5. Predicting Customer Revenue Using Linear Regression

Overview

In this chapter, you will learn how to solve business problems that require the prediction of quantities. You will learn about regression, a supervised learning approach to predict continuous outcomes. You will explore linear regression, a simple yet powerful technique that is the workhorse for predictive modeling in the industry. Then you will learn how to implement some key steps in the modeling process – feature engineering and data cleaning. Later, you will implement your linear regression models and finally interpret the results to derive business insights.

Introduction

Azra, a large, high-end, fast-fashion retailer that has operations all over the world, has approved its marketing budget for the latest campaign in a particular country. The marketing team is now looking to allocate the budget to each marketing channel, but they have many questions:

• How much should they spend on email? Read rates are low, but the quality of conversions is high.
• How about social media? It seems to be an effective channel in general.
• Should they do any offline promotions? If so, to what extent?
• How about paid search as a channel?

The company understands that each channel provides a different return on investment (ROI) – that is, some channels are more effective than others. However, all channels should be considered, nonetheless. Naturally, different distributions of allocation to these channels would provide different results. Incredibly low spending on a channel with great ROI is missed potential and high spending on an extremely...

Regression Problems

The prediction of quantities is a recurring task in marketing. Predicting the units sold for a brand based on the spend on the visibility (impressions) allocated to the brand's products is an example. Another example could be predicting sales based on the advertising spend on television campaigns. Predicting the lifetime value of a customer (the total revenue a customer brings over a defined period) based on a customer's attributes is another common requirement. All these situations can be formulated as regression problems.

Note

A common misconception is that regression is a specific algorithm/technique. Regression is a much broader term that refers to a class of problems. Many equate regression to linear regression, which is only one of the many techniques that can be employed to solve a regression problem.

Regression refers to a class of problems where the value to predict is a quantity. There are various techniques available for regression...

Feature Engineering for Regression

Raw data is a term that is used to refer to the data as you obtain it from the source – without any manipulation from your side. Rarely, a raw dataset can directly be employed for a modeling activity. Often, you perform multiple manipulations on data and the act of doing so is termed feature engineering. In simple terms, feature engineering is the process of taking data and transforming it into features for use in predictions. There can be multiple motivations for feature engineering:

• Creating features that capture aspects of what is important to the outcome of interest (for example, creating an average order value, which could be more useful for predicting revenue from a customer, instead of using the number of orders and total revenue)
• Using your domain understanding (for example, flagging certain high-value indicators for predicting revenue from a customer)
• Aggregating variables to the required level (for example, creating customer...

Performing and Interpreting Linear Regression

In Exercise 5.01, Predicting Sales from Advertising Spend Using Linear Regression, we implemented and saw the output of a linear regression model without discussing the inner workings. Let us understand the technique of linear regression better now. Linear regression is a type of regression model that predicts the outcome using linear relationships between predictors and the outcome. Linear regression models can be thought of as a line running through the feature space that minimizes the distance between the line and the data points.

The model that a linear regression learns is the equation of this line. It is an equation that expresses the dependent variable as a linear function of the independent variables. This is best visualized when there is a single predictor (see Figure 5.28). In such a case, you can draw a line that best fits the data on a scatter plot between the two variables.

Figure 5.28: A visualization of a linear regression...

Summary

In this chapter, you explored a new approach to machine learning, that is, supervised machine learning, and saw how it can help a business make predictions. These predictions come from models that the algorithm learns. The models are essentially mathematical expressions of the relationship between the predictor variables and the target. You learned about linear regression – a simple, interpretable, and therefore powerful tool for businesses to predict quantities. You saw that feature engineering and data cleanup play an important role in the process of predictive modeling and then built and interpreted your linear regression models using scikit-learn. In this chapter, you also used some rudimentary approaches to evaluate the performance of the model. Linear regression is an extremely useful and interpretable technique, but it has its drawbacks.

In the next chapter, you will expand your repertoire to include more approaches to predicting quantities and will explore...