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Instructions for Regression Analysis On the Graphing
Calculator
(To quit and exit this process on the graphing calculator at
any time, press the "2nd" key followed by the
"MODE" key.)
First, we will load the data into a table in the graphing calculator:
 | Press the "STAT" key on the graphing calculator. |
 | Select the "EDIT" function by using the DOWN arrow key to
position the cursor on the "1:EDIT" option and pressing the
"ENTER" key. |
 | A screen will be displayed in table format having column headings
"L1, "L2", "L3". |
 | To remove ALL existing data in these columns, use the arrow keys to
position the cursor ON the column heading, such as "L1". Then
press the "CLEAR" key followed by the "ENTER" key. This
will remove all existing data in column "L1". |
 | Remover ALL existing data in columns "L1" and "L2" if
they contain any data. |
 | Now the data is ready to be entered into the calculator. We are going to
enter the times in the "L1" column. To key in the first time of
"0", position the cursor in the "L1" column BELOW the
"L1" column heading. Now press the "0" key followed by
the "ENTER" key. This will list "0" as the first entry
in the "L1" column. Next press the decimal key "."
followed by each digit of the "Average of the Average Drop Times"
from the Data Analysis Chart for the height 10-inches. Then press the
"ENTER" key. Now the "Average of the Average Drop Times"
for 10-inches will be listed below the "0" entry in the
"L1" column. Continue this process until all "Average of the
Average Drop Times" are entered in the "L1" column in
ascending order. |
 | Now the height data is ready to be entered in column "L2".
Position the cursor in the "L2" column BELOW the "L2"
column heading. Remember to key in "0" as your first entry in
column "L2". Now continue to key in the heights in column
"L2" until all heights are entered in ascending order. |
 | To stop entering data and exit this screen, press the "2nd"
key followed by the "MODE" key. |
Next, we will set up the view for the graph:
 | To set up the view of the graph on the calculator, press the "2nd"
key followed by the "Y=" key located in the upper left-hand corner
of the calculator. (Note that the "Y=" key also stands for "STATPLOT".)
This will display the "STAT PLOTS" screen. |
 | Using the arrow keys, position the cursor on the first selection for
"1:Plot1" and press the "ENTER" key. This will display
the "Plot1 Plot2 Plot3" screen and "Plot1" will be
highlighted. |
 | Position the cursor on the word "ON" and press the
"ENTER" key. This will highlight the word "ON". (Note
that the word "Off" should NOT be highlighted.) |
 | Using the DOWN arrow key, position the cursor on the picture of the graph
having the points connected with a line. The graph pictures are listed as
"Type:". The graph having the points connected with a line is
usually located in the center of the first row of graphs. Press the
"ENTER" key to highlight this graph. |
 | Using the DOWN arrow key again, position the cursor ON the entry for
"Xlist:". This entry represents the x-axis on your graph which is
to be the "Average Drop Time" data that was entered in column
"L1" of the data entry table. Press the "2nd"
key followed by the "1" key followed by the "ENTER" key.
(Note that the "1" key also stands for "L1".) |
 | The cursor should be on the entry for "Ylist:" now. This entry
represents the y-axis on your graph which is to be the "Height"
data that was entered in column "L2" of the data entry table.
Press the "2nd" key followed by the "2" key
followed by the "ENTER" key. (Note that the "2" key also
stands for "L2".) |
 | The cursor should be on the entry for "Mark:" now. This entry
represents the symbol to be plotted on your graph for each specific (average
drop time, height) value of your data. Select the "square" by
positioning the cursor with the arrow keys on that mark. Now press the
"ENTER" key. The "square" mark should now be
highlighted. |
 | To exit this screen, press the "2nd" key followed by
the "MODE" key. |
 | Display the "STAT PLOTS" screen again by pressing the "2nd"
key followed by the "Y =" key. |
 | Look at the information displayed for "2:Plot2" and
"3:Plot3". If either or both of these Plots have "ON"
indicated next to them, they need to be turned "OFF". To turn OFF
Plot2, position the cursor on the selection for "2:Plot2" and
press the "ENTER" key. This will display the "Plot1 Plot2
Plot3" screen and "Plot2" will be highlighted. |
 | Position the cursor on the word "OFF" and press the
"ENTER" key. This will highlight the word "OFF". (Note
that the word "On" should NOT be highlighted.) |
 | Now exit this screen by pressing the "2nd" key
followed by the "MODE" key. |
 | Display the "STAT PLOTS" screen again by pressing the "2nd"
key followed by the "Y =" key. |
 | Look at the information displayed for "2:Plot2" and
"3:Plot3" again. If either or both of these Plots have
"ON" indicated next to them, they need to be turned
"OFF". Turn OFF the Plot as described in the previous steps. |
 | To exit this screen, press the "2nd" key followed by
the "MODE" key. |
Now we will modify the WINDOW settings:
 | The WINDOW settings are modified to enable us to see the graph correctly.
Press the "WINDOW" key to display the "WINDOW" screen. |
 | Using the arrow keys, position the cursor on the entry for "Xmin=".
Now press the "(-)" key followed by the decimal "." key
followed by the "1" key. DO NOT PRESS THE "ENTER" KEY.
The value "-.1" should now appear as the "Xmin=" entry. |
 | Use the arrow keys to position the cursor on the entry for "Xmax=".
Now press the decimal "." key followed by the "8" key.
DO NOT PRESS THE "ENTER" KEY. The value ".8" should now
appear as the "Xmax=" entry. |
 | Continue in the same manner using the arrow keys to position the cursor on
the following entries. Change the entries to those listed here. |
Xscl = .1
Ymin = -10
Ymax = 70
Yscl = 10
Xres = 1
 | Press the "2nd" key followed by the "MODE"
key to exit the "WINDOW" screen. |
Now we will view the graph:
 | To view the graph, press the "GRAPH" key located in the upper
right-hand corner of the calculator. |
 | On paper, make a copy of this graph to turn in to your teacher. Label the
x-axis "Time" and the y-axis "Height". The graph is
showing the rate of fall in terms of (height in inches)/(time in seconds).
Title your graph "Rate of Fall". |
 | To exit the graph on the calculator, press the "2nd"
key followed by the "MODE" key. |
 | The graph of the sample test data reflects a graph increasing
exponentially or by a power. |
Now we will use regression analysis to determine the equation of the
"Rate of Fall":
 | First, we must remove the zero entries from columns "L1" and
"L2" in the data entry table. |
 | Press the "STAT" key on the graphing calculator. |
 | Select the "EDIT" function by using the DOWN arrow key to
position the cursor on the "1:Edit" option and pressing the
"ENTER" key. |
 | A screen will be displayed in table format having column headings
"L1", "L2","L3". |
 | To remove the "0" entry from columns "L1" and
"L2", using the arrow keys, position the cursor on the
"0" entry. Then press the "DEL" key for delete. Repeat
this process to remove the "0" entry from the other column. |
 | Now press the "2nd" key followed by the
"MODE" key. |
 | Now press the "STAT" key to display the screen with column
headings "EDIT" "CALC" and "TEST". |
 | Use the arrow key to position the cursor on the column heading
"CALC". This will change the options displayed on the screen. |
 | Since the graph of our data showed "Time" increasing
exponentially by a power, we will use the DOWN arrow key to highlight the
"A|PwrReg" option. This stands for power regression. Now press the
"ENTER" key. The screen will display the word "PwrReg"
at the bottom of the screen with a blinking cursor following it. |
 | Press the "ENTER" key again. BE PATIENT. It will take a few
seconds before the next screen is displayed. |
 | The next screen will look similar to the following: |
PwrReg
Y = a*x^b
A = 179.9581443
B = 1.928335281
R^2 = .9981017564
R = .9990504273
Copy all of the above values from your calculator on your Data
Analysis Chart next to "Calculated Regression Analysis:". Note
that "Y= a * x^b" is the calculators way of displaying the math
equation
Y = a * (x^b).
Below the equation, the calculator displays the values of "a"
and "b" for the equation. The closer the "r =" value is
to "1", the more accurate the equation is.
 | Now press the "y =" key. "Plot1" should still be
highlighted at the top of the screen. For "Y1 =" enter the above
equation, substituting the values for "a" and "b" as
determined by the calculator in the previous step. For the above example
"179.9581443 * x^1.928335281" would be entered for "Y1=
". Also record this equation on the Data Analysis Chart in the
space labeled "Regression Analysis Equation:". |
 | Now use the arrow key to position the cursor ON the "=" sign in
the equation. Press the "ENTER" key to highlight the " =
" sign for "Y1 = ". |
Now we are ready to view the graph:
 | Press the "GRAPH" key. |
 | The calculator will first plot the data for the data entry table for
Plot1. Then the calculator will plot the graph of the above equation that
you entered for "Y1 = ". The two curves will plot on the same
graph. If your regression analysis was good, the two curves will look like
they lay on top of each other. |
 | To modify the "Y = " equation in order to "tweak" it
to make it more accurate for your data, press the "Y = " key
again. Try rounding the values for "a" and "b" to the
nearest whole number. Then press the "GRAPH" key to see if the two
curves appear to lie on top of each other more than before. |
 | You can continue to modify the values for "a" and "b"
to attempt to find the best equation for your data. |
 | Also, enter your equation that you determined from your Data Analysis
Chart that is recorded in the space labeled "Pattern Analysis
Equation" into the calculator and compare it to your data. Substitute
"Height" in your "Pattern Analysis Equation" with the
letter "y". Substitute "Time" in your equation with the
letter "x". Depending on how you wrote your "Pattern Analysis
Equation", you may need to rewrite the equation expressing
"y" in terms of "x" (i.e. y = …..) in order to enter
it into the calculator correctly. Enter your equation in place of the
calculated regression analysis equation for "Y1". Press the
"GRAPH" key to view the graph. |
 | Record the equation that you feel best fits your data on the Data
Analysis Chart for "Final Equation:" |
 | Record your conclusion for your 2nd hypothesis concerning a
ball's rate of fall on the Data Analysis Chart in the space for
"Conclusion". Does the ball gain speed as it falls, or does it
fall at a constant rate? |
 | Compare your equation with the scientific equation reflecting the motion
of a falling object that your teacher will give you. The value for
"height" in this equation should be in inches. Include a brief
discussion in your "Conclusion" about the comparison of these two
equations. |
 | Turn your graphs and Data Analysis Chart in to your teacher along
with a blank Evaluation Sheet. |
 | Congratulations! You have completed the "Exploring Gravity"
experiment. |
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