Types of Regression Techniques

A regression problem is when the output variable is a real or continuous value, such as “salary” or “weight”. Many different models can be used, the simplest is linear regression. It tries to fit data with the best hyperplane which goes through the points

Regression Analysis is a statistical process for estimating the relationships between the dependent variables or criterion variables and one or more independent variables or predictors. Regression analysis explains the changes in criteria in relation to changes in select predictors. The conditional expectation of the criteria is based on predictors where the average value of the dependent variables is given when the independent variables are changed. Three major uses for regression analysis are determining the strength of predictors, forecasting an effect, and trend forecasting.

Regression analysis is the primary technique to solve the regression problems in machine learning using data modelling. It involves determining the best fit line, which is a line that passes through all the data points in such a way that the distance of the line from each data point is minimized.

Types of Regression Testing Techniques

The different types of regression analysis techniques get used when the target and independent variables show a linear or non-linear relationship between each other, and the target variable contains continuous values. There are many types of regression analysis techniques, and the use of each method depends upon the number of factors. These factors include the type of target variable, shape of the regression line, and the number of independent variables.

1. Linear Regression

Linear regression is one of the most basic types of regression in machine learning. The linear regression model consists of a predictor variable and a dependent variable related linearly to each other. The model consists of a single parameter and a dependent variable has a linear relationship. When the number of independent variables increases, it is called the multiple linear regression model.

We denote simple linear regression by the following equation given below.

y = mx + c + e

where m is the slope of the line, c is an intercept, and e represents the error in the model.

It is used for predictive analysis. Linear regression is a linear approach for modelling the relationship between the criterion or the scalar response and the multiple predictors or explanatory variables. Linear regression focuses on the conditional probability distribution of the response given the values of the predictors. For linear regression, there is a danger of overfitting.

2. Logistic Regression

Logistic regression is one of the types of regression analysis technique, which gets used when the dependent variable is discrete. Example: 0 or 1, true or false, etc. This means the target variable can have only two values, and a sigmoid curve denotes the relation between the target variable and the independent variable. Logistic regression is used to find the probability of event=Success and event=Failure. Logit function is used in Logistic Regression to measure the relationship between the target variable and independent variables.

3. Ridge Regression

This is another one of the types of regression in machine learning which is usually used when there is a high correlation between the independent variables. This is because, in the case of multi collinear data, the least square estimates give unbiased values. But, in case the collinearity is very high, there can be some bias value. Therefore, a bias matrix is introduced in the equation of Ridge Regression. This is a powerful regression method where the model is less susceptible to overfitting.

It is a technique for analyzing multiple regression data. When multicollinearity occurs, least squares estimates are unbiased. A degree of bias is added to the regression estimates, and as a result, ridge regression reduces the standard errors. The formula for ridge regression is

$\beta = (X^{T}X + \lambda * I)^{-1}X^{T}y$ .

4. Lasso Regression

Lasso Regression is one of the types of regression in machine learning that performs regularization along with feature selection. It prohibits the absolute size of the regression coefficient. As a result, the coefficient value gets nearer to zero, which does not happen in the case of Ridge Regression. Due to this, feature selection gets used in Lasso Regression, which allows selecting a set of features from the dataset to build the model. In the case of Lasso Regression, only the required features are used, and the other ones are made zero. This helps in avoiding overfitting in the model. In case the independent variables are highly collinear, then Lasso regression picks only one variable and makes other variables shrink to zero.

Lasso regression is

$N^{-1}\sum^{N}_{i=1}f(x_{i}, y_{I}, \alpha, \beta)$ .

5. Polynomial Regression

Polynomial Regression is another type of regression in machine learning techniques in machine learning, which is the same as Multiple Linear Regression with a little modification. In Polynomial Regression, the relationship between independent and dependent variables, that is X and Y, is denoted by the n-th degree. It is a linear model as an estimator. Least Mean Squared Method is used in Polynomial Regression also. The best fit line in Polynomial Regression that passes through all the data points is not a straight line, but a curved line, which depends upon the power of X or the value of n. While trying to reduce the Mean Squared Error to a minimum and to get the best fit line, the model can be prone to overfitting. It is recommended to analyze the curve towards the end as the higher Polynomials can give strange results on extrapolation.

6. Stepwise Regression

This form of regression is used when we deal with multiple independent variables. In this technique, the selection of independent variables is done with the help of an automatic process, which involves no human intervention. This feat is achieved by observing statistical values like R-square, t-stats and AIC metric to discern significant variables. Stepwise regression basically fits the regression model by adding/dropping co-variates one at a time based on a specified criterion.

It is used for fitting regression models with predictive models. It is carried out automatically. With each step, the variable is added or subtracted from the set of explanatory variables. The approaches for stepwise regression are forward selection, backward elimination, and bidirectional elimination. The formula for stepwise regression is

$b_{j.std} = b_{j}(s_{x} * s_{y}^{-1})$ .

7. Bayesian Linear Regression

Bayesian Regression is one of the types of regression in machine learning that uses the Bayes theorem to find out the value of regression coefficients. In this method of regression, the posterior distribution of the features is determined instead of finding the least-squares. Bayesian Linear Regression is like both Linear Regression and Ridge Regression but is more stable than the simple Linear Regression.