Stata Wald Test: How to Test Coefficients in Linear Regression

The Wald test is a statistical method used to assess the significance of coefficients in linear regression models. In Stata, you can perform a Wald test using the test command.

Let's say you have a linear regression model with two independent variables, x1 and x2, and you want to test if their coefficients are significantly different from zero.

First, you need to estimate the linear regression model. Assuming your regression command is regress and the model is y = b0 + b1*x1 + b2*x2 + u, where y is the dependent variable, x1 and x2 are independent variables, b0, b1, and b2 are coefficients, and u is the error term.

regress y x1 x2

Next, you can use the test command for the Wald test. To test if the coefficient for x1 is significantly different from zero, use the following command:

test x1

If you want to test multiple coefficients simultaneously, you can list them together and use the logical operator & for 'and'. For example, to test if the coefficients for both x1 and x2 are significantly different from zero, use:

test x1 x2

After executing these commands, Stata will output the Wald statistic and the corresponding p-value. If the p-value is less than a certain significance level (typically 0.05), you can reject the null hypothesis and conclude that the coefficient is statistically significant.