# Regression statistics

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## What is regression?

Regression statistics is commonly used to determine the relationship between independent variables denoted by x, and dependent variables denoted by y, on a graph.

Apart from just telling the relationship, regression analysis also determines the strength of the relationship that lies between the two variables. The independent variable is a factor in the event that changes frequently and which directly affects a dependent variable that is the interest of the study.

Example: You decide to study the relationship between the junk eating habits of people and their weight.

Here, people’s junk eating habits is independent variable and weight is a dependent variable. As people eat more junk, they tend to put on more weight. Hence, we can say that as the independent variable value increases, the dependent variable value increases as well.

The above relation can be denoted in graphical representation:

In the above diagram, the scatterplots are nothing but data collected from a set of samples. The relationship turns out to be linear regression, as both independent variable and dependent variable increase together.

Line of best fit – it is a line that runs through the scatterplots covering most of it. it is not necessary to cover all the points, although it is not possible, as close as the points are to the line of best fit, the more strongly the variables are related to each other.

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## Calculating regression analysis?

Regression analysis begins to proceed on the footing of the regression model:

Y = α + β1X1 +…+ βkXk + ε

Where, Y is and X1, X2, … Xk are the exploratory variables that affect Y. ε is a residual variable which is the composite effect of the individual differences.

Besides the regression model, the analyst may also take the help of some observed changes in the dependent variable and independent variables in a sample of a population.

As a result, regression analysis yields estimate variables denoted by β1, β2, … βk. These estimates are derived from the values of coefficient that adds up to the average residual 0. The standard deviation of these residuals is very small.

The prediction equation of the summarized result looks like:

Ypred = a + b1X1 + … + bkXk

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## Why use regression analysis?

It is pretty obvious by now, that regression statistics can predict the behaviour of the dependent variable based on the changes in its corresponding independent variable. Apart from this, it also predicts the value of a dependent variable.

• In organisations, regression statistics can be used to determine the sales and finances of the firm.
• It can give you numbers on the progress of your departments and help you make better decisions for the organization.
• It helps you understand the requirements and supplies of the resources that move in and out of your firm.
• You can determine how various variables affect each other and how they are related to each other.
• Apart from sales and finances, regression statistical practices can help you understand customer performance.
• You can find out why customers are having similar issues with your brand, predict how they will respond to a certain decision.

You can gauge all sorts of patterns and changes in the organization and determine beforehand the results of particular decisions and processes.

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