list 60 examples of regression, explain, and give example prompt statements
Here is a list of 60 different types of regression models. For each, I've included a brief explanation of what it does and an example prompt of a question it could help answer.
The models are grouped by their primary function, such as modeling linear relationships, binary outcomes, count data, or survival times.
🏛️ 1. Foundational Linear Models
These are the most common types of regression, forming the basis for many other models. They are used when the dependent variable (the one you're predicting) is continuous.
Simple Linear Regression
Explanation: Models the relationship between one independent variable (X) and one continuous dependent variable (Y) using a straight line.
Example Prompt: "Analyze the relationship between years of experience and a person's salary."
Multiple Linear Regression
Explanation: Models the relationship between two or more independent variables (Xs) and one continuous dependent variable (Y).
Example Prompt: "Predict a house's sale price based on its square footage, number of bedrooms, and neighborhood crime rate."
Polynomial Regression
Explanation: A type of linear regression that models a non-linear relationship by adding polynomial terms (e.g., , ) as predictors.
Example Prompt: "Model the relationship between fertilizer concentration and plant growth, which we believe increases at first and then levels off."
Hierarchical Regression
Explanation: A multiple regression where the researcher adds variables into the model in a specific, theory-driven order to see how much new predictive power each new "block" of variables adds.
Example Prompt: "First, determine how much variance in an employee's job satisfaction is explained by salary alone. Then, determine how much additional variance is explained after adding variables for work-life balance and manager quality."
🧮 2. Regularization & Dimensionality Reduction
These models are extensions of linear regression designed to handle high-dimensional data (many predictors) and prevent overfitting by penalizing large coefficients.
Ridge Regression (L2 Regularization)
Explanation: A multiple regression that shrinks model coefficients towards zero to prevent overfitting, especially when predictors are highly correlated. It keeps all variables in the model.
Example Prompt: "Predict a patient's blood pressure using a dataset with 50 different genetic markers that are known to be correlated with each other."
Lasso Regression (L1 Regularization)
Explanation: Similar to Ridge, but it can shrink some coefficients all the way to zero, effectively performing automatic variable selection.
Example Prompt: "From a list of 100 different marketing behaviors, identify the most important drivers of customer spending and build a predictive model."
Elastic Net Regression (L1 + L2)
Explanation: A combination of Ridge and Lasso. It groups and shrinks coefficients for correlated variables and can also perform variable selection.
Example Prompt: "Build a model to predict stock returns using 200 economic indicators, many of which are grouped and highly correlated (e.g., multiple interest rate measures)."
Principal Component Regression (PCR)
Explanation: A technique that first applies Principal Component Analysis (PCA) to reduce a large set of correlated predictors into a smaller set of uncorrelated "components," and then runs a linear regression on those components.
Example Prompt: "Predict a car's fuel efficiency (MPG) using a dataset with 30 different engine and design specifications that are highly collinear."
Partial Least Squares (PLS) Regression
Explanation: Similar to PCR, but it creates its components by finding the variables that best explain both the predictors and the dependent variable. It's very popular in chemometrics.
Example Prompt: "Predict the sugar content of a fruit based on its near-infrared (NIR) spectrometer readings, which consist of 1,000 correlated wavelength measurements."
Least Angle Regression (LARS)
Explanation: An efficient algorithm for high-dimensional data that is similar to forward stepwise regression. It's often used to compute the entire path of Lasso solutions.
Example Prompt: "Develop a model for predicting tumor size based on thousands of gene expression levels, and show me how the model's coefficients evolve as we add variables."
🚦 3. Binary & Categorical Outcome Models
These models are used when the dependent variable is not a continuous number, but a category (e.g., "Yes/No," "Type A/B/C").
Logistic Regression (Binary)
Explanation: The most common model for predicting a binary (two-category) outcome, such as Yes/No, Pass/Fail, or Win/Lose. It models the probability of the outcome.
Example Prompt: "Predict the likelihood that a customer will churn (cancel their subscription) based on their account age, usage, and number of support tickets."
Probit Regression
Explanation: Very similar to logistic regression, but it assumes the probabilities follow a standard normal distribution (a "probit" link function) instead of a logistic distribution. The results are often nearly identical.
Example Prompt: "Analyze the probability that a student will be admitted to a graduate program based on their GRE scores and undergraduate GPA."
Complementary Log-Log (clog-log) Regression
Explanation: A binary outcome model used when the probability of one outcome is very rare or very common. It's asymmetric, unlike logistic or probit.
Example Prompt: "Model the probability of a product component failing, an event that is very rare, based on its operating temperature and material type."
Multinomial Logistic Regression
Explanation: Used when the dependent variable has three or more categories that are not in any natural order (e.g., "Car," "Bus," "Train").
Example Prompt: "Predict a consumer's choice of smartphone brand (e.g., Apple, Samsung, Google) based on their income, age, and preferred features."
Ordinal Logistic Regression (Proportional Odds)
Explanation: Used when the dependent variable has three or more categories that are in a specific order (e.g., "Low," "Medium," "High").
Example Prompt: "Predict a customer's satisfaction rating (e.g., 'Very Dissatisfied,' 'Neutral,' 'Very Satisfied') based on the quality of service they received."
🔢 4. Count Data Models
These models are used when the dependent variable is a non-negative integer (0, 1, 2, 3...), such as "number of..."
Poisson Regression
Explanation: The most basic model for predicting count data. It assumes the mean and variance of the count are equal.
Example Prompt: "Predict the number of customer complaints a store will receive per day based on the number of staff working and the day of the week."
Negative Binomial Regression
Explanation: An extension of Poisson regression for "overdispersed" count data, where the variance is much larger than the mean (which is very common).
Example Prompt: "Model the number of asthma-related ER visits per month in a city. This number varies wildly, so a Poisson model doesn't fit."
Zero-Inflated Poisson (ZIP) Regression
Explanation: A model for count data with a large number of zeros. It simultaneously models two processes: one for whether the count is zero or not, and one for the count if it's not zero.
Example Prompt: "Predict the number of fish caught by park visitors. Many visitors don't fish at all (zero count), while others catch a variable number."
Zero-Inflated Negative Binomial (ZINB) Regression
Explanation: Combines the features of Negative Binomial (for overdispersion) and Zero-Inflated (for excess zeros). This is a very flexible and common model for real-world count data.
Example Prompt: "Model the number of dental cavities in a population where many people have zero cavities, but among those who have them, the count is highly variable."
Hurdle (or Two-Part) Model
Explanation: Similar to zero-inflated models, but it models the "hurdle" of getting a non-zero count separately from the count itself. The key difference is that it assumes all zeros come from one single process.
Example Prompt: "Analyze cigarette consumption. First, model the probability that someone smokes at all (the 'hurdle'), and then, only for smokers, model how many cigarettes they smoke."
⏳ 5. Survival & Time-to-Event Models
These models are used to predict the time until an event occurs, such as death, equipment failure, or customer churn. They are defined by their ability to handle "censored" data (e.g., when the study ends before the event happens for some subjects).
Cox Proportional Hazards Regression
Explanation: The most popular survival model. It models the hazard (the instantaneous risk) of an event occurring, based on a set of predictors, without making assumptions about the shape of the survival curve.
Example Prompt: "Analyze how a new drug, patient age, and tumor stage jointly affect the risk of patient mortality over a 5-year study."
Accelerated Failure Time (AFT) Models
Explanation: An alternative to Cox. Instead of modeling the hazard, it models the time-to-event directly, assuming that predictors "accelerate" or "decelerate" the time to failure by some factor.
Example Prompt: "Model how different manufacturing materials directly affect the expected lifespan (in hours) of a lightbulb."
Parametric Survival Models (e.g., Weibull, Log-Normal)
Explanation: A type of AFT model where you assume the time-to-event follows a specific statistical distribution (like the Weibull, Exponential, or Log-Normal distribution).
Example Prompt: "We believe our mechanical components fail according to a Weibull distribution. Fit a model to predict time-to-failure based on operational stress."
🌳 6. Tree-Based & Ensemble Models
These are machine learning models that work by building many simple models (usually decision trees) and combining their predictions. They are highly accurate and flexible.
Decision Tree Regression
Explanation: A non-linear model that predicts a continuous value by learning a set of "if-then-else" rules to split the data into groups. The final prediction is the average of the group.
Example Prompt: "Create a simple, interpretable model to predict a baseball player's salary based on their age, home runs, and batting average."
Random Forest Regression
Explanation: An "ensemble" model that builds hundreds of different decision trees on random subsets of the data and predictors, then averages their predictions. It's robust and prevents overfitting.
Example Prompt: "Develop a highly accurate model to predict a river's water quality based on 50 different environmental sensor readings."
Gradient Boosting Regression (GBM)
Explanation: An ensemble model that builds trees sequentially. Each new tree is trained to correct the errors made by the previous trees, leading to a very powerful model.
Example Prompt: "Build a state-of-the-art model to predict my store's daily sales volume based on promotions, holidays, and weather data."
XGBoost (Extreme Gradient Boosting)
Explanation: A highly optimized and regularized version of Gradient Boosting, famous for winning many data science competitions. It's fast, efficient, and often the top-performing model.
Example Prompt: "I need the most accurate model possible to predict a user's click-through-rate on an ad, using a massive dataset of user and ad features."
📈 7. Non-Linear & Non-Parametric Models
These models are designed to capture complex, non-linear patterns in the data without assuming a specific line or curve.
k-Nearest Neighbors (KNN) Regression
Explanation: A simple non-parametric model. To make a prediction for a new data point, it finds the "k" (e.g., 5) most similar data points in the training set and averages their Y values.
Example Prompt: "Predict a new house's price by finding the 10 most similar houses that have already sold and averaging their prices."
Support Vector Regression (SVR)
Explanation: A machine learning model that tries to fit a "tube" (or "margin") around the data. It finds the line or curve that has the most data points within this margin, making it robust to outliers.
Example Prompt: "Model the relationship between engine speed and power output, focusing on a model that is not overly influenced by a few outlier measurements."
Multivariate Adaptive Regression Splines (MARS)
Explanation: A flexible model that automatically finds "knots" or "hinges" in the data to build a set of piecewise linear functions. It's good at modeling complex relationships and interactions.
Example Prompt: "Model how a chemical reaction's yield is affected by temperature, but the relationship changes shape completely at the boiling point. The model needs to find that 'hinge' automatically."
Isotonic Regression
Explanation: A non-parametric model used when the relationship between X and Y is known to be only increasing (or decreasing), but not necessarily linear.
Example Prompt: "Model the relationship between a drug's dosage and a patient's response, given that we know the response can only increase or stay flat as the dose increases."
Local Polynomial Regression (LOESS/LOWESS)
Explanation: A non-parametric technique that fits many small, localized regression models across the data to build a smooth curve. It's primarily used for visualization.
Example Prompt: "Create a smooth line that shows the trend in atmospheric CO2 levels over time, capturing the complex wiggles and long-term curve."
Generalized Additive Models (GAM)
Explanation: A flexible model that extends linear regression by allowing non-linear functions (like splines or smoothers) for each predictor, which are then "added" together.
Example Prompt: "Predict a city's air pollution level based on traffic (which has a linear effect) and temperature (which has a complex, U-shaped effect)."
Neural Network Regression
Explanation: A complex machine learning model inspired by the human brain. It uses interconnected "neurons" in "layers" to model extremely complex, abstract, non-linear patterns.
Example Prompt: "Predict the 2D position of a person's joints in an image (pose estimation) based on the raw pixel data."
Michaelis-Menten Model
Explanation: A specific, named non-linear model from biochemistry that describes the rate of enzymatic reactions. It has a characteristic "hyperbolic" shape.
Example Prompt: "Fit a curve to my lab data showing how enzyme reaction velocity changes with substrate concentration."
Dose-Response Model
Explanation: A class of non-linear models (often sigmoidal or S-shaped) used in toxicology and pharmacology to model the effect of a drug or substance at different doses.
Example Prompt: "Determine the EC50—the concentration of a new drug that produces 50% of its maximal effect—based on our experimental data."
🛡️ 8. Robust Regression
These models are designed to be "robust" to outliers. Unlike standard linear regression, where one bad data point can pull the entire line, these models ignore or down-weight outliers.
Huber Regression
Explanation: A compromise between standard (L2) regression and robust (L1) regression. It acts like standard regression for points near the line but like robust regression for outliers.
Example Prompt: "Predict sales based on ad spend, but our data has a few days with 'fat-finger' data entry errors that I want the model to treat as outliers."
M-Estimators
Explanation: A general class of robust regression models (Huber is one) that work by minimizing a function that gives less weight to large errors (residuals).
Example Prompt: "Fit a regression line to this dataset, but use a loss function (like the Huber loss) that is less sensitive to the extreme outliers."
S-Estimators
Explanation: A highly robust method that focuses on finding a model with a robust (small) "scale" (S) of the residuals, making it very resistant to outliers.
Example Prompt: "Analyze financial data that is known to have extreme 'black swan' event outliers, and fit a model that is not skewed by these events at all."
MM-Estimators
Explanation: A model that combines the high robustness of S-estimators with the high efficiency of M-estimators. It's a popular, all-around robust method.
Example Prompt: "I need a model that is both highly resistant to outliers and statistically efficient. Fit an MM-estimator to this industrial process data."
Least Trimmed Squares (LTS)
Explanation: A highly robust model that fits a line to a subset (e.g., 75%) of the data, completely ignoring the 25% of points with the largest errors.
Example Prompt: "Fit a regression line to my data, but first, 'trim' and completely discard the 10% of data points that are the biggest outliers."
Theil-Sen Estimator
Explanation: A very robust non-parametric method that calculates the slope as the median of the slopes between all pairs of points in the dataset.
Example Prompt: "Calculate the trend line for this dataset, but use a median-based method (Theil-Sen) that is immune to extreme outlier points."
Reduced Major Axis (RMA) Regression
Explanation: A model used when there is measurement error in both the X and Y variables (unlike OLS, which assumes X is perfect).
Example Prompt: "Analyze the relationship between two different, error-prone lab tests that are supposed to measure the same thing (e.g., two different blood tests)."
🖇️ 9. Censored & Truncated Models
These are specialized models used when the dependent variable is limited in some way.
Tobit Regression (Censored)
Explanation: Used when the dependent variable is "censored," meaning values are "piled up" at a minimum or maximum limit. For example, "hours worked" can't be negative, so many people are at a limit of 0.
Example Prompt: "Model the amount of money households donate to charity, where many households donate $0, but we want to model the potential donation amount."
Truncated Regression
Explanation: Used when data beyond a certain limit is not just piled up, but is completely missing from the dataset.
Example Prompt: "Analyze the test scores of students in a 'gifted' program, where we only have data for students who scored above a 130 IQ. We want to correct for this selection bias."
Heckman Selection Model (Treatment-Effects)
Explanation: A two-stage model that corrects for selection bias. It first models the probability of being included in the sample, then models the outcome, correcting for the bias.
Example Prompt: "Analyze the factors that determine wages, but we only observe wages for people who are employed. We need to correct for the fact that the 'unemployed' group is missing."
🌍 10. Spatial & Panel Data Models
These models are designed for data that has a specific structure, such as data collected across geographic space or over time.
Geographically Weighted Regression (GWR)
Explanation: A spatial model that runs thousands of local regressions instead of one global one. It shows how the relationships between X and Y change over geographic space.
Example Prompt: "Don't just give me one 'global' relationship between income and voting patterns for the whole country. Show me a map of how that relationship changes from county to county."
Pooled OLS (Panel Data)
Explanation: The simplest panel data model. It "pools" all data from all individuals and time periods together and runs one big regression, ignoring the panel structure.
Example Prompt: "Analyze the relationship between GDP and investment, using data from 20 countries over 10 years, and just treat all 200 observations as independent."
Fixed Effects Model (FEM) (Panel Data)
Explanation: A panel data model that controls for all stable, unobserved characteristics of each individual (e.g., a company's "culture" or a person's "genetics"). It analyzes within-individual changes.
Example Prompt: "Analyze how a state's minimum wage policy change affects its own employment level over time, controlling for all unique, unchanging features of that state."
Random Effects Model (REM) (Panel Data)
Explanation: A panel data model that assumes the unobserved individual characteristics are random and uncorrelated with the predictors. It's more efficient than FEM but has stronger assumptions.
Example Prompt: "Analyze how CEO experience affects firm performance, using a sample of 100 firms, assuming that each firm's unobserved 'baseline performance' is just random variation."
🔬 11. Other Specialized & Quasi-Experimental Models
Generalized Linear Models (GLM)
Explanation: A broad framework that "generalizes" linear regression. It allows the dependent variable to follow different distributions (like Poisson, Binomial, etc.) by using a "link function." Logistic and Poisson regression are both GLMs.
Example Prompt: "I need to model an outcome that is a percentage (bounded at 0 and 1). Fit a GLM using a binomial distribution and a logit link function."
Regression Discontinuity Design (RDD)
Explanation: A quasi-experimental model that estimates the causal effect of an intervention by looking at a "discontinuity" or "jump" in an outcome at a specific cutoff point.
Example Prompt: "To see if a scholarship (given to students with a >3.5 GPA) causes better grades, compare the post-college success of students who just got it (3.51 GPA) to those who just missed it (3.49 GPA)."
Structural Equation Modeling (SEM)
Explanation: A complex framework that models a network of causal relationships simultaneously, often including "latent" (unobserved) variables.
Example Prompt: "Test a complex theory: Does 'Academic Ability' (a latent variable measured by test scores) cause 'Career Success' (measured by income and job title), and is this mediated by 'Education Level'?"
Two-Stage Least Squares (2SLS)
Explanation: A model used in econometrics to handle endogeneity (when a predictor X is also caused by the outcome Y). It uses an "instrumental variable" that is correlated with X but not Y.
Example Prompt: "I want to estimate the effect of education on income, but they might cause each other. Use 'proximity to a college' as an instrumental variable to isolate the causal effect of education."
Bayesian Linear Regression
Explanation: A version of linear regression that uses Bayesian statistics. Instead of finding one "best" coefficient, it produces a probability distribution of what the coefficient is likely to be.
Example Prompt: "Fit a linear regression to my small dataset, but instead of just p-values, give me a 95% 'credible interval' representing the range of plausible values for the slope."
Quantile Regression
Explanation: A model that estimates the relationship between X and Y at different quantiles (e.g., 10th percentile, median, 90th percentile) instead of just the mean (like OLS).
Example Prompt: "Analyze the effect of education on income. I don't want the average effect; I want to know if education has a bigger impact on high-earners (90th percentile) than on low-earners (10th percentile)."
Log-Linear Analysis
Explanation: A model used to analyze contingency tables (cross-tabs). It uses a logarithmic transformation to model the frequency counts in each cell based on the main effects and interactions of categorical variables.
Example Prompt: "Analyze the association between gender, smoking status, and education level from a survey, and determine if there is a three-way interaction between them."
Stepwise Regression
Explanation: An automated (and often criticized) method for variable selection. It "steps" through the data, adding (forward) or removing (backward) variables one at a time to find a model with a good predictive score.
Example Prompt: "I have 50 potential predictors. Run an automated stepwise algorithm to find a 'good enough' model with a smaller subset of these variables."
Fractional Polynomial Regression
Explanation: A model that provides more flexibility than standard polynomial regression by allowing non-integer and negative powers (e.g., , ), which can fit a wider variety of curves.
Example Prompt: "Model the complex, non-linear relationship between age and a specific biomarker, and let the model test a wide range of power transformations to find the best fit."
Mixed-Effects Models (Hierarchical Linear Models)
Explanation: Used for nested or grouped data (e.g., students within classes, within schools). It models "fixed effects" (global variables like curriculum) and "random effects" (variation at each group level, e.g., the unique effect of each school).
Example Prompt: "Analyze the effect of a new teaching method on student test scores, using data from 1,000 students across 50 different classrooms. I need to account for the fact that students in the same classroom are more similar to each other."
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