# Multiple linear regression in TI-84 Plus

Advanced feature like multiple linear regression is not included in the TI-84 Plus SE. However, obtaining the regression parameters need nothing more than some built-in matrix operations, and the steps are also very easy. For a simple example, consider two independent x variables x1 and x2 for a multiple regression analysis.

Firstly, the values are input into lists and later turned into matrices. L1 and L2 are x1 and x2, and L3 is the dependent variable.

Convert the lists into matrices using the `List>matr()` function. L1 thru L3 are converted to Matrix C thru E.

Create an matrix with all 1s with the dimension same as L1 / L2. And then use the `augment()` function to create a matrix such that the first row is L1 (Matrix C), second row is L2 (Matrix D), and the third row is the all 1s matrix. In this example we will store the result to matrix F. Notice that since `augment()` takes only two argument at one time, we have to chain the function.

The result of F and its transform look like below.

Finally, the following formula is used to obtain the parameters for the multiple regression

`([F]t * [F])-1 * [F]t * [E]`

The parameters are expressed in the result matrix and therefore the multiple regression equation is

`y = 41.51x1 - 0.34x2 + 65.32`

See also this installment to determine the correlation of determination in a multiple linear regression settings also using the TI-84.