## Regressions on a TI-83 or TI-84

### Entering data

Suppose you want to calculate a regression with the data in the table below:

X Y
1 4
3 8
4 9
6 14
1. To enter your data into your calculator, get to the list editor. To do that, press the button, then pick the "Edit..." option. (Press .)
2. You should then see a table. Across the top should be L1, L2, and L3. If not, see below. If there is any data under L1 or L2, move the selection so you have the list highlighted, press the button, and then press the down arrow to clear the list.
3. When both lists are cleared, select the empty data in L1 by moving your selection over the "_ _ _ _ _ _". Start entering your X-values under L1. Make sure you enter the data in order.
4. When you are done entering the X-values, move to the L2 column and enter your Y-values. Make sure they are also in order. The data should line up across the screen like it does in the table above, giving you something like this picture:

If your lists don't show L1, L2, and L3 across the top, reset your stats list editor. To do this, press , select option 5, "SetUpEditor", and press twice.

### Performing a Regression

Do this once: Press , then to get to the catalog. Press and use the down arrow to scroll down to DiagnosticOn. Press twice. The calculator should return "Done". (You only need to do this once on any calculator unless you clear the memory.)
1. Press the button. Use the right arrow to select "CALC". Scroll down to the type of regression you would like to use. You can use a linear regression (LinReg(ax+b)), quadratic regression (QuadReg), cubic regression (CubicReg), quartic regression(QuartReg), an exponential regression (ExpReg), a power regression (PwrReg), or a logistic regression (Logistic). Once you've selected the regression you would like to use (usually LinReg or QuadReg), press . For more information on picking the correct type of regression, see "Plotting the Data", below.
2. Press and then to enter "L1", press the button. Next, hit and then to enter "L2", then press . Your screen should now show something like "LinReg(a+bx) L1,L2,".
3. Press , press the right arrow to select "Y-VARS", and press to select "Function...". Choose the function you would like to store your equation in and press . (You will likely want to use "Y1".) Your screen should now look something like the picture below. (The first part will change depending on which regression you have chosen to use.)
4. You can now press , and the calculator will calculate your regression. The screen will now show the results of the regression. The first line should indicate what Y is in terms of X. Any other variables (a, b, etc.) will be listed below the equation. An r2 value is also given. This indicates the quality of the regression. If the regression fits the data well, the r2 value will be close to 1. The closer to 0 the r2 value is, the lower quality the regression is. The regression screen looks like this:
5. For your convenience, the equation for the regression has now been stored in Y1 for graphing or estimating.

### Plotting the Data

1. To set up plots: (only necessary if you've changed it, but it's a good idea to check) Press and then to get to the "STAT PLOTS" screen. Select the first plot (it is selected by default), and press . Move the selection over the upper-left type (a graph with dots), and press . Move down to "Xlist", press and then to use L1 as your X-values, and press . In "Ylist", press and then to use L2 for Y-values. Select the data marker that looks best to you (I recommend the open box on the left), and press . Your screen should look something like this:
2. To turn on the plot once you've entered data, press . If "Plot1" isn't inverted (white text and black background), move the cursor up to select "Plot1", and press . The plot is now enabled.
3. To set up the graph display of your data, press and scroll down to "ZoomStat" and hit (or simply press once you've opened the Zoom menu). Your data should now be displayed. If you used the data above, the plot should look like this:
4. If you look at this graph before you perform the regression, you should be able to determine what type of regression would be best for your data. If the data looks like a line, a linear regression would likely work best. If the data looks like a quadratic curve (similar to x2), use a quadratic regression. Other types of functions generally have matching regressions you can use.
5. To turn off the plot when you're done, press , move up to "Plot1", and press to un-highlight "Plot1".

### Estimating other values

1. To estimate a value based on a regression you have just computed, press , and press the right arrow to get to the "Y-VARS" menu. Press to select a function, select the same function you used in the regression (most likely Y1), and press .
2. Press , enter the x-value you would like to estimate the value for, press , and then press . The screen should now show the new estimate, and look something like this: