Getting ŷ from Any x in a Regression on the TI-83/84/89

Summary:  The regression line represents the model that best fits the data. One important reason for doing the regression in the first place is to answer the question, what ŷ value does the model predict for a given x? This page shows you three methods, which all yield the same answer (aside from rounding).

See also:  Scatter Plot, Correlation, and Regression explains how to find the regression line from the data points.

Following that example, you could predict the likely temperature of the freezer at a dial setting of 4, for instance. That is the predicted value of y (ŷ), but the actual value (if you knew it) might be somewhat different. The closer r^* was to +1 or -1, the better your prediction.

Method 1: Trace on the Regression Line Graph (easiest)

You can make predictions while examining the graph of the regression line on the TI-83/84 or TI-89.

Advantages to this method: aside from being pretty cool, it avoids rounding errors, and it’s very fast for repeated predictions.

TI-83/84 Method

One time only, verify the format settings.	[2nd ZOOM makes FORMAT] Verify that you have CoordOn and ExprOn; the other settings aren’t important.
Activate tracing on the regression line.	[TRACE]
Look in the upper left corner to make sure that the regression equation is displayed.	If you see P:L1,L2 then press [▲] to display the regression equation.

Enter the x value.

Press the black-on-white numeric keys including [(−)] and decimal point if needed.   As soon as you press the first number, you’ll see a large X= appear at the bottom left of the screen. Enter any additional digits and press [ENTER].

The TI-83/84 displays the predicted y value (ŷ) at the bottom right and puts a blinking cursor at that point on the regression line.

TI-89/92 Method

Display the graph, if it’s not already on screen.	[◆] [GRAPH]
Trace the regression line, not the data points.	[F3] brings up the trace cursor. But note the P1 in the upper right corner of the screen. That tells you that you’re tracing the data points and not the regression line.   Press [▼] until the upper right displays 1 rather than P1.
The current x and y coordinates are displayed at the bottom of the screen. You can type your desired x the calculator will figure the corresponding ŷ.	Press the white-on-gray numeric keys including [(-)] and decimal point if needed. The xc coordinate changes to match your typing.   After entering your number, press [ENTER]. The calculator moves the cursor and displays the corresponding ŷ value.

Method 2: Use Calculated Regression Equation (fairly easy)

When you specified Y1 as the third parameter in your regression, your calculator stored the equation for y on the Y= screen, but you can actually use it on the home screen too.

Advantages of this method: you don’t have to type in the regression numbers, and rounding errors are essentially nil.

To find a predicted ŷ for x = 4, you want to enter the expression Y1(4). Here’s how:

Access Y1 in the usual way.	TI-83/84: [VARS] [►] [1] [1]	TI-89: [Y] [1]
Enter the x value in parentheses.	Both: [(] 4 (or whatever x you’re interested in), then [)] [ENTER].
You can then read off the result and round it appropriately. In this case, temperature of a freezer, I would not go to more than one decimal place: −7.6°.	TI-83/84:	TI-89:

Method 3: Enter an Ordinary Calculation (last resort)

The predicted ŷ is simply the y value that corresponds to your desired x: it’s just a point on the regression line ŷ = ax+b. You can do that calculation yourself, on the home screen.

Advantage of this method: you have no new TI-83/84 procedure to learn. Disadvantages: typing in the numbers is tedious and error prone, and you have to remember to type in extra digits to avoid the Big No-No.

1. Enter the a value, using more decimal places that you want in your final result. In the freezer example on page 201, you would enter −3.518.

2. Press the times [×] key. An asterisk * will appear on screen.

3. Enter your x value, which is 4 in our example.

4. Enter the b value, preceded by [+] or [−] as necessary. In the freezer example, you would enter +6.456.

5. You should now see −3.518*4+6.456 on your screen. Press [ENTER] to complete the calculation of ŷ.

Disadvantages of this method: it’s tedious and error-prone to re-enter regression constants after the TI-83/84 has computed them; also you can introduce rounding errors.