WORKSHEET FOR SOFTWARE:  GRAPHICAL ANALYSIS

(by Karen Vaughan, Pitt County Schools)

PART 1:  LINEAR DATA

Follow each step carefully.  
Open the Graphical Analysis icon on the computer.  Click OK.
 

PROBLEM #1-  CAN YOU PREDICT THE TEMPERATURE BY LISTENING TO CRICKETS?

This is an interesting phenomena.  The data window will be selected.  Enter the following real data.  Use the down cursor to enter the temperature as the x data and the number of chirps as the y data. 

Temperature (F)	59	65	73	82
Number of Chirps	76	100	120	132

1. Click Data on the menu bar, go to column options, click on x, OK, and change decimal places to 0, OK or Enter.  Do the same for the y.
   
2. Click anywhere on the Graph Window.  Click on Graph on the menu bar.
   
3. Click on Connecting Lines to deselect it,  look at the effect on the menu bar.
   
4. Click on Analyze on the menu bar.  Click on Automatic Curve Fit.  (this is also on toolbar, looks like "golden arch")
   
5. Click on Linear curve fit.  Click on OK.  Click OK, keep fit.
   
6. Click on box with the equation, hold and drag it away from the line.
   
7. Write on this paper the values for m and b as y= m x+ b (do not round off)
   Y =_____________   X =_______________
   This is the equation of the linear model for the phenomena of chirping crickets.
   
8. Click on Analyze.  Click on Interpolate.
   As you move the cross hair with the mouse you will see the x and y variables change in the box on your graph window.
   
9. Move the mouse until x=79 degrees.  What is the number of chirps that are predicted at this temperature?_________.  Notice that there is more than one answer, so round off the prediction.
   
10. Click on Zoom Out (it looks like a magnifying glass with OUT written) on toolbar and continue to use the mouse to analyze and predict the temperature when there are 157 chirps._______________
    
11. Click on Analyze, Examine, and move the cursor up and down the line.  Original data points will be compared with the points from the regression line.  Compare the original point (59, 76) with the prediction (59, ).
    
12. Click on Window on the menu bar, Graph Options, Background Grid, OK.  This is the give the dots on the background of your graph.
    
13. Change the domain by clicking on the maximum x on the graph and type in 125, enter.  Change the minimum x to 0.  Click on the min and max for the range and change y min to 0 and y max to 200.  You may need to move the equation box again.
    
14. Predict the number of chirps when the temperature is 32 degrees._______________(Round off).
    
15. Click on the Text Window and type "x=temperature in F and y=number of chirps of cricket".
    
16. To print copy, click on file, print, whole window, OK.
    
17. Click on File, New.
    Do not save problem #1 unless you want it for some other time.
     
     

PROBLEM # 2 CAN YOU PREDICT HOW MUCH MONEY YOU WILL MAKE DEPENDING ON THE NUMBER OF YEARS YOU CHOOSE TO STAY IN SCHOOL?

Click on the data window if it is not already selected.
Enter the following data that is based on a survey published in the News and Observer of ten 25 year old people stating their income and the number of years education completed.
 

years of education	8	10	12	12	13	14	16	16	18	19
income (thousands)	13	14	17	17.5	20.6	21	24	25	30	31

1. Click Data on menu bar, Column Options, click on x, OK.
   Go to rounding, and change the decimal places to 0.  Click OK.
   Do the same for y, but put 1 decimal place.
   
2. Click on Graph Window.  Click Graph on the menu bar.  Go to Connecting Lines, deselect it.
   
3. Click on Analyze on menu bar.  Click on Automatic curve fit, Linear, OK, OK, keep fit.
   
4. On the graph Window, click on box with equation, hold and move it away from the line.
   Write the equation of line, y=mx+b (Do not round off)
   Y =_____________ X =_______________.
5. Using the equation, make some predictions by doing the following:
   Click Analyze on menu bar.  If not already selected, select Interpolate.
   Move mouse until x=10 in the box, write the range of y values___________________and compute the average y=_____________(in dollars).  This means that with a 10th grade education, the model based on this research predicts that you can expect to make about this amount of money.  Remember to put a comma where the decimal is.  Look back to your data set for this problem and explain the reason that this should be done.
6. Compare this information to the data for a 12th grade education.  Use the mouse to find when x=12, the range of y values___________________, average these to get Y=_______________.  Subtract the predicted salaries, 12th grade-10th grade, and write down the estimated difference    in salary that completing high school can mean.________________
   
7. Use the same method to predict the salary that a person who has 2 years of education beyond high school. y=__________________
   
8. Click on Text window in the lowest left corner and type in the following:
   "This model predicts that a person with 14 years of education will make about (you fill in the amount)_______________________".
   
9. Comment on validity of this model and predictions________________________________
   ________________________________________________________________________
   
10. Print a copy of the entire screen.
    
11. Click on Graph Window.  Change the domain to 0<x<20 and the range to -20<y<30.
    Examine the y-intercept.  Interpret the meaning of this data.________________________________________
    
12. Print  a copy of this new graph, click on File menu bar, Print, Selected Display.  This will only print the new graph and notice that the size of the graph is larger.  Compare the printout for Problem#1 to Problem #2.  The first has a grid.  You must remember to select this if you want it in your printed copy.
    
13. To continue, click on File, New to get a clear window for problem #3,.
     

PROBLEM #3  JUST HOW LONG DO YOU NEED TO STUDY TO PASS ALGEBRA?

This data is actual data collected from an Algebra II class.  It  correlates the grade on a chapter test with the amount of time that the student said that he studied for the test the previous night.
 

time studied (min)	20	0	30	60	30	30	0	0	30	0	25	10	20	0	60	15	32	18	25	0	30	90	50	15
grade	72	64	70	81	60	58	51	88	61	55	46	51	67	49	54	73	88	69	43	54	95	100	90	65

1. Enter the data x as time studied and y as grade.  Adjust decimals on the data window.  Notice the mess of connected points.
   
2. Click on Graph Window.  Click on Graph on menu bar.  Click on Connecting lines to deselect.
   Change the domain 0<x<120 and the range 0<y<100.
   
3. Click on Analyze on menu bar.  Click on Automatic Curve Fit.  Click on Linear, OK, OK keep fit.
   Write the linear equation, y= m x + b.  (Do not round off)
   Complete:  Y=_________________X=________________
   Interpret Slope_______________________________________________
   Interpret the y intercept_________________________________________
   
4. Click Analyze on Menu bar.  Select Interpolate (if not already selected).
   Use this equation to predict the grade that you will probably make after studying
   30 minutes_________________60 minutes___________________ 90 minutes___________________
   
5. Predict the amount of time you need to study to make 100 on the test _________________________
   Convert that answer to hours and minutes.______________________
   
6. Click Window on the menu bar, Arrange Window, and pick the choice in the top left, OK.
   
7. Click on the text window and type in  a description of your data.
   File, Print, Whole Screen.
   NOTE:    The students in the class initially said that they studied about 30 minutes for a chapter test.  This data analysis convinced them that only studying the 30 minutes was not sufficient for the grades that they wanted to make.

   EXTENSION TO PROBLEM #3:  
   On the TI-82/83 Graphics Calculator, you have two choices for a linear regression line.    One is the Least Squares Line (linereg) which is the same as the one given here.  The other is the Median-Median Line (med-med) and is the best predictor when you have outlying data points such as someone who studies 120 minutes (2 hours) and makes a 35 on the test.  Put this data in the TI and find equations of both regression lines and make predictions:
    

	equation	0 minutes	30 minutes	60 minutes
lin reg
med-med

Print out a copy of the graph of these two lines from your TI by using the TI Link and its software.  Have the calculator showing the graph, connect the TI link to the computer and the calculator, open the TI software, select Link on the menu bar, select Get LCD for TI, select Printer (large), Receive, OK. (The TI83 software is very similar)

PART II:  NONLINEAR DATA

PROBLEM #4 - HANDSHAKE (QUADRATIC DATA)  
If each of the 35 students in a classroom shakes hands (without duplication), how many handshakes would that be?

First you need to collect some data and put it in the following chart:
 

# students	# handshakes
2
3
4
5
6

Notice that you cannot use 1 student because there would be no handshake. 

1. Enter the data in the two columns, using the cursor keys.  Click data on the menu bar, go to column options, click on x, OK, and change decimal places to 0, OK or enter.  Do the same for the y. 
2. Click anywhere on the Graph Window.  Click on Graph on the menu bar.  Click on Connecting Lines to deselect it.  This will get rid of the connections between the points.
   
3. Click on Analyze on the menu bar or the Automatic Curve Fit on the toolbar (looks like a 'Golden Arch').  Click on Quadratic curve fit.  Click on OK.  Click OK, keep fit.  Click on the box with the equation, hold and drag it away from the curve.
   
4. Write the equation of the quadratic model______________________________
   
5. Click on the largest x value at the bottom of the graph, delete it, type in 40, enter.
   Click on the largest y value at the left side of the graph, delete it, type in 700, enter.
   You may need to move the equation box again. 
6. Click on Analyze on Menu bar.  Click on Interpolate.  Move cursor up and down the curve and you will see the values for that are predicted by the equation.  Find the predicted value for 35____________________.
   There is a choice of several decimals when x=35; however, the decimals do not make any sense since we are looking for the number of handshakes. 
7. Enter this equation in your graphics calculator in the Yemen.  Then 2nd quit.  2nd Vas, #1 Function, #1 Y1, then type in (35), enter.  Compare the answer with the one you got from the computer.  Click on text window and type "For 35 students, the computer predicts______________and the graphic calculator predicts_____________".
   
8. Print a copy, click on file, print, whole window, OK.
   
9. Click on File, New.  Do not save this problem.
    
    

PROBLEM #5-BREAKING DISTANCE IN A CAR

    The NC Driver's Manual gives the following data for the stopping distance that a car goes after the brakes are applied when going a given speed:

speed(mph)	braking distance (ft/sec)
25	28
35	53
45	93
55	150

Enter this data in the data columns and follow the same procedure as you did in Problem #1 to get the quadratic fit.
Write the equation__________________________________________
Predict the braking distance when going 65 mph_________________75mph_____________________
Print out a copy of your worksheet.
Click on File, New, Do not save.
 

PROBLEM #6-A GAME OF DICE

    Two students have collected data by tossing 50 dice on the floor and removing all the one that show a 6, counted the rest so the data would be (1,#).  The tossed them again and repeated the process until all the dice were removed.  They have entered the data into their graphics calculator in L1 and L2.  Do not enter the last data point with (#,0).
            DATA:
 

x	# toss	0	1	2	3	4	5	6	7	8	9	10	11	12
y	# dice	50	42	36	30	25	21	18	15	10	7	5	4	2

 
They want to turn this project into their math teacher for a grade and plan to use Graphical Analysis software for a nice printed presentation.  Connect the graphics calculator to the computer with the TI Link.  Click File on Menu bar in software, Import 82/85.
On graphics calculator, do 2nd Link, #2Select, cursor down to L1, enter, L2, enter (you will see marks beside them) cursor to transmit, #1 transmit, (see data go into computer).
On computer click on graph window, deselect connecting lines.
Click Analyze on menu bar, Automatic Curve Fit, Exponential, OK, OK, keep fit.  (This will not be great.) Write down your equation.
You might also do the exponential curve fit on the TI graphics calculator and compare:

Print a copy:  Click on File, Close.  Do not save.

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