### Can We Predict the Future? Stocks, Class Data, and Raw Egg Regressions

Egg Bungee Jump Regression - Based on a lab by Dr. Holly Hirst. Work in a group of 5, but each person should answer the questions on a separate piece of paper. Bungee jumping looks pretty exciting. Today we will let you decide how long to make the bungee cord for a fragile jumper -- a raw egg. The goal is to make it exciting but not fatal for your jumper. A small prize will be given to the group that gets closest to the ground without harming their egg. There is only 1 egg per group. If your egg breaks, clean up and wash off the netting - which I need back for future use.
The Experimental Stage Gather your data as follows:
1. Make 3 jumps each with 2, 3, 4, and 5 rubber bands from a height of 1 meter. You may wish to use a pen, and hold it perpendicular to the top of the stick, so that you drop the egg sufficiently far away from the meter stick. Record how far the egg travels from the top of the meter stick to the point closest to the ground (12 data points). Be very careful with your egg - protect it from hitting anything and make sure that it doesn't swing back and hit the meter stick. Accuracy is important, so the same person should drop the egg each time, and the same person should be watching the meter stick each trial.
 Number of rubber bands Distance dropped in centimeters 2 2 2 3 3 3 4 4 4 5 5 5

Excel and Data Analysis Enter your data into excel, Click on the grey A box above the number of rubber bands data. The column will become highlighted. Click the shift key, hold this down and then then click on the grey B box above the distance data. Now both columns will be highlighted. Under the Insert menu, release on Chart. Click on XY (Scatter) and then on Marked Scatter. Click on one of the points on your graph. Under the Chart menu, release on Add Trendline. Click on Options and select the bottom two options (Display equation on chart and Display R-squared value on chart). Click on OK. Back on the chart, click on the equation of the line, hold down and drag it to the corner so that you can read the info.
2. REGRESSION LINE:                                                                    R2 VALUE:
3. Even with the variability in rubber bands and possible measurement inconsistencies, using the r2 value, your number of rubber bands should be a very strong predictor of the distance traveled because the stretch ability and similarity of the rubber bands shows a constant slope for the change in distance dropped / change in rubber bands. EXACTLY what prediction of the number of rubber bands required for 2.0 meters (200 cm) does the equation of the regression line give (plug in for the y-value and solve for x)? SHOW WORK!
4. The Contest Using the predicted number of rubber bands, the R2 value, and anything else you want to factor into your decision, decide how many rubber bands you will use for the 2.0 meter bungee jump. You may be creative and fold a rubber band in half. The team that comes closest to the ground without any egg damage wins. Build, but DO NOT TEST the bungee machine and then leave it alone in the bowl as you continue to work below.
Does Date predict Close? Repeat the above Excel process for the Date/Close columns.
5. Is the trend an upward trend, downward trend, or horizontal trend?
6. What is the R2 value written as a percent?

Does Volume predict High? Repeat the above Excel process for the Volume/High columns.
7. What is the R2 value written as a percent?
8. According to the chart in the HDYK book, what kind of predictor is Volume of High?
9. Critical Analysis: Lack of a Trend For most stocks, Volume will be a weak or no predictor of High. Take out your Excel chart from the stock packet and look for contradictions to a general trend between Volume (the bars at the bottom) and High (the tip tops). Ie find two consecutive days where the volume increases over time as the high increases, and two other consecutive days where the volume increases over time as the high decreases, or find some other similar information that would contradict a good fitting line relating volume and high. Apply the same reasoning as in the hw reading.

Class Data From the class highlights page, go to this lab, and then click on this Class Data Excel File.
Does Armspan predict Height? Follow the above Excel process for the Armspan and Height data.
10. What is the equation of the best fit line?
11. What is the R2 value written as a percent?
12. According to the chart in the HDYK book, what kind of predictor is Armspan of Height?
13. Take a look at this graph. This is some of the same data, but I removed points that contradicted the related text that accompanied Leonardo da Vinci's Vitruvian Man "The length of a man's outspread arms is equal to his height." What is the new slope of the line? What is the new r2 value written as a percent?
14. Critical Analysis: Ethics As a researcher, is it ethical to remove the points that I eliminated and keep the remaining points? Why or why not?
15. How does the removal of the points affect the line (is the line steeper or more horizontal)?
16. Critical Analysis: Impact on r2 value Using your knowledge of linear regression lines and predictors, explain why the removal of the problem points has such a huge effect on the r2 value. Be sure to address what it is the r2 value measures and relate this to your answer.
17. Critical Analysis: Stock Guarantees? If your r2 value for Does Date predict Close was 99.9%, would you be assured to make money in the stock market by using the line to predict the future performance and investing accordingly? Answer by referring to the related Stock Market readings from the past.