Regression problems are commonplace in machine learning, and the most common technique to solve them is regression analysis. It is based on data modeling and involves working out the best fit line, which passes through all the data points so that the distance between the line and each data point is minimal. While many different regression analysis techniques exist, linear and logistic regression are the most prominent ones. The type of regression analysis model we use will eventually depend on the nature of the data involved.
Let’s find out more about regression analysis and the different types of regression analysis models.
What is Regression Analysis?
Regression analysis is a predictive modeling technique for determining the relationship between the dependent (target) variables and independent variables in a dataset. It is typically used when the target variable contains continuous values and the dependent and independent variables share a linear or non-linear relationship. Thus, regression analysis techniques find use in determining the causal effect relationship between variables, time series modeling, and forecasting. For example, the relationship between the sales and advertisement expenditure of a company can be best studied using regression analysis.
Types of Regression Analysis
There are many different types of regression analysis techniques we can use to make predictions. Furthermore, the use of each technique is driven by factors such as the number of independent variables, the shape of the regression line, and the type of dependent variable.
Let us understand some of the most commonly used regression analysis methods:
1. Linear Regression
Linear regression is the most widely known modeling technique and assumes a linear relationship between a dependent variable (Y) and an independent variable (X). It establishes this linear relationship using a regression line, also known as a best-fit line. The linear relationship is represented by the equation Y = c+m*X + e, where ‘c’ is the intercept, ‘m’ is the slope of the line, and ‘e’ is the error term.
The linear regression model can be simple (with one dependent and one independent variable) or multiple (with one dependent variable and more than one independent variable).
2. Logistic Regression
The logistic regression analysis technique finds use when the dependent variable is discrete. In other words, this technique is used to estimate the probability of mutually exclusive events such as pass/fail, true/false, 0/1, etc. Hence, the target variable can have only one of two values, and a sigmoid curve represents its relationship with the independent variable. The value of probability ranges between 0 and 1.
3. Polynomial Regression
The polynomial regression analysis technique models a non-linear relationship between the dependent and independent variables. It is a modified form of the multiple linear regression model, but the best fit line that passes through all the data points is curved and not straight.
4. Ridge Regression
The ridge regression analysis technique is used when the data shows multicollinearity; that is, the independent variables are highly correlated. Although the least square estimates in multicollinearity are unbiased, their variances are large enough to deviate the observed value from the true value. Ridge regression minimizes the standard errors by introducing a degree of bias in the regression estimates.
The lambda (λ) in the ridge regression equation solves the multicollinearity problem.
5. Lasso Regression
Like ridge regression, the lasso (Least Absolute Shrinkage and Selection Operator) regression technique penalizes the regression coefficient’s absolute size. In addition, the lasso regression technique uses variable selection, which results in coefficient values shrinking towards absolute zero.
6. Quantile Regression
The quantile regression analysis technique is an extension of linear regression analysis. It is used when the conditions for linear regression are not met, or the data has outliers. Quantile regression finds applications in statistics and econometrics.
7. Bayesian Linear Regression
The Bayesian linear regression is one of the types of regression analysis techniques in machine learning that utilizes Bayes’ theorem to determine the value of the regression coefficients. Instead of finding out the least-squares, this technique determines the posterior distribution of the features. As a result, the technique has more stability than simple linear regression.
8. Principal Components Regression
The principal components regression technique is typically used to analyze multiple regression data with multicollinearity. Like the ridge regression technique, the main components regression method minimizes the standard errors by imparting a degree of bias to the regression estimates. The technique has two steps – first, principal component analysis is applied to the training data, and then, the transformed samples are used to train a regressor.
9. Partial Least Squares Regression
The partial least squares regression technique is one of the quick and efficient types of regression analysis techniques based on covariance. It is beneficial for regression problems where the number of independent variables is high with likely multicollinearity among the variables. The technique reduces the variables to a smaller set of predictors, which are then used to carry out a regression.
10. Elastic Net Regression
The elastic net regression technique is a hybrid of the ridge and lasso regression models and is useful when dealing with highly correlated variables. It uses the penalties from ridge and lasso regression methods to regularize the regression models.
Summary
Apart from the regression analysis techniques we discussed here, several other types of regression models are used in machine learning, such as ecological regression, stepwise regression, jackknife regression, and robust regression. The specific use case of all these different types of regression techniques depends on the nature of the data available and the level of accuracy that can be achieved. Overall, regression analysis has two core benefits. These are as follows:
- It indicates the relationship between a dependent variable and an independent variable.
- It shows the strength of the impact of independent variables on a dependent variable.
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