.
Sometimes a person’s arm span is equal to 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. Click on the plus sign to get a menu and add a table, if you choose.
Is the line
a good fit for the data? If so, explain why. If not, find the equation of a better line. 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.
Print Version
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.
Lesson Summary
People often collect data in two variables to investigate possible associations between two numerical variables and use the connections that they find to predict more values of the variables. Data analysis usually follows these steps:
Collect data.
Organize and represent the data, and look for an association.
Identify any outliers and try to explain why these data points are exceptions to the trend that describes the association.
Find a function that fits the data well.
Although computational systems can help with data analysis by graphing the data, finding a function that might fit the data, and using that function to make predictions, it is important to understand the process and think about what is happening. A computational system may find a function that does not make sense or use a line when the situation suggests that a different model would be more appropriate.