Regression models identify trends in a dataset and predict outcomes based on the trends they have analyzed and identified.

Linear and Logistic Regression are two types of regression models that are similar but carry out their functions in distinct ways. They're also two fundamental techniques in machine learning that predict outcomes by analyzing previously provided data.

Both Linear and Logistic Regression are supervised learning models that appear intertwined – so distinguishing between them can be confusing, as they share the same notion of predicting outcomes based on the input variables.

But here's the main difference: Linear Regression focuses on predicting continuous values, while Logistic Regression is designed specifically for binary classification (Yes or No). So although they have similar-sounding names, there are key differences in their applications, equations, and objectives.

In this article, you'll learn about the similarities and differences between Linear and Logistic Regression, explore key characteristics of each, and learn how to choose between them.

How Linear and Logistic Regression Make Predictions

Linear Regression

Linear regression is the simplest form of regression, assuming a linear (straight line) relationship between the input and the output variable. In simple terms, it harnesses the power of a straight line.

The equation for simple linear regression can be expressed as  y = mx + b, where:

• y is the dependent variable
• x is the independent variable
• m is the slope
• and b is the intercept.

In a house price dataset, the independent variables are columns used to predict the price of the house, such as the “Area”, “Bedrooms”, “Age”,  and “Location”. The Dependent variable will be the “Price” column – the feature to be predicted.

Logistic Regression

Logistic Regression is a powerful supervised machine learning technique. It helps categorize outcomes into two groups by assuming a Linear relationship between the features and the outcome and then calculating the possibility that the outcome will fall into one group or the other.

The mathematical equation calculates an output based on the relationship and the output is then transformed using a sigmoid function to constrain it between 0 and 1. Here it is:

$$y = e^(β0 + β1X1 + β2X2+… βnXn) / (1 + e^(β0 + β1 x 1 + β2 x 2 +… βn x n))$$

Where:

• y gives the probability of success of the y categorical variable
• e (x) is Euler’s number, the inverse of the natural logarithm function or sigmoid function, ln (x)
• β0 is the y-intercept when all independent input variables equal 0
• β1X1 is the regression coefficient (B1) of the first independent variable (X1), the impact value of the first independent variable on the dependent variable
• βnXn is the regression coefficient (BN) of the last independent variable (XN), when there are multiple input values

This is commonly employed in areas like Spam detection and for medical diagnosis. It is used to interpret the likelihood of an observation falling into a specific class.

What are the Similarities between Linear and Logistic Regression?

1. Linear Relationship: Both linear and logistic regression assume a linear relationship between the input features and the output.
2. Supervised Learning: Both are supervised machine learning algorithms, meaning they require labeled training data.
3. Limitations: Both algorithms have similar limitations including:
• Non-linear relationships between input and output variables will lead to inaccurate results.
• Unclean data and missing values will lead to poor model performance. You can read more on data cleaning here.
• Both models are prone to overfitting, which reduces the use of feature selection.

What are the Differences between Linear and Logistic Regression?

1. Output Type: Linear regression predicts continuous output (for example, the price of a house) on a straight line graph, while logistic regression predicts probabilities for binary classification (like if a patient has cancer or not) on an S-shaped curve.
2. Equation and Activation Function: Linear regression uses a simple linear equation while logistic regression uses the logistic function (sigmoid) to transform the output into probabilities.
3. Loss Function: Linear regression minimizes the sum of squared differences, while logistic regression minimizes the logistic loss (log loss).
4. Type of Supervised Learning : Linear regression is a regression model. Logistic regression is a classification model.

When to Use Linear vs Logistic Regression for Your Data Projects

You can use Linear Regression to solve problems where the relationship between variables can be reasonably approximated by a straight line. This means it's well-suited for understanding gradual changes or trends, rather than abrupt jumps or complex relationships. Some examples of these use-cases are:

• House Price prediction
• Identifying Relationships
• Market Trends and Analysis
• Scientific Research
• Price Estimation
• Understanding Impact

On the other hand, Logistic Regression is a powerful tool for understanding binary events and making predictions based on the features given. It excels in calculating the probability of an outcome being "Yes" or "No".  This applies to a wide range of scenarios like:

• Fraud Detection
• Spam filter
• Applications in Medicine
• Customer Churn
• Probability Estimation

What Are Other Types of Regression Models?

Linear and Logistic regression are not the only regression models available. There are other models you can use where linear and logistic regression fail:

• Ridge regression is a regularization technique used to reduce the complexity of a model by introducing a small amount of bias. It makes the model less susceptible to overfitting.
• Lasso regression is a regularization technique which also reduces the complexity of a model. It avoids overfitting by reducing the coefficient to become closer to zero. It is particularly useful when feature selection is crucial
• Polynomial regression captures non-linear relationship using a curved line. It directly addresses the limitations of linear and logistic regression by modeling a non-linear relationship between variables.

Conclusion

Linear and logistic regression share the fundamental concept of a linear relationship between input variables and output variables. But their applications, mathematical equations, and use cases differ significantly.

Understanding these differences is crucial when choosing the appropriate model for a given problem.

This article has shed light on their inner workings and use cases, thereby equipping you to make the right and informed choice. Make sure you explore further to increase your knowledge and skills, and take the time to learn more complex machine learning models that will best fit your data problems.

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