In this article, we are going to understand regression analysis, its importance, as well as the types of regression in machine learning.

## Regression Analysis

Regression analysis is a statistical technique that seeks to assess the strength of the connection between one or more dependent variables. It helps in the analysis of those factors. *Firstly, we must define a dependent and independent variable:*

**Dependent variable**: The dependent variable is the variable that we are attempting to anticipate or comprehend.

**Independent variable(s)**: These are the elements that impact the target variable and give information about their connection with it.

*Secondly, the formula for calculating regression analysis is as follows:*

*where:*

**Y**i = dependent variable**f**= function**Xi**= independent variable**B**= unknown parameters**ei**= error

### Example

For example, you may be wondering if there is a link between how much you eat and how much you weigh. Regression analysis comes into play here. It will provide you an equation for a graph, such as a scatter plot, and will assist you in making predictions about your data. If you’ve been losing a lot of weight in the last few months, it will help you forecast how much you’ll weigh in a year if you keep losing weight at the same rate. The other independent element that affects your weight is how much you eat. If you eat more, your weight will increase. Similarly, if you eat less, your weight will decrease.

## Importance of Regression Analysis

Regression analysis is useful because it can be used within an organization to identify the extent to which certain independent factors influence dependent variables.

The purpose of regression analysis is to produce meaningful and actionable business insights.

You can model many independent variables using regression analysis and the types of regression in machine learning.

Regression analysis includes both continuous and categorical variables.

Polynomial expressions represent curvature mathematically.

Finally, regression analysis also assists in controlling the independent variables. In simple words, regression analysis controls every variable in your model statistically.

The best way of solving regression errors in ML is regression analysis. This is done through data modeling. Basically you plot your data points on a chart and run the best fit line through them. Eventually in this manner you will be able to predict each data point’s probability of incurring error. Remember that the closer they are to the line, the smaller the prediction error.

## Types of Regression in Machine Learning

*The following are the types of regression in machine learning:*

### Linear Regression

Linear regression is a model that posits a linear connection between two variables, one of which is the input variable represented by x and the other being the single output variable represented by y. In other words, ‘y’ is the linear combination of the input variables ‘x’.

*The following is the formula for calculating linear regression:*

*Where:*

- Yi = a dependent variable
- f = a function
- Xi = an independent variable
- B = the unknown parameters
- ei = error

When variables are linked linearly, linear regression is applied. It is frequently used in predictive analysis.

*It can also be termed as:*

- Multiple Regression
- Multivariate Regression
- Ordinary Least Squares (OLS)

### Logistic Regression

Logistic regression is a classification and regression technique at the same time. It helps in the prediction of a binary outcome, such as yes/no, 1/0, true/false, and so on. In logistic regression, the dependent variables are categorical, which means they can only accept integral values indicating various classes. It is a subset of the Generalized Linear Model algorithm class. This approach expects a linear relationship between the link function and the independent variables rather than a linear relationship between the dependent and independent variables. In logistic regression, a sigmoid curve depicts the relationship between the target and independent variables. Despite the fact that it is a linear technique, the predictions are modified with the logistic function. As a result, we can no longer interpret the predictions as a linear combination of input variables as we could in linear regression.

*The following are the types of logistic regression:*

**Binary Logistic Regression**: This assists us when the dependent variable is wholly binary.

**Multinomial Logistic Regression**: This assists us when the dependent variable has nominal or unordered variables.

*The Multinomial Logistic Regression can be classified into two types. They are as follows*:

**Ordered Multinomial Logistic Regression**: This assists us when the dependent factor has ordered values.

**Nominal Multinomial Logistic Regression**: This assists us when the dependent factor has unordered categories.

### Ridge Regression

This type of regression assists us in predicting the coefficients of multiple regression models when there is a high correlation between the independent variables.

To explain this better, the least square estimates in multi collinear data gives unbiased values. Therefore, if the collinearity is very high, there exists some bias value.

T*he following are the effects of multi collinear data:*

- Multicollinearity produces inaccurate estimates of the regression coefficients and also increases the standard errors of these coefficients.
- It also degrades the data and gives an incorrect p-value.
- Basically, it reduces the predictive power of the model.

It is the ridge regression that has a bias matrix in the equation to solve such errors. Ridge regression decreases this error by adding a degree of bias to the regression estimates.

## Real-World Applications of Regression

Now that we have understood few types of regression, let us see where all it can be applied.

*The following are some real-world applications:*

**Predictive Analysis**: Regression analysis helps in anticipating future prospects and dangers for a company. Insurance providers, for example, use it to assess policyholder creditworthiness and the number of claims that are made in a certain period of time.

**Error Correction**: It also helps in the identification of mistakes in judgement and assists businesses in making proper judgments that will benefit them in the future.

**Uncover Meaningful Patterns**: A company has a large amount of raw or unstructured data that has yet to be examined. There is a tiny possibility that such data might offer important insights. Regression Analysis can discover a link between various variables and uncover patterns that can contribute to the success of a firm.