So are we counting down the weeks yet? I certainly know my Year 12's are! It is post-Trials now and most of them have to perk themselves back up and get going again. We have almost completed the course - just the Three Median Regression Line (TMRL) to go. I overheard some of our teachers today saying that they think that the TMRL is a monster of a procedure, and I would have to agree. There are so many steps to remember, and from my years of teaching General, I know a lot of kids have trouble remembering those steps.

I recall speaking to one teacher from a different school who said that he doesn't really give the TMRL much attention - it is too hard, too much work and such a small chance they'll be asked something about it. That would have been a shame for the 2004 kids who had a question in their HSC on it worth 5 marks.

This lesson is not going to go through the steps of how to get the TMRL. It is simply going to be a black-box use of the calculator on getting the equation of the line. I'll leave the teaching and the 'best way to present it to the kids' up to you. If you have any ideas about teaching it, please feel free to reply to me. It might start a nice little forum piece!

So this particular lesson is to help all those kids (and teachers) who find getting the equation of the TMRL difficult.

Lesson 4
The data we'll use is from a One Lesson Wonder we have at CasioEd. If you would like to download the .pdf version of it, just click here. It deals with forensics and is a really good activity for the kids.

Part 1 - Entering data in STAT mode
We are going to find the TMRL using the correlation between a person's height and the length of their middle finger. The data is shown below.

Turn on your calculator and enter STAT mode by using your keypad and press EXE (figure 1). Make sure all the lists are empty. Remember you can use the arrows on your keypad to move around the columns. To delete any content, press 'des' (F6) and you will see two delete options - one is DEL and the other is DEL-A (figure 2).

• DEL just deletes the single element that the cursor is on,
• DEL-A will delete the entire column that the cursor is in.

Press DEL-A and then YES (F1) for any column that holds data (figure 3). Move the cursor to the first row in List 1. Start entering the heights from the table above. This is done by typing the number and pressing EXE. Now enter the middle finger lengths into List 2.

Part 2 - Displaying the data
We are going to create a scatter graph. The command down the bottom of the screen we are looking for GRPH (F1) (figure 4). You may have to press 'des' (F6) to get to it. Enter GRPH (F1) and then SET (F6) (figure 5). This is where we tell the calculator the details of our graph. I can't emphasise enough to my kids that when they go to GRPH or CALC (homework 1) in STAT mode that they must go to SET everytime!

You will see at the top of the screen that we are setting up StatGraph1 (you could have 3 graphs going at the same time if you wished). Let's go through each of the settings (figure 6). Use your down arrow to move the bar down a row.

• Graph Type - Scat (F1)
• XList - List1 (F1)
• YList - List2 (F2)
• Frequency - 1 (we don't have a frequency column so each piece of data is counted as a single entry)
• Mark Type and Graph Color - what ever you fancy.

Press EXE and then GPH1 (F1). You should have a lovely speckle of dots (figure 7).

Part 3 - Equation of the TMRL
When you have your graph displayed, you will see all different types of regressions. Med (F2) is the one we want. Press F2 and you will see the equation is calculated, y = 0.38888x + 13.04629 (figure 8).

There are two options at the bottom of the screen - you can draw it or copy it. Let's copy it first. Press COPY (F5) and you will be taken to the GRAPH mode (figure 9). The bar is on Y1. Press EXE now to enter it in Y1. You can move the bar down to any other one if you wish and press EXE. You are then taken back to the regression screen and it looks as though nothing has happened but something has, and we will look at it in just a second.

Let's now draw the line through the points to see how it looks (figure 10). Press DRAW (F6) and you will see the line drawn through the data. Notice if you try to use Trace (SHIFT F1) you can only trace the points, not the line. This is why we copied it to GRAPH mode.

Part 4 - Graph the equation
Press your MENU key and enter GRAPH mode. Your graph is there stored in Y1. You can draw it and trace on it now by pressing DRAW (F6) (figure 11).

One last thing. Tracing is often not a good method to get coordinates from. The calculator only lands on the coordinates where there is a pixel on the screen. Instead, press MENU and enter TABLE mode. You will still have the equation stored in Y1 and there you can set the values for x that you want to calculate by going to RANG (F5).

Part 5 - Extra exercise
Just for a little exercise, here is another data set. See if you can calculate the equation of the TMRL.

The TMRL equation should be y = 0.76x + 13.9

That it! Well done. Please feel free to forward any questions or comments to me by replying to this email or the contact us page at CasioEd (link below).

Marty Schmude