Getting ŷ from Any x in a Regression on 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 two methods of answering that question.

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

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

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 multiple 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 x coordinate changes to match your typing.   After entering your number, press [ENTER]. The calculator moves the cursor and displays the corresponding ŷ value.

Caution:  ŷ = 267.15 yd is the predicted or expected distance for a club-head speed of 102 mph. But that does not mean any particular golf ball hit at that speed will travel that exact distance. You can think of ŷ as the average travel distance that we would expect for a whole lot of golf balls hit at that speed.

Method 2: Use Calculated Regression Equation (if necessary)

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 to one more decimal place than the original data. So for x=102 mph, ŷ = 267.1 yards.	TI-83/84:	TI-89:

Again, please observe the Caution above.