### What is Regression Analysis?

Regression analysis is a form of predictive modelling technique which investigates the relationship between a **dependent **(target) and **independent variable (s)** (predictor). This technique is used for forecasting, time series modelling and finding the causal effect relationship between the variables.

Using regression is an important tool for analyzing data and for modeling.

### Why is using regression important?

Regression analysis is important because it’s used as a tool to predict an outcome by comparing a variable or multiple variables.

For example, you are trying to predict the sales growth of a company based on certain economic conditions. You have some recent data in front of you and it shows some growth of twice the economic growth in the year. Therefore, you can use recent and past data on the company to do some predictions based on the information you have.

### How does this benefit the company?

- You can predict how sales and other growth opportunities arise based on the relationships of those variables
- You can predict the strength of the company among other economic conditions and yield tangible results
- You will have a base and avoid possible pitfalls in the future

There’s many types of regression analysis, but I’m going to cover the basic and most common techniques, which is Linear Regression.

### What is Linear Regression?

Linear Regression establishes a relationship between **dependent variable (Y)** and one or more **independent variables (X)** using a **best fit straight line** (also known as regression line).

It is represented by an equation **Y=a+b*X + e**, where a is intercept, b is slope of the line and e is error term. This equation can be used to predict the value of target variable based on given predictor variable(s).

A simple linear regression fits a straight line through the set of n points.

#### Regression Formula:

Regression Equation(y) = a + bx Slope(b) = (NΣXY – (ΣX)(ΣY)) / (NΣX^{2} – (ΣX)^{2}) Intercept(a) = (ΣY – b(ΣX)) / N

### Example:

Suppose you are working at a restaurant and you’re trying to figure out your future tips. Based on the data you have, how do you figure the predictions for tips?

Write the tip formula based on the output:

Y= 0.1515x + 11.4666

Y=(0.15151515 + 11.46666667)=11.618188182

Total = 11.618188182 will be your next tip

11.61818182 |

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