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
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 = ____.____