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Teacher Resources

Calculator Review

Texas Instrument calculators TI-83 and TI-84 are recommended for completing the activities in this module. The following guides are based on the operation of the TI-83 and TI-84 models.

For accessibility, the TI-84 Plus with the Orion add-on is recommended.

> Entering Data into Lists
> Creating a Scatter Plot
> Linear Regression
> Graphing a Regression Equation
> Residuals

Online Graphing Resources

> Shodor Applet opens in new window
> Desmos Graphing Calculator opens in new window
> Cubic Function Explorer opens in new window
> Graphical Function Explorer opens in new window


Entering Data into Lists

In math class, you may be asked to analyze and graph a set of real-world data.  When you have a set of real-world data, first you must enter the data into lists in your graphing calculator.
The calculator lists display the following data:  List 1 includes the values 4, 5, 6, 7, and 8.  List 2 includes the values 48, 80, 110, 160, and 220
First, make sure your lists are clear.  Press
calculator stat buttoncalculator 1 button

If your lists are not clear, such as this list:
Go to the top of each list by using the
up arrow and press
calculator clear buttoncalculator enter button
The calculator lists display empty lists.
Repeat for each list that has data until
all lists are empty.

Note:  If you accidentally delete a list, press:
calculator stat buttoncalculator 5 buttoncalculator enter button

Now, we will enter the data below into the graphing calculator:

Year

0

1

2

4

9

Height of Tree (feet)

2

3.5

5.5

7.5

12

Since the independent variable is the year, we will enter the year values into L1.  The dependent variable (height of tree) values should be entered into L2.
Press
The calculator lists display the following data:  List 1 includes the values 1, 2, 3, 4, and 9.  List 2 includes the values 2, 3.5, 5.5, 7.5, and 12.calculator 0 buttoncalculator enter buttoncalculator 1 buttoncalculator enter buttoncalculator 2 button
calculator enter buttoncalculator 4 buttoncalculator enter buttoncalculator 9 buttoncalculator enter button

Now press
calculator right arrow buttoncalculator 2 buttoncalculator enter buttoncalculator 3 buttoncalculator decimal point buttoncalculator 5 buttoncalculator enter button
calculator 5 buttoncalculator decimal point buttoncalculator 5 buttoncalculator enter buttoncalculator 7 buttoncalculator decimal point buttoncalculator 5 button
calculator enter buttoncalculator 1 buttoncalculator 2 buttoncalculator enter button

Creating a Scatter Plot

Using the cost of milk data from the last practice section, we will now view the graph of the scatter plot using the graphing calculator.
The calculator lists display the following data:  List 1 includes the values 0, 1, 2, 3, 4, 5, 6.  List 2 includes the values 1.37, 1.39, 1.4, 1.39, 1.43, 1.44, and 1.48.
Your list screen should look like this: 

To return to the main screen, press
calculator second  buttoncalculator mode  button


The calculator stat plot screen is displayed and Plot 1 is highlighted.Then press
calculator second  buttoncalculator y equals button

Select 1: Plot 1

 

The calculator plot 1 screen is displayed.  The scatter plot is highlighted.  The x-list is list 1 and the y-list is list 2.Now press the following to match the
screen to the right:

calculator enter buttoncalculator down arrow buttoncalculator down arrow buttoncalculator second  buttoncalculator 1 button
calculator enter buttoncalculator second  buttoncalculator 2 buttoncalculator enter button

Now, you must adjust the window to view the graph.  According to your data, the years are from 0-6 and the cost of milk range from 1.37 to 1.48, so press:

The calculator window screen is displayed.  The x-min is 0, x-max is 10, with a scale of 1.  The y-min is 1, the y-max is 1.75 with a scale of 0.05.calculator window buttoncalculator 0 buttoncalculator enter buttoncalculator 1 buttoncalculator 0 button
calculator enter buttoncalculator 1 buttoncalculator enter buttoncalculator 1 buttoncalculator enter button
calculator 1 buttoncalculator decimal point buttoncalculator enter buttoncalculator 5 buttoncalculator enter button
The calculator scatter plot for the data is displayed with the given window above.calculator decimal point buttoncalculator enter buttoncalculator 5 buttoncalculator enter button

Now press
calculator graph button

 

If you are not happy with the window, you can always return to the window screen and adjust the values for maximum, minimum, or scale values.

When you are finished viewing the graph and ready to return to the main screen, press
calculator second  buttoncalculator mode  button

Note:  An alternative way to adjust the window is to press

calculator zoom buttoncalculator 9 buttonThe ZOOM”  window is displayed.  Button 9 represents “ZoomStat”
The scatter plot using the Zoom 9 feature is displayed.


Linear Regression

Since most of the data we encounter in the real-world is not perfect, it is often hard to find an equation to fit the data perfectly.  If the data seems to follow a somewhat linear pattern, we need to find the equation for the line of best fit.  To do this we use the linear regression function on the graphing calculator.

Using the tree growth data from the last practice section, we will now determine the equation for the line of best fit.The calculator lists display the following data:  List 1 includes the values 1, 2, 3, 4, and 9.  List 2 includes the values 2, 3.5, 5.5, 7.5, and 12.


Your list should have the following:

:  The calculator calculate screen is displayed. Entry 4: Linear Regression is highlighted.

First to return to your main screen, press
calculator second  buttoncalculator mode  button

Now press
calculator stat buttoncalculator right arrow buttoncalculator 4 buttoncalculator enter button
The calculator main screen is displayed after the linear regression is run.  The screen displays equation y equals ax + b, where a equals 1.080708661, and b equals 2.641732283.

The screen to the right shows the linear
regression equation.  The slope of the line is
the a-value and the y-intercept of the line is
the b-value.  To write the equation for line of
best fit, always round to at least three decimal
places: y = 1.081x + 2.642.   .

When finished, you can clear your main screen by pressing
calculator clear button

Graphing a Regression Equation

It is important to look at the graph of the regression equation on the same grid as the scatter plot to see just how well the graph of the regression equation fits the scatter plot.

We will use the Mass of the Pennies data to illustrate the steps for displaying the graph of a regression equation on the same grid as a scatter plot.
The calculator lists display the following data:  List 1 includes the values 4, 8, 12, 16, 20, and 24.  List 2 includes the values 20.2, 31, 40.8, 42, 52.6, and 61.4.
Your list should look like this:     

 

 

 

The calculator window screen is displayed.  The x-min is 0, x-max is 30, with a scale of 1.  The y-min is 0, the y-max is 70 with a scale of 2
Now adjust your window to match
the following:

 

When finished, press
calculator graph button
The calculator scatter plot for the data is displayed with the given window above.

Recall that the next step in this process involves calculating the regression equation for the data. Since the Mass of the Pennies data appears to be linear we will use the steps below to determine the linear regression equation for this data.

Press
calculator second  buttoncalculator mode  buttoncalculator stat buttoncalculator right arrow buttoncalculator 4 button
The calculator scatter plot for the data and line of best fit is displayed with the given window above.calculator vars buttoncalculator right arrow buttoncalculator 1 buttoncalculator 1 buttoncalculator enter button

Your linear regression equation should reappear.

The calculator screen to represent the linear regression is displayed.  Y equals a x plus b, where a equals about 1.94 and b equals about 14.13.


Now to view the graph, press
calculator graph button.

This linear regression equation seems to be a good fit, as most of the data points are either touching the line or are close to the line.

Residuals

Once you have found a regression equation you can calculate the residuals. 
The calculator stat plot screen is displayed and Plot 1 is highlighted.

calculator second  buttoncalculator y equals  buttoncalculator 1 button

Change the Ylist to Resid:
The calculator plot 1 screen is displayed.  The scatter plot is highlighted.  The x-list is list 1 and the y-list is list 2.calculator down arrow buttoncalculator down arrow buttoncalculator down arrow buttoncalculator second  buttoncalculator stat button

Press the calculator down arrow buttonkey until you see Resid,
press calculator enter button then calculator graph button

To adjust the window of the graph, press
calculator zoom buttoncalculator 9 button

To see the actual residual values you may trace the points on the graph.