From Transactions to Tendencies: Predict When a Buyer Is About to Cease Shopping for

January 23, 2026

1

how math can clear up so many issues in the true world. Once I was in grade college, I definitely didn’t see it that manner. I by no means hated math, by the way in which, and neither did I’ve hassle studying many of the primary ideas.

Nonetheless, I confess that for many of the lessons past the traditional arithmetic, I often thought, “I’ll by no means use that for something in my life”.

These had been different occasions, although. There was no Web, no knowledge science, and computer systems had been barely a factor. However time passes. Life occurs, and we get to see the day after we will clear up essential enterprise issues with good previous math!

On this put up, we are going to use the well-known linear regression for a special drawback: predicting buyer churn.

Linear Regression vs Churn

Buyer churn hardly ever occurs in a single day. In lots of instances, prospects will regularly scale back their buying frequency earlier than stopping utterly. Some name that silent churn [1].

Predicting churn will be achieved with the normal churn fashions, which (1) require labeled churn knowledge; (2) generally are advanced to clarify; (3) detect churn after it already occurred.

Then again, this mission exhibits a special resolution, answering a less complicated query:

Is that this buyer
slowing down the purchasing?

This query is answered with the next logic.

We use month-to-month buy developments and linear regression to measure buyer momentum over time. If the shopper continues to extend their bills, the summed quantity will develop over time, resulting in a development upward (or a optimistic slope in a linear regression, if you’ll). The alternative can be true. Decrease transaction quantities will add as much as a downtrend.

Let’s break down the logic in small steps, and perceive what we are going to do with the info:

Combination buyer transactions by month
Create a steady time index (e.g. 1, 2, 3…n)
Fill lacking months with zero purchases
Match a linear regression line
Use the slope (transformed to levels) to quantify shopping for conduct
Evaluation: A damaging slope signifies declining engagement. A optimistic slope signifies rising engagement.

Properly, let’s transfer on to the implementation subsequent.

Code

The very first thing is importing some modules right into a Python session.

# Imports
import scipy.stats as stats
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

Then, we are going to generate some knowledge that simulates some prospects transactions. You’ll be able to have a look at the whole code on this GitHub repository. The dataset generated brings the columns customer_id, transaction_date, and total_amt, and can seem like the subsequent image.

Dataset generated for this train. Picture by the creator.

Now we are going to create a brand new column that extracts the month of the date, so it turns into simpler for us to group the info later.

# Create new column month
df['mth'] = df['transaction_date'].dt.month

# Group prospects by month
df_group = (
    df
    .groupby(['mth','customer_id'])
    ['total_amt']
    .sum()
    .reset_index()
)

Right here is the outcome.

Grouped knowledge. Picture by the creator.

If we shortly examine if there are prospects who haven’t made a transaction each month, we are going to discover a couple of instances.

That leads us to the subsequent level. We’ve to ensure that, if the shopper doesn’t have at the very least one buy per 30 days, then now we have so as to add that month with a $0 expense.

Let’s construct a operate that may do this and likewise calculate the slope of the shopper’s purchasing development.

This operate appears monumental, however we are going to go over it in smaller chunks. Let’s do that.

Filter the info for a given buyer utilizing Pandas question() technique.
Make a fast group and examine if the shopper has at the very least one buy for each month.
If not, we are going to add the lacking month with a $0 expense. I carried out this by merging a brief dataframe with the 12 months and $0 with the unique knowledge. After the merge on months, these durations lacking will probably be rows with NaN for the unique knowledge column, which will be crammed with $0.
Then, we normalize the axes. Keep in mind that the X-axis is an index from 1 to 12, however the Y-axis is the expense quantity, in 1000’s of {dollars}. So, to keep away from distortion in our slope, we normalize all the things to the identical scale, between 0 and 1. For that, we use the customized operate min_max_standardize.
Subsequent, we are able to plot the regression utilizing one other customized operate.
Then we are going to calculate the slope, which is the primary outcome returned from the operate scipy.linregress().
Lastly, to calculate the angle of the slope in levels, we are going to enchantment to pure arithmetic, utilizing the idea of arc tangent to calculate the angle between the X-axis and the linear regression slope line. In Python, simply use the features np.arctan() and np.levels() from numpy.

# Standardize the info
def min_max_standardize(vals):
    return (vals - np.min(vals)) / (np.max(vals) - np.min(vals))

#------------

# Fast Perform to plot the regression
def plot_regression(x,y, cust):
  plt.scatter(x,y, coloration = 'grey')
  plt.plot(x,
          stats.linregress(x,y).slope*np.array(x) + stats.linregress(x,y).intercept,
          coloration = 'crimson',
          linestyle='--')
  plt.suptitle("Slope of the Linear Regression [Expenses x Time]")
  plt.title(f"Buyer {cust} | Slope: {np.levels(np.arctan(stats.linregress(x,y).slope)):.0f} levels. Constructive = Shopping for extra | Adverse = Shopping for much less", dimension=9, coloration='grey')
  plt.present()

#-----

def get_trend_degrees(buyer, plot=False):

  # Filter the info
  one_customer = df.question('customer_id == @buyer')
  one_customer = one_customer.groupby('mth').total_amt.sum().reset_index().rename(columns={'mth':'period_idx'})

  # Test if all months are within the knowledge
  cnt = one_customer.groupby('period_idx').period_idx.nunique().sum()

  # If not, add 0 to the months with out transactions
  if cnt < 12:
      # Create a DataFrame with all 12 months
      all_months = pd.DataFrame({'period_idx': vary(1, 13), 'total_amt': 0})

      # Merge with the prevailing one_customer knowledge.
      # Use 'proper' merge to maintain all 12 months from 'all_months' and fill lacking total_amt.
      one_customer = pd.merge(all_months, one_customer, on='period_idx', how='left', suffixes=('_all', ''))

      # Mix the total_amt columns, preferring the precise knowledge over the 0 from all_months
      one_customer['total_amt'] = one_customer['total_amt'].fillna(one_customer['total_amt_all'])

      # Drop the momentary _all column if it exists
      one_customer = one_customer.drop(columns=['total_amt_all'])

      # Type by period_idx to make sure appropriate order
      one_customer = one_customer.sort_values(by='period_idx').reset_index(drop=True)

  # Min Max Standardization
  X = min_max_standardize(one_customer['period_idx'])
  y = min_max_standardize(one_customer['total_amt'])

  # Plot
  if plot:
    plot_regression(X,y, buyer)

  # Calculate slope
  slope = stats.linregress(X,y)[0]

  # Calculate angle levels
  angle = np.arctan(slope)
  angle = np.levels(angle)

  return angle

Nice. It’s time to put this operate to check. Let’s get two prospects:

C_014.
That is an uptrend buyer who’s shopping for extra over time.

# Instance of robust buyer
get_trend_degrees('C_014', plot=True)

The plot it yields exhibits the development. We discover that, despite the fact that there are some weaker months in between, general, the quantities have a tendency to extend as time passes.

Uptrending buyer. Picture by the creator.

The development is 32 levels, thus pointing properly up, indicating a robust relationship with this buyer.

C_003.
This can be a downtrend buyer who’s shopping for much less over time.

# Instance of buyer cease shopping for
get_trend_degrees('C_003', plot=True)

Downtrending buyer. Picture by the creator.

Right here, the bills over the months are clearly lowering, making the slope of this curve level down. The road is 29 levels damaging, indicating that this buyer goes away from the model, thus requires to be stimulated to return again.

Earlier than You Go

Properly, that may be a wrap. This mission demonstrates a easy, interpretable strategy to detecting declining buyer buy conduct utilizing linear regression.

As an alternative of counting on advanced churn fashions, we analyze buy developments over time to establish when prospects are slowly disengaging.

This easy mannequin may give us an important notion of the place the shopper is transferring in the direction of, whether or not it’s a higher relationship with the model or transferring away from it.

Actually, with different knowledge from the enterprise, it’s potential to enhance this logic and apply a tuned threshold and shortly establish potential churners each month, based mostly on previous knowledge.

Earlier than wrapping up, I want to give correct credit score to the unique put up that impressed me to study extra about this implementation. It’s a put up from Matheus da Rocha that you will discover right here, on this hyperlink.

Lastly, discover extra about me on my web site.

https://gustavorsantos.me