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Rate of change in probability

For the wells dataset you have already fitted a logistic regression model with the model formula switch ~ distance100 obtaining the following fit $$ log(\frac{\mu}{1-\mu}) = 0.6060 - 0.6219\times distance100 $$

In this exercise you will use that model to understand how the estimated probability changes at a certain value of distance100, say 1.5 as depicted in the figure below.

Recall the formulas for the inverse-logit (probability)

$$ \mu = \frac{exp(\beta_0+\beta_1x_1)}{1+exp(\beta_0+\beta_1x_1)} $$

and the slope of the tangent line of the model fit at point \(x\):

$$ \beta*\mu(1-\mu) $$

Dataset wells and the model wells_GLM are loaded in the workspace.

This exercise is part of the course

Generalized Linear Models in Python

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Hands-on interactive exercise

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

# Define x at 1.5
x = ____

# Extract intercept & slope from the fitted model
intercept, slope = ____.____
Edit and Run Code