Not all sets of data points can be modeled

well by linear functions. For some data, we

want to find the best quadratic model or polynomial

model or exponential model. The

process is not linear regression, but quadratic

regression or polynomial regression or exponential

regression.

We can have the calculator do these other

types of regression in the same manner as

linear regression. For example, suppose we

want to model the following data with the

quadratic function of best fit.

We still enter the data in STAT Edit… and

then press **STAT** and choose the **CALC** submenu.

But now choose **5:QuadReg** for quadratic

regression. Then press **VARS**; move

RIGHT to select **Y-VARS**; hit **ENTER** for

Function; and then highlight whichever Y=

you want to put the equation into and press

ENTER.

And so our quadratic function is

[It works similarly for other types of regression. Just

choose the other type instead of LinReg or QuadReg.]

Suppose we want to plot the data

shown in the table. We will make

what’s called a scatterplot:

1. Press STAT.

2. Hit ENTER to choose 1:Edit.

3. This is where you enter points. L1 is like the x-column in our table; L2 is
the y-column. We don’t need L3.

- To clear an entire column of data, use the arrows to highlight the name of the column (L1, for example) and type CLEAR and then ENTER. Do not hit DEL, as this will delete the entire column and its name!

- If you need to remove just a single number, you can use the arrows to highlight it and then hit DEL.

Enter your data as shown.

4. Now, we need to turn on the statistical graph. Hit yellow button 2nd and then Y= to access STAT PLOT.

5. Hit **ENTER** to choose **1:Plot1…**

6. Now make sure that **On** is highlighted and the
rest of the choices are as below. If they are not, use your arrows to move to
the appropriate choice and type ENTER.

7. Hit **ZOOM** and choose option **9: ZoomStat**
(you may need to use the arrows to scroll down to find it—or just do **Zoom **
and then 9 for short). And there we have it!

Statisticians have developed a particular method, called
the

"method of least squares," which is used to find a “line of best

fit” for a set of data that shows a linear trend. The algorithm

seeks to find the line that minimizes the total error. These

algorithms are programmed into the graphing calculator and

are available for student use. The technical name of the process

for finding the line of best fit is linear regression.

1. Press STAT.

2. Press the RIGHT ARROW button to move to the CALC submenu.

3. Select 4:**LinReg(ax+b)** by moving to

highlight it and pressing ENTER (or just

typing 4). Do NOT hit ENTER again...

4. To make things easier, we want to automatically put the
equation of the line of

best fit into Y= so it will be graphed on top of the data. To

do this, press VARS; move RIGHT to select Y-VARS; hit

ENTER for Function; and then highlight whichever Y= you

want to put the equation into and press ENTER.

Now you get the following screen:

Press ENTER to run the command.

Your calculator returns the following screen:

What this tells you is that the line of best fit is

given by a linear equation y = ax + b, but that a

= 2.2 and b = 1.633333333. In other words, the

equation is

Y = 2.2x + 1.633333333

Notice that, if you press **Y=** now, the equation

has been automatically put in!

Finally, hit GRAPH and you can see the line

graphed along with the points of data!

IMPORTANT NOTE: Sometimes, after using

the STATPlot in one problem, it interferes with

regular Y= graphing in another problem, causing

an error. If this happens, try turning the STATPlot

off when you don’t need it for a problem.

To do this:

1. Press **2nd a**nd **Y= **to access STATPlot.

2. Press 4 to select PlotsOff and then hit** ENTER.**