Unit 3 of Welcome to the Graphs of Life: Analyzing Graphs of Own Creation
Objectives
1. You will be able to create graphs based on data you've created.
2. You will be able to identify the kind of graph that your graph is.
3. You will be able to identify the kind of relation of your graph.
4. You will be able to draw a line of best fit for your graph.
Finding Regressions
We have already seen one type of "regression" or equation which approximates the points on a graph - linear regression. Let's establish a systematic way to find such lines of best fit on your TI-83 Plus calculator. A regression is a line which "best fits" the graph and describes the shape that the points on the graph take, as we've seen from linear regression in day 1 of unit 2.
For our purpose, text within [ ] brackets will represent the text on a button on your calculator.
How to Enter Points into Your Calculator
File:Findingthelineofbestfit.pdf
1. Press [Stat]
2. Press [Enter] on selection 1: Edit
3. To clear data, move cursor to L1 and L2 and hit [Clear]
4. Enter values for x in L1 and values for y in L2, press [Enter] after every value
Test Regressions
In every case, record the value of R or compute the value from R^2. Find the regression with the closest R value to 1 or -1. The equation given for this regression will be the equation that best fits the data. Record each equation given for your reference.
1. For a linear regression, press [Stat] then highlight "Calc" and select choice 4: LinReg(ax+b). Press [Enter]. Record the value of R.
2. For a quadratic regression, select choice 5: QuadReg. Record the value of R.
3. For a cubic regression, select choice 6: CubicReg. Record the value of R.
4. For a quartic regression, select choice 7: QuartReg. Record the value of R.
5. For an exponential regression, select choice 0: ExpReg. Record the value of R.
Examples to Try
Find the line of best fit or regression for the following set of points: (0,1) ; (1,2) ; (2,4) ; (3,8)
Find the regression for the following set of points: (0,0) ; (1,2) ; (2,9); (3,26)
Activity: Class Discussion
What is the best regression of each set of points?
To Graph Oneself
Follow the link to the project "To Graph Oneself". This project will use your graph recognition skills and understanding of the relationship between equations and graphs on a graph which you create from scratch based on your own data.
Peer Evaluation
After you have completed the To Graph Oneself project, you will evaluate the project of one of your peers. Comment on the following:
1. Are the graph constructed properly from the data?
2. Do the regressions match the graph?
Reflection
What have you learned in this unit, including the project? How is regression useful in the real world? How does graphing relate to your life? What are some other ways that graphing might relate to your life?