  # TI-89 Regression: Linear, Trigonometric & Exponential

TI 89 > How to find linear regression on ti-89

Contents:

## 1. How to find linear regression on TI-89: Steps

Watch the video or read the steps below:

Sample problem: Find a linear regression equation (of the form y = ax + b) for x-values of 1, 2, 3, 4, 5 and y-values of 12.5, 9, 6.3, 3, and 1.

Step 1: Press APPS then go to the Data/Matrix Editor screen using the arrow keys, then press ENTER.

Step 2: Scroll down to 3: New using the down arrow key. Press ENTER.

Step 3: Press the down arrow to scroll to the Variable box. Enter your name by pressing the ALPHA key and using the alphanumeric keypad (the white letters to the top right of every key on the lower half of the calculator).

Step 4: Press ENTER twice.

Step 5: Fill your x-values in the first column (c1):

• Press 1, then ENTER.
• Press 2, then ENTER.
• Press 3, then ENTER.
• Press 4, then ENTER.
• Press 5, then ENTER.

Step 6: Scroll to the beginning of the second column by pressing the right and up arrow keys. Enter your y-values in the second column. Press ENTER after you enter each y-value.

• Press 12.5, then ENTER.
• Press 9, then ENTER.
• Press 6.3, then ENTER.
• Press 3, then ENTER.
• Press 1, then ENTER.

Step 7: Press F5. The calculator’s cursor will flash on Calculation Type. Press the right arrow key to bring up a scroll down menu. Use the down arrow key to select 5: LinReg. Press ENTER.

Step 8: Press the down arrow key to the next row (x). Enter c1 using the alphanumeric keypad (the ALPHA button then a close parenthesis ), then 1). This tells the calculator where your x-variables are.

Step 9: Press the down arrow key to the next row (y). Enter ALPHA ) 2: this puts c2 into the space. Press ENTER twice. The calculator returns the value of a and b for you to enter into the equation y’=ax+b (in our equation, a = -2.9 and b = 15.06).

Step 10: Insert the calculator’s result into the equation y’ = ax+b: y’ = -2.9x+15.06

That’s How to find Linear Regression on TI-89!

## 2. TI-89 Regression (Trigonometric). Trigonometric regression is performed when a scatter plot of data suggests a trigonometric, or wave like appearance. If you view a scatter plot on the TI-89, you’ll discover that the dots travel in waves. You could probably also guess that your data is trigonometric by looking at the up and down pattern of the y-values (for example, 18 to 17 and back to 18 again). While a scatter plot can give you an idea of the function’s behavior, it isn’t very good for predictions, unless you throw in a bit of guesswork. The most accurate way to make predictions about a data’s future behavior is to find an equation that best fits the data. If your data seems to fit a wave, then your best fit equation is likely achieved with a trigonometic regression.

## 3. Trigonometric Regression on the TI-89: Steps

Example Problem: Find the trigonometric regression equation for the following data set:

x: 1,2,3,4,5,6,7,8,9
y: 18.4,18.1,17.8,17.7,17.8,18.1,18.5,19.0,19.3

Before beginning, make sure your data is typed into a list. Watch the first minute of this video if you aren’t sure how to make a list.

Step 1: Press APPS and then use the cursor keys to scroll to the Data/Matrix Editor. Press ENTER.

Step 2: Select 1 for Current.

Step 3: Press F5 for Calc. A new screen will appear.

Step 4: Type your x-values into column c1 and your y-values into column c2.

Step 5: Move your cursor to the Calculation Type box, press the right-cursor key and select B:SinReg.

Step 6: Type the location of your x-data into the “x” box. For example, if your x-values are in list c1 then type “c1.”

Step 7: Type the location of your y-data into the “y” box. For example, if your y-values are in list c2 then type “c2.”

Step 8: Move the cursor to the Store ReqEQ line and then press the right cursor key. Move the cursor to y1(x) and then press ENTER. A window will pop up with the a and b for the trigonometric regression equation y=abx. The trigonometric regression equation will also appear in the y1= line of the Y= screen. This particular regression equation is .93781sin(.46732)*x+2.88273+18.63905.

## 4. TI-89 Regression (Exponential). Exponential regression is a way for you to fit a function to data. For example, you might have the following data set:
x: 1,2,3,4,5,6,7
y: 334, 269, 193, 140, 105, 67
By looking at the data, you might be able to guess that the data fits a decreasing exponential function (the y-values decline sharply). But what if you were asked what the next number in the series was? You could take a good guess (by looking at the data you might guess 20), but a more accurate way of “guessing” is to fit the data to an equation and then use that equation to calculate a y-value for an x-input. Exponential regression is how you figure out what that equation is. While exponential regression by hand is cumbersome, the TI-89 calculator can tell you what the regression equation is in a matter of a few key strokes.

## Exponential Regression on the TI-89: Steps

Example Problem: Find the exponential regression equation for the following data set:

• x: 1,2,3,4,5,6
• y: 334, 269, 193, 140, 105, 67

Step 1: Create a scatter plot. If you aren’t familiar with creating lists to generate a scatter plot, watch the first minute of this video. Creating a scatter plot will show you the general curve, ensuring that you’re making the correct regression (the dots should loosely fit a curve).

Step 2: Press APPS and then use the cursor keys to scroll to the Data/Matrix Editor. Press ENTER.

Step 3: Press 1 for Current.

Step 4: Press F5 for Calc. A new screen will appear.

Step 5: Move your cursor to the Calculation Type box, press the right-cursor key and select 4:ExpReg.

Step 6: Type the location of your x-data into the “x” box. For example, if your x-values are in list c1 then type “c1.”

Step 7: Type the location of your y-data into the “y” box. For example, if your y-values are in list c2 then type “c2.”

Step 8: Move the cursor to the Store ReqEQ line and then press the right cursor key. Move the cursor to y1(x) and then press ENTER. A window will pop up with the a and b for the regression equation y=abx. The exponential regression equation will also appear in the y1= line of the Y= screen. This particular regression equation is 490.631792*.726657x.

Tip: When performing exponential regression, your y-values must be greater than zero.