Regression vs Logistic Regression: Which is Better?
The answer to “which is better” depends entirely on your specific problem and the type of outcome variable you are trying to predict. Both linear regression (often simply called regression) and logistic regression are valuable techniques in supervised learning, but they serve different purposes:
1. Purpose and Outcome
- Linear Regression:
- Objective: Predicts a continuous numerical outcome.
- Example Use Cases: Forecasting house prices, estimating temperatures, or predicting sales revenue.
- Output: A continuous value determined by a linear combination of the input features.
- Logistic Regression:
- Objective: Predicts a binary outcome (or categorical outcomes through extensions such as multinomial logistic regression).
- Example Use Cases: Determining whether an email is spam or not, diagnosing whether a patient has a disease (yes/no), or predicting customer churn (churn/no churn).
- Output: Probabilities that an observation belongs to a particular class, typically converted into class labels.
2. Key Differences in Approach
| Aspect | Linear Regression | Logistic Regression |
|---|---|---|
| Type of Outcome | Continuous numerical values | Categorical/binary outcomes |
| Model Equation | y=β0+β1×1+⋯+βnxn+ϵy = \beta_0 + \beta_1 x_1 + \dots + \beta_n x_n + \epsilony=β0+β1x1+⋯+βnxn+ϵ | log(p1−p)=β0+β1×1+⋯+βnxn\log\left(\frac{p}{1-p}\right) = \beta_0 + \beta_1 x_1 + \dots + \beta_n x_nlog(1−pp)=β0+β1x1+⋯+βnxn (logit transformation) |
| Interpretation | Predicts an exact value; coefficients represent the expected change in yyy per unit change in xxx | Predicts the probability of an outcome; coefficients indicate the change in log-odds |
| Assumptions | Assumes linearity, homoscedasticity, and normally distributed errors. | Assumes a logistic function relationship; errors are not assumed to be normally distributed. |
| Loss Function | Minimizes mean squared error (MSE). | Maximizes the likelihood (or minimizes log-loss). |
3. Which One Is “Better”?
- Linear Regression Is Better When:
- Your target variable is continuous and you need to predict exact numerical values.
- The relationship between the predictors and the outcome is approximately linear.
- Logistic Regression Is Better When:
- Your target variable is binary or categorical.
- You need to estimate probabilities or classify observations into distinct groups.
4. Final Thoughts
Neither model is inherently superior overall; each is “better” for a specific type of problem:
- Use Linear Regression when you’re dealing with continuous data and want to understand how changes in your predictors affect a numerical outcome.
- Use Logistic Regression when you need to classify observations into categories or predict probabilities for binary outcomes.
Ultimately, the choice depends on the nature of your data and the specific objectives of your analysis. In many real-world applications, the decision is clear based on whether the outcome is continuous or categorical.
Let me know if you need more details or further examples!