Date: October 18, 1998
Grade Level: 9, 10, 11, 12
Subject(s):
Description:
This lesson plan gives a set of real-life data values for students to graph. Instructions are given on how
to use the TI-83 graphing calculator to graph the points, as well as calculate and then graph the line of regression.
Goals: Have students learn that when data is collected and graphed, predictions can sometimes be made on what will happen in the future. This is done using a "linear regression equation".
Objectives: Students will:
1. Use 2 data lists, plot the data, not on graph paper but on the TI-83 graphing calculator.
2. Calculate and then graph a line of regression on the TI-83 calculator based on the data given, then make predictions
about what might happen in the future using the line of regression.
Materials:
Use the lesson plan here as an example, then apply it to the other examples I've included.
Linear Regression Line --- a ³best fitting² line for a certain group of data that have been plotted. This
allows you to make predictions about where other points would most likely fall.
Example: Below is a table of asteroid names, their average distances from the sun (in millions of
miles), and their orbital periods (the time it takes them, in years, to revolve around the sun).
Question 1: About how long would it take an asteroid that is 230 million miles from the sun to make 1 revolution?
Question 2: If an asteroid was discovered, and astronomers knew that its orbital period was almost exactly 4 years, about how far would you predict this asteroid to be from the sun?
| Asteroid Average Distance Orbital Period |
1. Make a scatterplot of the table above on your graphing calculator.
2. Graph the Linear Regression Equation in the form y = mx + b
Answer to Question #1 above: ³It takes about ______ years for an asteroid that is 230 million miles from the sun to make
one revolution.²
Answer to Question #2 above: ³An asteroid that has an orbital period of 4 years could be predicted to be about _______________ miles from the sun.²
Instructions for Creating a Scatterplot and Linear Regression Line on the TI - 83 Calculator
1. Let¹s begin solving the asteroid problem given above by entering our data points into 2 lists in the calculator. The lists are
found under the STAT key.
2. To enter or edit data points, which is what we want to do, you must use the EDIT menu.
3. So, hit STAT, then the EDIT menu, then edit again. Enter the values for the asteroids¹ distances into the first list, which the calculator creatively calls L1. Enter the asteroids¹ orbital periods into the second list, L2.
4. To plot these data points on a graph, we must create a ³stat plot²; this key is located above the ³Y=² key, just below the
screen on the far left. Hit the STAT PLOT key.
5. Now, you must choose Plot 1 by turning it dark, or selecting it, by moving the cursor on top of it (use the arrow keys). Now, hit ENTER; now that you¹re inside the Plot 1 area, turn it on by selcting ON, then hit ENTER.
6. Select the first graph to draw, let the Xlist be L1 andt let the Ylist be L2. The bottom line inside here lets you
choose what kind of marks you want on your graph: dots, little plus signs, or little squares. Select whichever one you like
best. We are now ready to graph!
7. In order to see your points on the graph, we must set the window up accordingly.
Hit the WINDOW key. Our lowest X value (smallest distance) in L1 is 204.4 , so let¹s let Xmin = 200.
Our largest X value is 257.4 , so let Xmax = 260. Since the difference between Xmax and Xmin is 60 , let the Xscl = 10.
That way, our x-axis will show 6 marks each 10 units apart. Similarly, let Ymin = 3, Ymax = 6, and Yscl = 1.
8. Now graph the scatterplot by hitting GRAPH.
***If you don¹t see your scatterplot, here are a couple of possible reasons why:
b. If nothing appears on your graph, you may not have turned Plot 1 on. Do STAT PLOT, then turn Plot 1 on.
Now, hit GRAPH again.
c. Your ³Window² is not set up as you thought it was. Hit WINDOW and check it.
You should get:
a = .0196
b = -.3963
You can write these values down and then go into the Y= menu, then manually type in
y = .0196x - .3963
OR, you can ³import² these values, letting the calculator copy them in for you. To do this, hit the
³y=² key. (Clear out any equations currently in here.) Put the cursor to the right of \Y1 = . Let¹s find the linear regression
equation and put it here.
Hit the VARS key located just below the ³down arrow² key. Go to #5, ³statistics², and enter this. See the new menu at the
top? The regression equation is under the EQ menu, so select EQ using the right arrow key. Now, choice #1 is RegEQ...
select this one, then hit ENTER. Your regression equation should have been copied into the Y1 = section of the calculator,
and it should be in the form y = ax + b. Now, hit GRAPH, and you should see the line of regression cut through the
scatterplot.
YOU DID IT!!!
10. You can now hit the TRACE key to answer Question 1 about how many years it takes an asteroid to make one revolution, given its distance. Simply hit TRACE, hold down the right arrow key until the x -value at the bottom of the screen is around 230, and record the corresponding y - value. To answer Question 2, get the y - value to be near 4, and record the corresponding x - value to predict the distance.
Other problems and the solutions for their lines of regression follow.
Practice #1 - High School and College GPAs
Practice #2 - Chirping Frequency and Temperature for the Striped Ground Cricket
*NOTE: When doing the next problem, you can use L1 and L2 again, or L3 and L4 if you want to keep the previous data in
L1 and L2. If you use L3 and L4, you must remember to turn Plot 1 off (since it is using L1 and L2) and turn Plot 2 on, using
L3 and L4 inside of Plot 2. Also, don¹t forget to change the ³window², or range, for the new problem, or you probably won¹t
see your scatterplot when you hit GRAPH.
|
|
Let High School GPA be your x values (List 1) and College GPAs be your y values (List 2).
1. Make a scatterplot of the data. (You may need to clear your old statistics and your old
graph: CLRSTAT and CLRDRAW)
2. Find the Regression Equation in the form y = mx + b
3. Graph the Regression Equation on your scatterplot to make sure it looks like the
best - fitting line.
4. a.) If you earn a 3.80 GPA in high school, predict what you would get in college for your
Freshman year. Freshman year GPA would be _______.
b.) If a freshman in college got a 3.60 GPA, what would she have got for her high
school GPA? High School GPA would have been _______.
|
|
Let chirps / sec be your x values (List 1) and temp., °F be your y values (List 2).
1. Make a scatterplot of the data. (You may need to clear your old statistics and your old
graph: CLRSTAT and CLRDRAW)
2. Find the Regression Equation in the form y = mx + b
3. Graph the Regression Equation on your scatterplot to make sure it looks like the
best - fitting line.
4. a.) If you had a listening device and used it in the morning when you woke up and
measured a striped ground cricket chirping at a rate of 18 chirps per second, how
warm would you say the ground temperature is?
³The ground temp. would be _______.²
b.) If the ground temperature reached 95°F, at what rate would you expect those little
guys to be chirping? ³They would be chirping at _______ chirps / second.²
| Asteroids: y = .0196x - .3963 |
| High School vs. College GPAs: y = .728x + .257 |
| Chirps vs. Ground Temp. y = 3.291x + 25.232 |
Use the answer sheet provided to have students give their answers to the additional problems I've given.
Check students' calculators as they work to see how they're doing.
The teacher will keep busy helping students troubleshoot problems!