***Applications**: Relationship between one independent and one dependent variable, e.g., predicting income based on education level.
***Requirements**: Linear relationship, normal distribution of errors, homoscedasticity (constant variance of errors), independence of errors.
***Multiple Linear Regression**
***Applications**: Relationship between multiple independent variables and one dependent variable, e.g., predicting house prices based on location, size, and age.
***Requirements**: Same as simple linear regression but for multiple independent variables.
### 2\. **Logistic Regression**
***Binary Logistic Regression**
***Applications**: Predicting a binary outcome, e.g., disease prediction (disease/no disease).
***Requirements**: Dependent variable is binary, independent variables can be continuous or categorical, no perfect multicollinearity.
***Multinomial Logistic Regression**
***Applications**: Predicting a categorical variable with more than two non-ordered categories, e.g., choice of transportation method (car, bus, bike).
***Requirements**: Dependent variable has more than two categories that are not ordered.
***Ordinal Logistic Regression**
***Applications**: Predicting an ordered categorical variable, e.g., satisfaction scale (very dissatisfied to very satisfied).
***Requirements**: Dependent variable is ordinal, proportional odds assumption (effects of independent variables are constant across categories).
### 3\. **Poisson Regression**
***Applications**: Modeling count data, e.g., number of car accidents per year.
***Requirements**: Dependent variable is a count variable, events are independent, event rate is constant.
### 4\. **Negative Binomial Regression**
***Applications**: Modeling over-dispersed count data, e.g., number of emergency room visits by chronically ill patients.
***Requirements**: Same as Poisson regression, but variance greater than the mean.
### 5\. **Quantile Regression**
***Applications**: Analyzing the distribution of a dependent variable, e.g., wage distribution at different quantiles (median, upper quartile).
***Requirements**: No specific assumptions about the distribution of errors, robust to outliers.
### 6\. **Ridge Regression**
***Applications**: Dealing with multicollinearity in linear regression, e.g., predicting marketing expenditures.
***Requirements**: Independent variables are highly correlated.
### 7\. **Lasso Regression**
***Applications**: Variable selection and regularization, e.g., genomic data analysis.
***Requirements**: Same as ridge regression but sets some coefficients to zero.
### 8\. **Elastic Net Regression**
***Applications**: Combining advantages of ridge and lasso, e.g., complex economic models.
***Requirements**: Data exhibits both high multicollinearity and the need for variable selection.
***Requirements**: Relationship between independent and dependent variables is polynomial.
### 13\. **Spline Regression**
***Applications**: More flexible fits than linear models, e.g., time series analysis.
***Requirements**: Data exhibits non-linear trends.
### 14\. **Log-Log Regression**
***Applications**: Modeling multiplicative relationships, e.g., economies of scale in production.
***Requirements**: Both variables are positive and can be logged.
### 15\. **Generalized Linear Models (GLM)**
***Applications**: Various distributions of the dependent variable, e.g., binomial, Poisson, gamma distributions.
***Requirements**: Dependent variable follows one of the distributions in the GLM framework.
### 16\. **Nonlinear Regression**
***Applications**: Non-linear relationships between variables, e.g., pharmacokinetics.
***Requirements**: The relationship between independent and dependent variables is non-linear and known.
These regression types offer various tools for analysis and prediction based on the nature of the data and the underlying relationships between variables.
