Binary and linear regression
Thank you for reading this post, don't forget to subscribe!Thank you for reading this post, don't forget to subscribe!Binary and linear regressions are both popular techniques used in statistical modeling and machine learning to analyze and predict relationships between variables. However, they differ in their specific applications and assumptions.
Binary Regression (Logistic Regression):
✍Binary regression, often referred to as logistic regression, is used when the dependent variable is binary or categorical, taking one of two possible outcomes. It is commonly used for binary classification problems, where the goal is to predict the probability of an observation belonging to one of the two classes. For example, predicting whether an email is spam or not spam, or whether a customer will churn or not churn.
✍Logistic regression uses a logistic function (also known as a sigmoid function) to model the relationship between the independent variables and the probability of the binary outcome. The logistic function maps any real-valued number to a value between 0 and 1, which can be interpreted as the probability of belonging to a particular class.
The model estimates the coefficients of the independent variables, and the probability of the binary outcome is calculated using the logistic function. The model can also provide additional insights, such as the importance of each independent variable and the odds ratio.
Linear Regression:
Linear regression is used when the dependent variable is continuous and the relationship between the independent variables and the dependent variable is assumed to be linear. It is widely used for predicting and understanding the relationship between variables in regression analysis.
In linear regression, the goal is to find the best-fitting line that minimizes the sum of squared differences between the observed dependent variable values and the values predicted by the linear model. The model estimates the coefficients (intercept and slopes) that define the line. The coefficients provide information about the direction and magnitude of the relationship between the independent variables and the dependent variable.
Linear regression assumes that the relationship between the independent variables and the dependent variable is linear, and that the errors follow a normal distribution with constant variance (homoscedasticity).
In summary, binary regression (logistic regression) is used for binary classification problems, modeling the probability of a binary outcome, whereas linear regression is used for predicting and understanding the relationship between continuous variables.
Multiple linear regression
Multiple linear regression is a statistical modeling technique used to examine the relationship between a dependent variable and multiple independent variables. It extends simple linear regression, which considers only one independent variable, to incorporate several predictors.
In multiple linear regression, the relationship between the dependent variable (often denoted as “Y”) and the independent variables (often denoted as “X1,” “X2,” etc.) is represented by the following equation:
Y = β0 + β1X1 + β2X2 + … + βnXn + ε
In this equation:
Y is the dependent variable or the variable we want to predict.
X1, X2, …, Xn are the independent variables, also known as predictors or regressors.
β0, β1, β2, …, βn are the regression coefficients, representing the impact of each independent variable on the dependent variable.
ε is the error term, which accounts for the variability in Y that is not explained by the independent variables.
The goal of multiple linear regression is to estimate the regression coefficients (β0, β1, β2, …, βn) that minimize the sum of squared errors between the observed values of the dependent variable and the predicted values based on the independent variables. This estimation is typically done using a method called ordinary least squares (OLS).
Multiple linear regression makes several assumptions, including linearity, independence of errors, homoscedasticity (constant variance of errors), and absence of multicollinearity (high correlation among independent variables).
Once the regression coefficients are estimated, the model can be used to make predictions on new data by plugging in the values of the independent variables into the equation.