# Wald Test for Logistic Regression

The Wald test can be demonstrated using example from the previous post on the likelihood test for logistic regression. Again, assuming a confidence level of 95%. The hypothesis setting is a little different because this test targets individual parameter in the regression model:

Null hypothesis: A1=0
Alternative hypothesis: A1≠0

To test the hypothesis, the statistic below is obtained using the following equation:

( ma × mb × ma)-1

where ma and mb are matrices and defined as below.

ma consists of the `x1 `and `x2 `variables as first and second row, and all 1s as the third row. In the TI Nspire, the function `colAugment `is convenient to construct matrix from multiple lists.

The next step involved determining the y hat values from the regression model for each data row.

Once determined, the matrix mb can be defined as below. It is a diagonal matrix with values correspond to the equation of `y_hat × (1 - y_hat)`. Notice how `constructMat` worked with the piece-wise expression for this diagonal matrix.

The calculation can then be performed. The final results as shown in the second equation below is then used for determination of the P-value of χ² distribution in 1 degree of freedom.

Since the value is less than 0.05, the conclusion is to reject the null hypothesis A1=0 and accept the alternative hypothesis A1≠0.