What are the differences between linear and logistic regression?

If fit via OLS, it doesn't assume that errors are normally distributed, since the Gauss-Markov theorem doesn't require it for the point estimates to be BLUE. This normality plays an essential role during inference about the parameters (marginal effects). While not mandatory, it also makes an important diagnostic tool to check if no unaddressed patterns left in data, which can point to model misspecification and presence of influential observations and/or outliers (the two aren't the same) - through studentized residuals, Cook's distance, DFBETA and DFFIT measures The conditional (!) normality is important, however, if we fit the model via maximum likelihood estimation within the Generalized Linear Model framework (Nelder-Wedderburn).

Linear and logistic regression are predictive modeling techniques with different purposes. Linear Regression: Purpose: Predicts continuous variables. Output: Continuous values via a linear equation. Assumptions: Linear relationships, normal error distribution, homoscedasticity, independence of errors. Logistic Regression: Purpose: Predicts categorical variables, usually binary. Output: Probabilities for binary outcomes. Assumptions: Linear relationship between logodds and variables, independent observations, minimal multicollinearity. In summary, linear regression is for continuous outcomes, while logistic regression is for binary or categorical outcomes.

Linear regression is used for predicting continuous outcomes with a straight-line relationship, while logistic regression is used for predicting categorical outcomes with a probabilistic approach. Linear Regression: Predict the patient's cholesterol level. Approach: You use linear regression to find a relationship between the health data and cholesterol level, resulting in an equation like: cholesterol = 0.5 * age + 1.2 * blood_pressure + 0.8 * cholesterol_level + 50. Logistic Regression: Predict whether the patient has a heart disease (yes or no). Approach: You use logistic regression to find a relationship between the health data and the probability of having heart disease. The model will output a probability between 0 and 1.

Consider predicting student test scores (continuous values) based on study hours and difficulty (independent variables). This is called linear regression. What if you want to categorize students as passing (1) or failing (0) based on attendance and homework completion? Here is where logistic regression comes into play. It is based on linear regression, but it uses a sigmoid function to convert the output to a probability (0-1). The key: Linear Regression predicts a number (e.g., estimated test score). Logistic Regression predicts a probability (for example, 85% chance of passing). Setting a threshold (typically 0.5) allows for the classification of students (passing if >0.5, failing if <0.5), basically yes/no outcomes.

I remember a project early in my career where I had to predict customer churn for a telecommunications company. Initially, I approached the problem with linear regression, thinking that predicting the likelihood of churn could be handled by predicting a continuous score. However, the results were not satisfactory, and the model's predictions were not making sense in the context of binary outcomes. After some research, I realized that logistic regression was more appropriate for this binary classification problem. By switching to logistic regression, I was able to model the probability of a customer churning and then classify them based on a threshold (e.g., if the probability was greater than 0.5, the customer was predicted to churn).

From my experience so far, very few people actually truly understand the inner working of logistics regression. Many think it's fitting an S curve, while that is partially true, that is, in fact, not the complete truth. The log part of the logistic regression and the goodness of fit are concepts many are confused over. You are actually fitting a line and not a curve while solving for your equation, it's just that the modelling is happening in a different transformed plane than compared to the one people look at generally without transformation. Actually reading further on these helps a lot in understanding widely mistaken concepts about the technique.

Logistic regression is a powerful tool for binary classification. It predicts probabilities between 0 and 1, using the logit function to transform probabilities into a continuous scale. The logistic (sigmoid) function maps real values into the (0, 1) interval, ideal for binary outcomes. Coefficients are estimated via Maximum Likelihood Estimation (MLE), representing log-odds changes. The model extends to multiclass problems with techniques like one-vs-all (OvA). Regularization (L1 and L2) helps prevent overfitting, making logistic regression both versatile and robust for various classification tasks.

For dichotomous outcomes, its called binary logistic regression. Sigmoid curve shaped model is usually created to fit the model. But logistic regression can be also in a multinomial form, where it generalizes to multiclass problems. Keep in mind that it can also be multivariable or multiple logistic regression where there are multiple independent variables.

Different types of logistic regression can fit binary, ordinal, or non ordered discrete variables. Though usually one is referring to a binary variable when discussing logistic regression. Logistic regression essentially transforms the linear regression such that the result is bounded by 0 and 1 so that the result can be understood as a probability of the binary outcome. While linear regression can be applied to binary data, and often was in the past, given modern software packages there is essentially no reason to do this. Other than that, the basic linear form and ability to transform the explanatory features to fit nonlinear relationships is close to the same as the linear regression. Therefore, logistic regression is very popular.

This technique is applied when we want to predict a categorical variables. In a simple way it is used for classification problems. For example: Customer churn prediction

There are multiple purposes of using logistic and linear regression models depending on the problem. Lets try to simplify them to 5 categories. 1. To assess the presence association between variables (eg. in Biomedical Research). 2. To explore the nature of associations (weak, strong etc. high predictive power, low predictive power etc.) 3. To use the models in the real word (to deploy them in actual software and make actual predictions). 4. Some forms of regression can be used a a part of Causal inference framework such as instrumental variable regression. 5. Regression principles are the basis of state of the art models such as Deep Learning (Neural Networks), XGBoost and so on.

In my current role, We utilized logistic regression to develop a model that classifies the propensity of customers to purchase insurance based on vehicle characteristics. The model considers variables such as mileage, expiry date, model year, make, and state. By training the model with historical data, we were able to accurately predict the likelihood of a purchase, which significantly improved our targeted marketing efforts.

Para interpretar el resultado de la regresión lineal de manera efectiva, es crucial examinar los coeficientes de todas las entidades. Estos coeficientes proporcionan información sobre cómo cada característica influye en la variable objetivo. Normalmente, los coeficientes más altos indican un mayor impacto de la característica correspondiente en la variable objetivo. Sin embargo, es esencial tener en cuenta que esta interpretación es válida bajo ciertas condiciones. Específicamente, asume que no hay término de intersección o multicolinealidad entre las características. Por lo tanto, al interpretar el resultado de un modelo LR, es imperativo tener en cuenta estos factores.

The choice between linear regression and logistic regression depends on the nature of the variable being predicted. Both techniques are essential for statistical modeling but serve different purposes. Linear regression is used for continuous dependent variables. For example, it predicts a patient's cholesterol level based on age, body mass index (BMI), physical activity level, and diet, yielding a specific numerical value like 200 mg/dL. Logistic regression is used for categorical binary dependent variables. For instance, it predicts whether a patient has heart disease based on the same variables, modeling the probability of the event occurring, with the output being a probability between 0 and 1.

Linear regression is the model that we used to predict the outcomes of continuous data. Where the relationship between two (in simple regression relationship between 'x' and 'y') or more than two (which is multiple linear regression where 'y' remains the dependent outcome variable but 'x' are many, like x1,x2..etc.) is being established with the use of train data and then after get validated with the help of test data to ensure the accuracy. Similarly logistics regression lies on the same conditions with a different approach to deal with categorical data as the output variable and are same in the manner of simple and multiple terms as linear regression and formula get changed to (e) terms to form the 'S' like curve called Sigmoid function.

To interpret the output of linear regression effectively, it's crucial to examine the coefficients of all the features. These coefficients provide insights into how each feature influences the target variable. Typically, higher coefficients indicate a stronger impact of the corresponding feature on the target variable. However, it's essential to note that this interpretation holds true under certain conditions. Specifically, it assumes that there is no intercept term or multicollinearity among the features. Therefore, when interpreting the output of a LR model, it's imperative to consider these factors. By doing so, we can gain a more accurate understanding of how the features contribute to the prediction of the target variable.

As a simple rule, Logistic Regression is the best option when the outcome you are looking to predict is BINARY (Yes/No, Sick/Not sick, Active/Passive, True/False, Pass/Fail, etc.) otherwise Linear Regression or other types of Regressions, like Polynomial, Ridge, Lasso, Quantile, Bayesian, Principal Components, Elastic Net, Partial Least Squares, Elastic Net, etc).

Let's also add that marginal effects can facilitate the interpretation or the logistic regression. For a case with just single 2-level categorical predictor and absence of covariates, the average marginal effect is equivalent to the difference in probabilities between the two classes, which - if tested - reproduces 1:1 the classic Wald's z test for difference in 2 proportions. For the linear regression the marginal effects are 1:1 the model coefficients (assuming treatment contrast used).

Linear regression and logistic regression, pivotal in predictive modeling, differ notably in foundational assumptions. Linear regression, rooted in classical statistical principles, requires adherence to linearity, independence, homoscedasticity, and normality assumptions for unbiased inference. In contrast, logistic regression, lauded for adaptability, liberates itself from linearity constraints. It navigates real-world complexities sans the rigid demand for normally distributed residuals, providing practitioners a versatile framework. This emphasizes the need for precise regression selection, tailored to dataset intricacies.

Assumptions 1. Independence - both algorithms ensure that the observations made are independent of each other. 2. Normality- it ensures that the errors are normally distibuted. While logistic regression has no such assumptions. 3. Linearity - in linear regression dependent and independent variables are proportional to each other. That is their relationship is linear. While in logistic regression linearity is logit

Assumptions of linear regression are fundamental to understanding its applicability and limitations. Here they are: Linearity: The relationship between the independent variables and the target is assumed to be linear. Independence of Observations: Each observation in the dataset is assumed to be independent of the others. Homoscedasticity: The variance of the errors is constant across all levels of the independent variables. Normality of Errors: The errors are assumed to follow a normal distribution. No Multicollinearity: There should be no exact linear relationship among the independent variables. Adhering to these assumptions ensures the validity and reliability of the results obtained from linear regression analysis.

Logistic regression is advantageous over linear regression in its flexibility regarding assumptions. Unlike linear regression, which requires linearity, homoscedasticity, and normally distributed errors, logistic regression does not assume a linear relationship between independent and dependent variables. Additionally, it does not require normally distributed residuals. This flexibility makes logistic regression suitable for a broader range of applications, such as medical diagnosis, where predictors may not have a straightforward linear relationship with the outcome, and ensures more robust results in various real-world scenarios.

On the contrary, linear regression require less assumptions than virtually any other model to include logistic regression. Homoskedasticity and normal errors are only required for hypothesis testing and even then, generalized versions of standard errors and larger samples negate these issues. Linear regression provides the best average linear effect even given a nonlinear relationship no different than correlations or raw averages. Through variable transformation, nonlinear relationships are easily and accurately fit. Finally, it is logistic regression that requires stronger distribution assumptions as it is, by necessity, estimated by maximum likelihood. Though, ironically, these issues are always ignored.

Both are *regression* algorithms, contrary to incorrect claims that "logistic regression is not a regression" (logistic r. was invented exactly for solving regression problems, years before using it for classification). Both model the conditional expected value of the response. In experimental research, like clinical trials, both are used: - to test complex hypotheses about treatment effect through contrasts (simple effects) - to explore the impact of predictors on the conditional response (marginal effects), log-odds or probability - followed by the AN(C)OVA (an. of deviance for log. r.) the main and interaction effects can tested - to predict probability for the IPW and propensity matching - to test MCAR pattern in missing data

Linear regression is beneficial to businesses on inventory management, budgeting and strategic planning. It also aids investors and financial institutions in making data driven investment decisions. On the other hand, logistic regression assists banks and other financial institutions in making lending decisions and managing credit. It can also enable marketers to tailor campaigns and improve ROI.

DATA MODELS FROM INDIAN ARMY my work in army dealt with data analysis for various facets of MRO. So both the regressions make sense at different level of application. Whereas demand forecasting for VED analysis was formalized based on linear regression MRLS was hinged towards logistic regression model. The best and challenging part of analysis was for equipment which were at high tech threshold low quantity ones which had high impact on operations.

Both linear and logistic regression play crucial roles in understanding factors and predicting outcomes. -Suppose you work for an e-commerce company and want to predict whether a customer will make a purchase based on their browsing behavior. -You gather data on customer interactions (e.g., time spent on site, number of product views) and whether they eventually made a purchase (yes or no). Logistic regression models the probability of a purchase based on these features. -By understanding these probabilities, you can tailor marketing strategies to encourage potential buyers.

Logistic regression is an excellent choice for initial binary classification tasks. Its simplicity allows easy implementation without extensive hyperparameter tuning. It provides interpretable insights into feature importance and is relatively robust to overfitting, especially with smaller datasets. Applying logistic regression systematically as a first step helps identify potential challenges like class imbalance. If it performs reasonably well on training and testing data, it establishes a strong baseline for further model development using more complex algorithms like XGBoost or deep learning. Pros: - simplicity - interpretability - robustness make it a valuable tool Cons: - May not outperform more advanced ML models

Linear regression is used for predicting continuous outcomes, while logistic regression is used for predicting categorical outcomes. Linear regression models the relationship between independent variables and a continuous dependent variable, aiming to minimize the difference between actual and predicted values. Logistic regression models the probability that a given input belongs to a particular category using the logistic function, which constrains the output to be between 0 and 1. Linear regression uses ordinary least squares to estimate parameters, while logistic regression uses maximum likelihood estimation. Additionally, linear regression produces a straight line or plane, while logistic regression produces an S-shaped curve.

Linear regression predicts continuous outcomes, while logistic regression predicts binary outcomes. Linear regression fits a straight line to data, aiming to minimize the sum of squared errors. Logistic regression models the probability of a binary outcome using the logistic function, yielding values between 0 and 1.

Considering logistics, the simple outcomes as binary answer seem to be preferred, but linearity of continuous results can build up better probability understanding. So choose your poison