# Linear Regression vs. Logistic Regression: Know the Difference

By Shumaila Saeed & Dua Fatima || Published on July 12, 2024

**Linear Regression predicts continuous outcomes, focusing on the relationship between dependent and independent variables. Logistic Regression, in contrast, predicts categorical outcomes, used for classification problems.**

## Key Differences

Linear Regression is utilized for predicting a continuous variable, such as house prices, based on one or more predictor variables. It aims to establish a linear relationship between the dependent and independent variables, providing a straight-line prediction model. Logistic Regression, however, is designed for binary or multinomial classification tasks, like spam detection, where the outcome is categorical, not continuous. It estimates probabilities using a logistic function, transforming the linear combination of inputs into a value between 0 and 1.

Dua Fatima

Jul 12, 2024

Linear Regression outputs are unbounded, Logistic Regression outputs are probabilities that are bounded between 0 and 1. This fundamental difference dictates their application areas: Linear Regression for forecasting values and Logistic Regression for determining the likelihood of belonging to a class.

Dua Fatima

Jul 12, 2024

Error measurement in Linear Regression is typically done through methods like Mean Squared Error (MSE), focusing on the difference between the actual and predicted values. Logistic Regression, on the other hand, uses metrics like Log Loss to measure the performance of a classification model, focusing on the probability error.

Shumaila Saeed

Jul 12, 2024

Linear Regression assumptions include linearity, homoscedasticity, and normality of residuals, requiring a linear relationship between the independent and dependent variables. Logistic Regression does not assume a linear relationship between the independent variables and the logit of the dependent variable but still requires the independent variables to be linearly related to the log odds.

Shumaila Saeed

Jul 12, 2024

Linear Regression is sensitive to outliers, which can significantly affect the regression line and subsequently the forecasted values. Logistic Regression is generally more robust to outliers, as it predicts probabilities; outliers have less impact on the classification boundaries.

Shumaila Saeed

Jul 12, 2024

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## Comparison Chart

### Assumptions

Linearity, homoscedasticity, normality of residuals

Linearity in log odds, no multicollinearity

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Jul 12, 2024

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## Linear Regression and Logistic Regression Definitions

#### Linear Regression

Predicts a continuous outcome based on independent variables.

Predicting house prices based on square footage and location.

Dua Fatima

Feb 26, 2024

#### Logistic Regression

Used for binary classification problems.

Determining if an email is spam or not spam.

Dua Fatima

Feb 26, 2024

#### Linear Regression

Can be extended to multiple regression for multiple independent variables.

Using both age and weight to predict blood pressure.

Hifza Nasir

Feb 26, 2024

#### Logistic Regression

Outputs probabilities of class memberships.

Predicting the probability that a tumor is malignant or benign.

Shumaila Saeed

Feb 26, 2024

#### Linear Regression

Estimates the relationship between variables using a straight line.

A linear regression model may show that salary increases with years of experience.

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Feb 26, 2024

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#### Logistic Regression

Does not require a linear relationship between dependent and independent variables.

Can predict outcomes based on categorical data, like drug effectiveness.

Dua Fatima

Feb 26, 2024

#### Linear Regression

Requires assumptions about the distribution of variables.

Assumes that residuals are normally distributed for accurate predictions.

Dua Fatima

Feb 26, 2024

#### Logistic Regression

More robust to outliers in classification tasks.

Outlier observations have less influence on determining the decision boundary.

Hifza Nasir

Feb 26, 2024

#### Linear Regression

Sensitive to outliers, which can skew predictions.

A very large house sale price can distort the regression line.

Shumaila Saeed

Feb 26, 2024

#### Logistic Regression

Uses the logistic function to model data.

Logistic regression may estimate the likelihood of a student passing based on hours studied.

Shumaila Saeed

Feb 26, 2024

## Repeatedly Asked Queries

#### Why is the logistic function important in Logistic Regression?

The logistic function transforms the linear equation to output probabilities, ensuring the output values fall between 0 and 1.

Dua Fatima

Jul 12, 2024

#### Can Linear Regression be used for classification?

While theoretically possible by setting thresholds, it's not ideal due to its continuous nature and sensitivity to outliers. Logistic Regression is preferred for classification.

Shumaila Saeed

Jul 12, 2024

#### Can you use Linear Regression for time series analysis?

Yes, but it's limited to linear trends and often requires additional techniques to handle autocorrelation and non-stationarity.

Shumaila Saeed

Jul 12, 2024

#### What makes Logistic Regression robust to outliers?

Its classification decision is based on probabilities and thresholds, making it less sensitive to extreme values compared to Linear Regression's continuous output.

Shumaila Saeed

Jul 12, 2024

#### Is it necessary for the dependent variable in Linear Regression to be normally distributed?

The normality assumption applies to the residuals of the model, not the dependent variable itself.

Shumaila Saeed

Jul 12, 2024

#### What are the limitations of Linear Regression?

It cannot handle non-linear relationships without transformations and is sensitive to outliers and multicollinearity.

Shumaila Saeed

Jul 12, 2024

#### What is the main difference between Linear and Logistic Regression?

Linear Regression is used for predicting continuous outcomes, while Logistic Regression is used for predicting categorical outcomes.

Dua Fatima

Jul 12, 2024

#### How does Logistic Regression handle more than two categories?

It uses multinomial Logistic Regression or extends to a One-vs-Rest approach to accommodate multiple classes.

Shumaila Saeed

Jul 12, 2024

#### How does Linear Regression deal with categorical variables?

Categorical variables can be included in a Linear Regression model through dummy coding, allowing the model to incorporate their effects.

Hifza Nasir

Jul 12, 2024

#### How do you interpret the coefficients in Logistic Regression?

Coefficients represent the change in the log odds of the dependent variable for a one-unit change in the predictor.

Shumaila Saeed

Jul 12, 2024

#### What happens if Linear Regression assumptions are violated?

Violating assumptions can lead to inaccurate estimates and predictions, making model validation and assumption testing critical.

Hifza Nasir

Jul 12, 2024

#### Why is multicollinearity a concern in Logistic Regression?

Multicollinearity among predictors can obscure the significance of independent variables, making it hard to discern their effects.

Dua Fatima

Jul 12, 2024

#### Can Logistic Regression be used for non-linear relationships?

Yes, through feature engineering or polynomial regression, non-linear relationships can be modeled.

Dua Fatima

Jul 12, 2024

#### Can the outcome of Logistic Regression be greater than 1?

No, the logistic function ensures the outcome is always between 0 and 1, representing probabilities.

Hifza Nasir

Jul 12, 2024

#### How do you choose between Linear and Logistic Regression?

The choice depends on the nature of the dependent variable: use Linear Regression for continuous outcomes and Logistic Regression for categorical outcomes.

Dua Fatima

Jul 12, 2024

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About Author

Written by

Shumaila SaeedShumaila Saeed, an expert content creator with 6 years of experience, specializes in distilling complex topics into easily digestible comparisons, shining a light on the nuances that both inform and educate readers with clarity and accuracy.

Co-written by

Dua Fatima