A linear regression is a statistical method that fits a straight line to a set of data points. It is used to model the relationship between a dependent variable (y) and an independent variable (x). The equation of the line is of the form y = ax + by=ax+b, where aa is the slope and bb is the y-intercept. A linear regression can help us estimate the values of aa and bb, as well as measure how well the line fits the data.
Finding linear regression on a ti-89 calculator is easy and can be done in two ways: using the LinReg( function or using the Stats/List Editor application. In this article, we will explain both methods with examples.
Using the LinReg( function
The LinReg( function is a built-in function on the ti-89 calculator that can find the equation of the linear regression line for a set of data points. For example, suppose we have the following data points:
| x | y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 5 |
| 4 | 7 |
| 5 | 8 |
To find the linear regression using the LinReg( function, follow these steps:
- Press the
ONbutton to turn on the calculator. - Press the
MODEbutton and make sure thatEXACTis selected for the exact/approximate mode. - Press the
HOMEbutton to go to the home screen. - Press the
2NDbutton and then press the0button to access the catalog of functions. - Scroll down until you see the
LinReg(function and pressENTERto select it. - Enter the x-values and the y-values separated by commas. For our example, we would enter
{1,2,3,4,5},{2,4,5,7,8}. - Press the
)button to close the parentheses and pressENTERto calculate the linear regression.
The calculator will display the equation of the line as y = 1.4x + 0.6. This means that the slope of the line is 1.41.4 and the y-intercept is 0.60.6.
Using the Stats/List Editor application
The Stats/List Editor application is a custom application that can be downloaded and installed on the ti-89 calculator. It can perform various statistical operations, such as finding the mean, median, mode, standard deviation, and more. For example, suppose we have the following data points:
| x | y |
|---|---|
| 2 | 3 |
| 4 | 6 |
| 6 | 8 |
| 8 | 11 |
| 10 | 13 |
To find the linear regression using the Stats/List Editor application, follow these steps:
- Download the application from this website and transfer it to your calculator using the TI Connect software.
- Press the
ONbutton to turn on the calculator. - Press the
APPSbutton and scroll down to the optionStats/List Editorand pressENTERto select it. - Press the
ENTERbutton again to run the application. - Press the
F1button and then press the1button to create a new list. - Enter the name of the list and press
ENTER. For our example, we would enterL1. - Enter the x-values in the list, pressing
ENTERafter each value. For our example, we would enter2,4,6,8, and10. - Press the
2NDbutton and then press theF1button to create another new list. - Enter the name of the list and press
ENTER. For our example, we would enterL2. - Enter the y-values in the list, pressing
ENTERafter each value. For our example, we would enter3,6,8,11, and13. - Press the
F4button and then press the1button to access the one-variable statistics menu. - Enter the names of the lists that you want to analyze separated by commas. For our example, we would enter
L1,L2. - Press the
ENTERbutton to calculate the statistics. - Scroll down until you see the
aandbvalues, which are the slope and the y-intercept of the line.
The calculator will display the slope as 1.2 and the y-intercept as 0.6. This means that the equation of the line is y = 1.2x + 0.6y=1.2x+0.6.
Summary
In this article, we learned how to find linear regression on a ti-89 calculator using two methods: using the LinReg( function and using the Stats/List Editor application. Linear regression is useful for modeling the relationship between two variables and making predictions. We hope this article was helpful and informative. For more information on linear regression and other statistical concepts, you can check out this website.