Welcome to Linear Regression day 5 with
Barbie Bungee

It's time now to use these linear regression skills to actually design something. We're going to create a bungee line for Barbie that will give her the most thrilling, yet safe, fall from a height of 3 meters.


Barbie is an adventure seeker to the max. She loves the thrill of death defying activities. She believes the adrenaline rush makes her hair more lustrous and her waistline thinner; so she will pay big bucks to the company which gives her the most thrilling ride. In the back of her mind though, she wants to be sure that she's really safe.

To design the best bungee line, follow the steps below.

Step 1: Gather the following materials:

  1. About 30 rubber bands all the same size
  2. A meter stick or yardstick
  3. An old doll
  4. A pencil
  5. A ruler
  6. A piece of graph paper
Step 2: Connect two rubber bands with a slipknot.
Then wrap one end repeatedly around Barbie's ankles. Be sure the rubber band is on tight enough not to fall off when she is being dropped.

Step 3: We will measure Barbie's height without rubber bands then we will drop Barbie from the top of a meter stick, and measure the lowest point that her head reaches. We will do this six times, adding a rubber band each time.

The more bands we add, the lower she will drop. You can record your data in a chart that looks like this:

Number of bands
(x)
Lowest point head reaches in cm
(y)
0
.
1
.
2
.
3
.
4
.
5
.
6
.
NOTE: when you drop your doll, you may need to tie her hair back so that you can get an accurate reading from the meter stick


If you have two or three people working together, one person can hold the meter stick, and the others can drop the doll, and take the measurements.

If you are alone however, you will need to secure the meter stick to a wall with tape. Be sure that it is vertical, and that the zero is at the TOP.

Now you will need to get a "baseline" measurement. That means you record the height of your doll without rubber bands adding length. Be sure that she is stretched out completely with her hands at her sides.

Record this amount next to the zero rubber bands in the chart.

Next we drop her with one rubber band attached to her ankles.

Hold the band tight at the top of the yardstick, and simply let Barbie drop from the head-down position you see above.

She won't swing; she will just lightly bounce.

This is the tricky part. You need to observe the LOWEST spot her head reaches during the bounce. The final resting spot is NOT the lowest spot.

You will probably have to drop her two or three times to get an accurate lowest reading. It really helps to have another person watch too.

Now its time to start adding more bands. Once again use a slipknot to connect a second band to the bungee line. (Remember the band wrapped around her ankles does not count in the length of the line.)

Drop her with the two rubber bands attached to her ankles.

Hold the band tight at the top of the yardstick, and simply let Barbie drop from the head-down position.

She should bounce a bit more than she did with just one rubber band.

The amount of bounce will get markedly larger as you add bands!

Remember, you may need to drop her several times to get an accurate reading of the LOWEST spot her head reaches.

 

Step 4: Now that you have your seven pieces of data, set up a titled and labeled graph. Click HERE if you need graph paper, and plot your data.

 

Step 5: Draw a line of best fit.

 

Step 6: Select two points of your line, write their coordinates, and determine the slope of your line using the slope formula:

 

Step 7: Substitute the slope you found in step 6 and one of your two points into the equation y=sx+i, and solve for i. Then write the equation for your line.

Step 8: Use your equation to determine how many rubber bands would be needed to drop Barbie from your ceiling to your floor. ( You will need to measure this distance in cm.)

 

Step 9: Now consider the SAFETY issue vs. the THRILL issue.

If you put the number of bands on that you found in step 8, her head will reach the floor, she will crack open her skull, and die. You will then be sued for negligence and will lose your business and owe her family millions of dollars that you don't have.

On the other hand, if you shorten the bungee line TOO MUCH, the ride may not be thrilling enough, and Barbie will pay her big bucks to your competitor. You will lose clients and your business will suffer.

So make a decision on how many bands you want to use, then attach that many bands to Barbie's line using slipknots like above.

Step 10: Now it's time to drop her and see if she dies or has a great time.

It's fun to try this regression experiment along with another person or team. If you each use a different doll, get different data and develop your own equations, then you can each drop your dolls and see who gives the most thrilling ride.

************************

For more work with regressions check out these: day 1 activity |
day 2 activity | day 3 activity | day 4 activity | Barbie Bungee Activity

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