Well Runs Dry - Activity 2 Problem
Linear regression is the process of finding a linear equation to describe real life situations that increase or decrease in a line. Lots of things out there do!
Here's a recipe for finding the equation:
- Gather data points
- Graph them
- Draw your "line of best fit"
- Select two points on the line
- Find the slope between the two points
- Use the slope and one of the points to find the equation
Let's look at an example that we like to call THE SECRET, MESSAGE, WHISPER, CHAIN.
Did you ever play that game when you were a kid where you whisper something into someone's ear and then they whisper the message to the person beside them and then that person whispers the message to the person beside them and so on until you get to the end of the chain?We recently played this game with six people. We recorded the time it took to reach the end of the chain for only one person being told, then for two people passing it on, and then for three, four, five, and six. It took longer each time we added a person, and we thought that maybe an equation could describe the process, so we did a regression.
It turns out we were right.
You can describe this process with an equation.
PART 1
Use the following table of our results to determine the linear equation that describes this data. You should do this BY HAND and also using your CALCULATOR. SHOW ALL WORK ON HANDOUT.
No.
of persons told the secret
(x) |
Seconds
to reach the end of chain
(y) |
|
(1
|
3) |
|
(2
|
7) |
|
(3
|
9) |
|
(4
|
11.5) |
|
(5
|
14) |
|
(6
|
19) |
Use the equation (calculator equation will be most accurate) to answer the following equations:
1. How long will it take 100 people to pass the message?
2. How many people could hear the message in 1 hour?
When you are finished, turn in your HANDOUT and pick up your homework (Activity 2 - Graphing Line of Best Fit)
