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Logistic Regression: Predicting the Power of Yes or No

Michael Lee, MBA
Jun 16
4 min read

We’ve talked about analyzing means, proportions, relationships, and even uncovering patterns — but what happens when the question is binary? When the outcome is simply yes or no, churn or stay, click or ignore, accept or reject?

That’s where Logistic Regression comes in — a powerful predictive analytics technique that helps us answer exactly that.

🧾 A Brief History of Logistic Regression

Logistic regression dates back to the early 19th century when it was developed to model population growth. In the 1830s, Belgian mathematician Pierre-François Verhulst introduced the logistic function to describe how populations grow rapidly at first, then slow down and level off — forming an S-shaped curve.

Later, this concept was adapted for statistical classification in the 20th century, where it gained popularity in fields like epidemiology, economics, and machine learning. Today, it's one of the most commonly used techniques for binary classification problems.

📍 What is Logistic Regression (and how is it different from Linear Regression)?

At first glance, logistic regression may look like linear regression’s cousin. But while linear regression predicts continuous outcomes (e.g. salary, revenue, score), logistic regression predicts probabilities of categories — typically a binary outcome.

For example:

Will a candidate accept the job offer or not?
Will the user click on your ad or skip it?
Will the loan applicant default or pay back?

Here’s the key difference:

Linear regression fits a line through the data points to estimate values.
Logistic regression fits an S-shaped curve (sigmoid function) that squashes predictions between 0 and 1 — making it ideal to express probability.

Once that probability crosses a chosen threshold (often 0.5), we assign a label: yes or no.

Do We Still Use Hypothesis Testing?

Yes. Like other regression models, logistic regression involves hypothesis testing.

Null hypothesis (H₀): The predictor has no effect on the outcome.
Alternative hypothesis (H₁): The predictor affects the outcome.

If the p-value is less than the threshold (usually 0.05), we reject H₀ and say the predictor is statistically significant.

🎯 Why Use Logistic Regression?

It’s one of the most interpretable models in predictive analytics — you can explain it clearly to stakeholders, and the math behind it is elegant and efficient.

More importantly, logistic regression is great when:

The outcome is categorical (usually binary).
You want a probability, not just a yes/no.
You want to understand which factors increase or decrease that probability.

It also serves as a foundation for more advanced classification algorithms — from decision trees to neural networks.

✍🏼 Example 1: Job Offer Acceptance

Let’s say you’re in HR and want to predict whether a job candidate will accept your offer. You have data from previous applicants, including:

Salary offered
Number of interview rounds
Time taken to offer
Distance to office

You run a logistic regression model and find:

Higher salary increases acceptance probability
Longer time to offer decreases it
Too many interview rounds lowers acceptance

Now, you not only get predictions, but actionable insights.

✍🏼 Example 2: Customer Churn in a Subscription Business

You’re working in customer success and want to reduce churn. Your predictors:

Monthly usage hours
Days since last login
Number of support tickets submitted

A logistic regression shows:

Higher support tickets increase churn probability
Frequent usage reduces churn likelihood

Based on this, you create a flag system to proactively reach out to high-risk users.

✍🏼 Example 3: Loan Default Prediction

In the finance sector, banks use logistic regression to predict default risk. Variables include:

Income level
Credit score
Loan amount
Past defaults

With enough data, logistic regression helps set interest rates and approve or reject applications based on predicted default probability.

✍🏼 Example 4: Email Marketing Response

A marketer wants to predict whether customers will respond to an email campaign.

Variables: Age group, past purchases, time of day sent, device type.
Outcome: Clicked (1) or Didn’t Click (0).

Logistic regression identifies that younger customers using mobile devices are more likely to click if emails are sent during lunchtime.

📈 What Does the Output Look Like?

Key parts of a logistic regression output:

Coefficient: How much each variable affects the log odds of the outcome
Odds Ratio: Exponentiated coefficient; how the odds of a yes/no change
P-value: Whether the predictor is statistically significant
Accuracy / Confusion Matrix: Model performance

We’ll break this down more in the next article with an actual HR case.

⚙️ Where Can You Run Logistic Regression?

You don’t need fancy software to run logistic regression. Here are a few options:

Excel (with add-ins like Real Statistics)
Python (using libraries like scikit-learn or statsmodels)
R (built-in glm() function)
SPSS / SAS / Minitab
Power BI (with R/Python integration)

We’ll start with Excel and Python examples in this series.

⚠️ Common Pitfalls

Predicting beyond binary (e.g. 3+ categories)? You’ll need multinomial logistic regression.
Assuming linearity between predictors and the outcome? Logistic doesn’t work that way — it assumes linearity with the log odds, not the probability.
Interpreting coefficients directly like linear regression? Don’t — use odds ratios instead for business meaning.

🛠️ What’s Next?

In our next article, we’ll build a logistic regression model to predict whether a candidate accepts a job offer — with Excel and a real-world dataset.

We’ll also cover:

How to interpret the coefficients
How to evaluate the model with accuracy, precision, recall
Visuals that make your insights come alive

Stay tuned.

👩🏻‍💻 Want hands-on experience in foundational analytics? While logistic regression is a more advanced topic, you can build your base in our 2-day workshops: