Probability and Statistics > TI 89 > How to find linear regression on ti-89

**Contents**:

- TI-89 Regression (Linear).
- TI-89 Regression (Trigonometric).
- TI-89 Regression (Exponential).
- Quadratic Regression (opens in new window).

## 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

**Sample 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. See: How to enter data into a list on the TI 89.

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=ab^{x}. 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

* Sample 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, check out this article on how to create lists on the TI 89. 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=ab^{x}. The exponential regression equation will also appear in the y1= line of the Y= screen. This particular regression equation is 490.631792*.726657^{x}.

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

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I took the following data set and by first difference and then ratio, came up with the exact function (exponential) that fits the data. y = (3^x) + 2 It was pretty easy to do without calculator. DATA SET:

X= 1,2,3,4,5,6 Corresponding Y= 5,11,29,83,245,731

When I put this data set into a TI-84 or TI-89 and select ExpReg, it returns y = 1.5728(2.7406^x0 It seems that the calculator cannot handle this simple case. Can you analyze and let me know what I am missing.

I graphed 1.572*2.7406^x on a graphing calculator, and it is the graph for your data. Can you clarify what your issue is?

on the TI-89 how to I turn my linear equation into a graph. if I push the graph button it don’t create a graph so I’m sure i’m missing a step.

Thank you for your help