Computing Wald statistic

In the previous exercise you fitted a model with width variable and assessed the relationship of the explanatory and response variable. In this exercise you will assess the significance of the width variable by computing the Wald statistic.

Also note that in the model summary the Wald statistic is presented by the letter z which means that the value of a statistic follows a standard normal distribution. Recall the formula for the Wald statistic:

$$ z=\frac{\hat\beta}{SE} $$

where $\hat\beta$ is the estimated coefficient and $SE$ its standard error.

The fitted model crab_GLM and crab dataset have been preloaded in the workspace.

This is a part of the course

“Generalized Linear Models in Python”

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Exercise instructions

Using .params extract and print model coefficients and save as intercept and slope.
Save and print covariance matrix as crab_cov.
Compute and print the standard error std_error by extracting the relevant element using the covariance matrix.
Compute and print the Wald statistic.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Extract coefficients
intercept, slope = ____.____

# Estimated covariance matrix: crab_cov
____ = crab_GLM.____
print(____)

# Compute standard error (SE): std_error
____ = np.____(____.loc['width', 'width'])
print('SE: ', round(____, 4))

# Compute Wald statistic
wald_stat = ____/____
print('Wald statistic: ', round(____,4))

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