AP Statistics: Describing Relationships between Variables (The Candy Grab Activity)
Overview
THis is an activity that can be used to introduce Linear Regression or the relationship between two numerical variables. Studetns will do an activity, make graphs, and answer questions about the relationship between hand span and the number of candies grabbed. Then they will be asked to do an exploration on their own.
Intro to Describing relationships between Quantitative Variables
Investigating relationships between variables is central to what we do in statistics. When we understand the relationship between two variables, we can use the value of one variable to helo us make predictions about the other variable. Earlier this year we studied relationships between categorical variables, such as membership in an environmental club and snowmobile use for visitors to Yellowstone National Park. The association suggests that members of environmental clubs are less likely to own or rent snowmobiles than nonmembers.
In this activity, we will investigate relationships between two quantitative (numerical) variables. Does knowing how much money a Major League Baseball team spent on its players tell us anything about how many wins that team will have? What can we learn about the price of a used car from the number of miles it has been driven? Can Students with larger hands grab more candy? The following pages will guide you and your class throguh this activity.
Candy Grab Activity
Give students about 5 minutes in pairs or groups to write down the lists.This activity is best done face to face. I have them in small groups, but we put all candy grab and hand span data on the board.
Take time to discuss the list of things that will be important to answer this question.
Some of the things that should be discussed:
Precision in measuring the hand span. What units (mm, cm, in)?
Should the hand be stiff or relaxed?
What about long finger nails?
How long do you have to keep the candy in your hand? What if some falls after you grab it?
Should everyone use the same hand or thier dominant hand?
Before we begin this activity, I want you to take some time to write down the things you think are important in deciding the answer to our question of interest?
How much candy can you grab?
Can students with a larger handspan grab more candy than those with smaller handspans? 
Make your list in your notebook or on a word document.
Candy Grab Activity
Can students with a larger handspan grab more candy than those with smaller handspans?
Today we will investigate this question.
 Measure the span of your dominant hand to the nearest mm. Handspan is the distance from the tip of the thumb to the tip of the pinkie finger on your fully stretchedout hand. Handspan = ________ mm
 Use the same hand to grab as many candies as possible from the container. You must grab the candies with your fingers pointing down (no scooping!) and hold the candies for 2 seconds before counting them. After counting, put the candy back into the container. Record your data in the spreadsheet.
 Use the applet at www.statsmedic.com/applets (2 Quantitative Variables) to make a scatterplot. Sketch below. Be sure to clarify which varible is the EXPLANATORY variable and which is the RESPONSE varible (p. 153 TPS6e)
Your scatterplot should be made using the guidelines from page 155 in your text.
Candy Grab Continued
Now lets analyze our data and scatter plot. Answer the following questions in your group. Be complete in answering each question.
 Describe the relationship displayed in the scatterplot. (see p. 156157 in TPS6e)
 Use the applet to find the line of best fit. Record it below. (line of best fit information on p. 176178 in TPS 6e)
 What is the slope of the line? Interpret the slope in context. (see p. 181 in TPS6e)
 What is the yintercept of the line? Interpret the yintercept in context. (p. 181)
Candy Grab Activity: Extension activity
Now it is your turn. Using the what you learned and practiced as you did this activity, complete the following problems in your group.
How much candy can Lebron grab?
LeBron James has four NBA MVP Awards, three NBA Finals MVP Awards, and two Olympic Gold Medals. But how many candies can he grab?

 One of the Algebra classes collected the following data:
Handspan (x)  18  18.5  19  19  19.5  20  20  20.5  20.5  21  21  22  22.5  22.5  23  23 
Candies (y)  14  16  19  18  21  19  22  23  22  24  27  28  25  30  34  35 
2. Use the applet to find the line of best fit. Record it below.
3. Lebron James has a handspan of 23.5 cm. Use the equation of the line to predict how many candies Lebron can grab. Show your work?
4. When Lebron visited East Kentwood High School in 2012, he attempted the candy grab and was able to grab 38 candies.
a. Add this point to the scatterplot
b. Was this value higher or lower than what you predicted?
c. By how much? Show your work.
 Your teacher will now measure their handspan. Handspan = ______
 Predict how many candies your teacher can grab. Show your work.
 Your teacher will now attempt the candy grab. Number of candies = _______
 Using the data for your teacher:
a. Add this point to the scatterplot
b. Was this value higher or lower than what you predicted?
c. By how much? Show your work.