Sometimes you may want to test hypotheses about the parameters after a linear
regression analysis. On this page, we show a couple of examples of how to
perform these hypothesis tests using the **lmatrix** and **kmatrix**
subcommands in the **glm** procedure. These examples will use data set https://stats.idre.ucla.edu/wp-content/uploads/2016/02/hsb2-2.sav. Let’s say that we have run a
linear regression model as follows.

glm write with female read math /print=parameter /design=female read math.

Written as a regression equation, we have the following:

**write** = b_0 + b_1* **female** + b_2***read** + b_3***math**,
where b_0 = 11.896, b_1 = 5.443, b_2 = .325 and b_3 = .397.

## Example 1

Let’s say that we want to test if the coefficient for **read** is equal to
the coefficient for **math**. The **lmatrix** subcommand allows us to specify our
hypothesis test in terms of the linear combination of the regression
coefficients. In our case, our null hypothesis is that b_2 = b_3, or
equivalently, b_2-b_3 = 0. This leads to our **lmatrix** subcommand with 1 following
the variable **read** and -1 following the variable **math**.

glm write with female read math /print=parameter /design=female read math /lmatrix = 'math = read' read 1 math -1.

In the output, we see the difference between the two parameters is -.072 = (.325 – .397), as we expected. What the output also gives is the standard error for the difference and the confidence interval. The Test Results table shows the F-value and the p-value.

## Example 2

Let’s say that we want to test if the coefficient for **female** is equal to 4.2.
In order to do this, we need to use the **kmatrix** subcommand, because we
are testing if the value is something other than 0. You might want to do
this, if, for example, you had regression coefficients from a previous model and
you wanted to see if they were equal to the coefficients obtained with your
current model. To keep the example simple, we will test only one variable
(**female**) in this example.

glm write with female read math /print=parameter /design=female read math /lmatrix = 'female' female 1 /kmatrix 4.2.

## Example 3

Let’s say that we want to test if the coefficient for **female** is equal to 4.2
and that the coefficient for **read** is equal to the coefficient for **math**. This
will be a two degree-of-freedom test since there are two hypotheses that we want
to test simultaneously. Notice that the values specified on the **kmatrix**
subcommand are listed in the same order as the tests listed on the **lmatrix**
subcommand.

glm write with female read math /print=parameter /design=female read math /lmatrix = 'test' female 1; read 1 math -1 /kmatrix 4.2; 0.