PLOT DATA ANDTHE CURVE OF BEST FIT TI-83

Transcription

1 PLOT DATA ANDTHE CURVE OF BEST FIT TI-83 Jose H. Giraldo The process for the topics we want to cover will be illustrated with an example. Consider the data in the table below. Time (t) Population (P) We want to enter the data in the calculator, plot it and find a curve that fits these data. ENTERING THE DATA Follow the steps bellow. The screen you will see at each stage should look like the one displayed below the instruction. START BY TURNING THE CALCULATOR ON. 1. Press STAT 2. Press ENTER or 1 to see the LISTS. The lists may be empty or they may have some data points. 3. TO CLEAR THE LISTS In case a list has data, move the cursor to the top, using the arrow keys, to highlight it (in this case L 1 ). 4. Press CLEAR and return to the list using the arrow. 5. Repeat steps 3 and 4 to clear any other list. 6. Go to L 1 and enter the values corresponding to time. After typing each value press ENTER ENTERING DATA AND CURVE FITTING. TI-83. Dr. Giraldo 8/30/00 Page 1

2 If by mistake you enter a wrong value, scroll up, select the value and enter the correct one. If you want to remove a value, select it and press DELETE. 7. In L 2 enter the values of P If you decide to insert a value, select the place in the list where you want to insert it. This value is highlighted now, press 2 nd Insert. The entry you will use appears as zero. Now you can enter the desired value. Observe that when you enter the second datum value for list L 1, at the bottom of the screen you see L 1 (2)=1. It means that the second value in list 1 is 1. Likewise L 2 (1)=17.8 means that the first value in list 2 is 17.8 TO PLOT THE DATA For our plot we will consider the values in L 1 as the x values, and the values in L 2 as the y values. You will see that we can take as x or y values any desired list. This is how it is set up. 1. Press 2 nd Y= 2. Press ENTER or 1 3. Select ON Since the X List is L 1, to enter it use 2 nd 1. To enter L 2 use 2 nd 2. In the following steps we will set the window so that we can see all the data points. 4. Press ZOOM 5. Scroll down to number 9, or enter 9. This window guarantees that the data will be displayed on the screen. 6. Press ENTER to display the data. By pressing TRACE and use the arrow key you can see the coordinates of each point. RENAMING LISTS The information you enter is stored in the calculator as L 1 and L 2. However we can assign names to these lists and store them so that they can be retrieved later on as needed. Let s say we want to call L 1 TIME, and L 2 POPUL (only up to five characters for a list name). To ENTERING DATA AND CURVE FITTING. TI-83. Dr. Giraldo 8/30/00 Page 2

3 type a name use the GREEN KEYS (the alphabet). To do it press 2 ND ALPHA and then type the corresponding letters. I will indicate the steps to rename list L 1. After that as practice you will rename L 2 as POPUL In the home screen (2 nd QUIT) enter L 1,press STO, type TIME and press ENTER Your list is store in the LISTS folder. To see what lists you have stored press 2 nd STAT (LISTS) To see this list in a table format we need to insert it. Go to STAT 1:Edit. Move the cursor to the top of any of the lists. In this case I chose L 3. Press 2 nd DELETE (INSERT) Press 2 nd STAT (LISTS) Select TIME and press ENTER. The name shows up at the bottom of the screen. Press ENTER again and you will see the list. Now do the same to enter list L 2 as POPUL DELETING UNWANTED DATA VALUES Sometimes we want or need to remove data points from the plot to use only part of the plot, which is of interest to us. Of course one choice is to go to the list and do it one by one. However, when we have a large set of data points there is a more efficient way to do it. ENTERING DATA AND CURVE FITTING. TI-83. Dr. Giraldo 8/30/00 Page 3

4 Firs of all we need to obtain the plot that we want to modify. In case you need to reuse the original data, make sure you create a new list that you can store and later use. The plot we obtained before is the one we want to modify. This is the screen we should start on to make the changes to the data (to do this, see TO PLOT THE DATA above). For our purpose we want to see just the piece of the graph that looks like the peak of the mountain. Do as indicated below: From the LISTS menu select OPS and go to item 8:Select ( Press ENTER (it will take to the home screen). Select the lists names (x, y lists) from the LIST menu Press ENTER and you will see the graph that asks you for the first data value you want to see (Left Bound?) Move the cursor to the first point you want to see Press ENTER and you are prompt to select the last data value (Upper Bound?) Move the cursor to the last data point to be displayed. Press ENTER and you will see the portion of the graph you wanted to select. The lists have changed. ENTERING DATA AND CURVE FITTING. TI-83. Dr. Giraldo 8/30/00 Page 4

5 TRANSFERING DATA FROM CALCULATOR TO CALCULATOR To transfer data between calculators you need the link cable. Attach this to the port at the end at the bottom of the calculator. MAKE SURE IT IS TIGHT, if not you can not transmit data. Press LINK To receive, select RECEIVE and wait until it is done. To send, choose what you want to send. In this case we will send lists TIME and POPUL After selecting the list, select TRANSMIT and press ENTER. Done indicates that you were successful. SORTING THE DATA Some times you need to arrange the data in ascending or descending way. In case you want to sort L 2 be sure that the corresponding values of L 1 are kept, so the total data does not change. This is how it is done. Press STAT ENTER to see To order the data in ascending order, press STAT, 2 ENTERING DATA AND CURVE FITTING. TI-83. Dr. Giraldo 8/30/00 Page 5

6 In this case we want to order the values of L 2. So we need to enter (L 2, L 1 ). Press 2 nd 2, 2 nd 1 ENTER Go back to the lists window to see the new ordering. CURVE FITTING With the TI-83 not only can we find a certain type of curve that best FITS the data points, but also its equation. From the data we collected (shown below) we may decide to fit it with a quadratic (parabola) or cubic curve. This is the sequence of commands to achieve this: 2. Go to STAT 2. Move the cursor to CALC 3. Select CubicReg or enter 6 4. Press ENTER and type what you see on the window. ENTERING DATA AND CURVE FITTING. TI-83. Dr. Giraldo 8/30/00 Page 6

7 To enter Y 2 follow this sequence: 1. Press VAR 2. Select Y-VARS from the top and select 1 3. Select Y 2 as the location for the equation. 4. When you press ENTER you see The last command tells the calculator to find the cubic regression of list 2 vs. list 1. This is the information on cubic regression Press Y= and you will see the equations pasted to Y 2 Hit GRAPH and you will see the graph. These steps are shown below. One final comment. In case you want to delete a LIST from memory, you have to go to MEMORY (in yellow), choose DELETE, and now select what you want to delete. Another easier way is to rename the old list for a new one. Try this. ENTERING DATA AND CURVE FITTING. TI-83. Dr. Giraldo 8/30/00 Page 7