## Definition

**Regression Analysis** is one of the most widely used tools in business analysis. It is the process of analyzing the relationship between variables.

Basically, if there are two variables, the variable that acts as the basis of estimation is called the independent variable, and the variable whose value is to be estimated is known as the dependent variable.

It is used to derive a response variable as a result of one or more variables that can drive the predictions.

The dependent variable is also popular as a predictor, response, and endogenous variable while the independent variable is known as an explanatory, regressor, and exogenous variable.

## Types of Regression analysis

### 1.Linear Regression

Basically two kinds of linear regression analysis: **Simple regression** and **multiple regression**.

Simple regression uses a single explanatory variable and multiple regression uses many numbers of explanatory variables.

Once the results are derived it will further help in predicting the dependent variable when the independent variable is a known factor and this is done with the help of regression statistics.

### Formulas for linear regression

Equation for simple regression:

Y= a+bX+u

Where, Y= Dependent variable

X= Independent(Explanatory) variable

a= Intercept, b= Slop, u= The regression residual

Equation for Multiple regression:

Y= a+bX1+cX2+dX3+eX4+…….+tXt+u

Where, Y= Dependent variable

X1, X2, X3, X4= Independent (Explanatory) variables

a= Intercept, b,c,d= Slops, u= the regression residual

Regression residual is the difference between the forecast value and observed value.

Regression analysis includes variables like Linear regression and Non-linear regression.

**Linear** regression is basically a straight-line relationship and **non-linear **is the one that has a curved relationship.

The data used in this method can be cross-sectional where data is collected from the same time period and time series in which data collected is observed only at specific points in the same time.

Simple linear regression is not suitable for big-size data. Here only one dependent and one independent variable, the relationship is linear between independent and dependent variables, and the type of regression line is a straight line.

Multiple linear regression contains one dependent variable and multiple independent variables.

### 2. Stepwise Linear Regression

This type of regression analysis is helpful when we work with multiple independent variables. In stepwise regression, we use three methods.

- Forward calculation
- Backward elimination
- Bidirectional end

### 3. Polynomial Regression

Polynomial regression is useful when the relationship between independent and dependent variables is non-linear.

This type of regression is suitable for curvilinear data. The power of the independent variable is more than one in this type of regression.

### 4. Logistic Regression

When the dependent variable is discrete we call it logistic regression. It is useful to manage data that has two potential outcomes.

SAS, Statistica, R packages are some tools that help to calculate logistic regression.

1 dependent variable (dichotomous), 2+ independent variable(s) (interval or ratio or dichotomous)

### 5.Ridge Regression

This type of regression is utilized for the examination of data acquired from multiple regression.

### 6. Lasso Regression

This type of regression is the same as ridge regression, but the only difference is that the information being sustain is not normal.

### 7.ElasticNet Regression

This type of regression is useful when dominant independent variables are more than the one between many corresponded independent variables.

This is a combination of ridge and lasso regression methods.

## Uses of Regression Analysis

- It helps in devising a functional relationship between two variables.
- It is one of the widely used tools in economic and business research where statistical interpretations are highly valued as their analysis is based more on cause and effect relationships.
- Helps in predicting the dependent variable value from the independent variable values.
- The coefficient of correlation and coefficient of determination can be established with the help of regression coefficients.

**Procedure for selecting variables:**

- Step-wise regression
- Forward selection
- Backward elimination

## Few major things you need to keep in mind while working with regression analysis

- Don’t give responsibility to your analyst to identify what is affecting the sales market. According to Redman, it is the manager’s duty or responsibility to identify the factors that affect the sales market.
- Data collection is one of the important tasks. Collect accurate data and be careful while collecting it. Make sure you collected it from trustworthy sources.
- Do not neglect the error term while calculating regression analysis. If you avoid the error term, then the result will be uncertain. Redman says that if the regression explains 90% of the relationship, then it is fine. But it is not fine when the regression explains 10% of the relationship and you act like it is 90%. From Redman’s point of view, regression analysis does not tell how rain affects the sales, but it tells the rain may affect the sales.
- Do not let data put back your sixth sense. Analyze yourself about the suitability of the result with your understanding of the present situation.

Get more definitions about Regression analysis and other ERP related terms here.