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  3. Intermediate Regression with statsmodels in Python
  • 1

    Parallel Slopes

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    Extend your linear regression skills to parallel slopes regression, with one numeric and one categorical explanatory variable. This is the first step towards conquering multiple linear regression.

  • 2

    Interactions

    Explore the effect of interactions between explanatory variables. Considering interactions allows for more realistic models that can have better predictive power. You'll also deal with Simpson's Paradox: a non-intuitive result that arises when you have multiple explanatory variables.

  • 3

    Multiple Linear Regression

    See how modeling and linear regression make it easy to work with more than two explanatory variables. Once you've mastered fitting linear regression models, you'll get to implement your own linear regression algorithm.

  • 4

    Multiple Logistic Regression

    Extend your logistic regression skills to multiple explanatory variables. You’ll also learn about logistic distribution, which underpins this form of regression, before implementing your own logistic regression algorithm.

Initializing

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Logistic regression algorithm

Let's dig into the internals and implement a logistic regression algorithm. Since statsmodels's logit() function is very complex, you'll stick to implementing simple logistic regression for a single dataset.

Rather than using sum of squares as the metric, we want to use likelihood. However, log-likelihood is more computationally stable, so we'll use that instead. Actually, there is one more change: since we want to maximize log-likelihood, but minimize() defaults to finding minimum values, it is easier to calculate the negative log-likelihood.

The log-likelihood value for each observation is $$ log(y_{pred}) * y_{actual} + log(1 - y_{pred}) * (1 - y_{actual}) $$

The metric to calculate is the negative sum of these log-likelihood contributions.

The explanatory values (the time_since_last_purchase column of churn) are available as x_actual. The response values (the has_churned column of churn) are available as y_actual. logistic is imported from scipy.stats, and logit() and minimize() are also loaded.

Anweisungen 1/2

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Complete the function body.

  • Unpack coeffs to intercept and slope, respectively.
  • Calculate the predicted y-values as the intercept plus the slope times the actual x-values, transformed with the logistic CDF.
  • Calculate the log-likelihood as the log of the predicted y-values times the actual y-values, plus the log of one minus the predicted y-values times one minus the actual y-values.
  • Calculate the negative sum of the log-likelihood.
  • Return the negative sum of the log-likelihood.