EDUCBA

EDUCBA

MENUMENU
  • Free Tutorials
  • Free Courses
  • Certification Courses
  • 360+ Courses All in One Bundle
  • Login

Statistical Analysis Regression

By Priya PedamkarPriya Pedamkar

Home » Data Science » Data Science Tutorials » Big Data Tutorial » Statistical Analysis Regression

Statistical Analysis Regression

Introduction to Statistical Analysis Regression

Statistical Analysis Regression uses the statistics methods such as mean, median, normal distributions to figure out the relationships between the dependent and independent variables, to access the relationship strength between the variables and for modelling the new relationship among them, as it involves various variations such as simple linear, multilinear and non-linear where the non-linear regression is mainly used for complicated datasets in which the independent and dependent variables shows the nonlinear relationship.

Mean: Mean or statistical mean is derived from adding all the numbers and then divide by how many numbers are there.

Start Your Free Data Science Course

Hadoop, Data Science, Statistics & others

Standard deviation: Standard deviation is a measure used to quantify the amount of variation in a set of data.

Standard deviation = Squared root of variance i.e., S

Variance = Squared of Standard deviation i.e., S2

Standard deviation statistical analysis

Normal distribution: For regression analysis, we follow the normal distribution. It is a probability distribution. In normal distribution mean is equal to median which is equal to mode (mean = median = mode). It is also called bell-curved distribution.

Normal distribution

Regression in statistics is the relationship between the mean value of one variable i.e., output and its related values of other variables i.e., time and cost.

Regression analysis will help in providing an equation for a graph so that predictions can be made for the data.

Popular Course in this category
Statistical Analysis Training (10 Courses, 5+ Projects)10 Online Courses | 5 Hands-on Projects | 126+ Hours | Verifiable Certificate of Completion | Lifetime Access
4.5 (6,071 ratings)
Course Price

View Course

Related Courses
Hadoop Training Program (20 Courses, 14+ Projects, 4 Quizzes)MapReduce Training (2 Courses, 4+ Projects)Splunk Training Program (4 Courses, 7+ Projects)Apache Pig Training (2 Courses, 4+ Projects)

Examples:

  • We can use regression analysis in marketing to determine the best groups that should be targeted in the marketing campaign.
  • The simplest example of regression analysis is – when there is a connection between how much you eat and how much you weigh; regression analysis can help you quantify the same.

So, from the above example, we understand that regression analysis in statistics is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.

In simple words, regression is the best guess at using a set of data to make a prediction.

Need for Statistical Analysis Regression

We know that the correlation coefficient is also a statistical relationship between two variables and it only gives us the degree of relationship or association. It cannot help us in predicting or estimating the response variable for a given independent variable. Here the response variable is also known as the dependent variable.

We need statistical analysis regression for the below reasons: –

  • To explain the variations in the dependent variable as a result of using a number of independent variables.

Example: When we examine the factors that influence profit volume in a company. Here profit volume is considered as a dependent variable because it may be affected by other variables.

  • To describe the nature of a relationship in a precise manner by way of the statistical equation.
  • To use the prediction and forecasting problems.
  • To help in removing an unwanted factor.
  • For identifying potential relationships between business variables and address any possible outcomes or solutions between them.

Decision-makers of a company can use regression analysis results for making important decisions that add significant business values to the growth of the company.

How to Perform Statistical Analysis Regression?

Regression analysis is used to predict future results by analyzing the present and past data.

Case study:

The below example shows us a basic understanding of how regression analysis is performed

Let us perform a regression analysis of sales volume for a doll manufacturing company.

Consider the below

Sales Volume for the manufacturing company (Target) = Y

Here Predictors are:

  • Price = X1
  • Doll A model = X2
  • Year = X3
  • Other Aspects = X4

Consider the level of impact of each predictor or variable equal to b. The level of X1 impact is b1, X2 it is b2 and so on. Now we have the coefficients – b1,b2,b3..bn

Here the value of Y can be affected by one or more combinations of all independent variables.

We can use simple linear regression formula for sale volume:

Y = b1X1 + b2X2 + b3X3 + ….. + bnXn

By this, we can understand that regression analysis uses observations data to estimate the values of the coefficient of b1,b2,b3,.., bn. Post this we can predict sale volume (Y) using the below formula. Here sale volume is estimated so we call it Ŷ.

Statistical Analysis Regression 1

Please note that Y ≠ as Ŷ and Ŷ is just an estimated value.

So to correct the value of Y we do the below

Y =  Ŷ ± error

In other words, y equal to y had a plus-minus error.

What if we understood that in our regression model there is no impact of X1, X2, X3, and X4 on Ŷ

In another way, the values of b1,b2,b3, and b4 are equal to zero then sales volume is equal to 0

Below will be the formula:

Statistical Analysis Regression 2

Therefore Sales volume = Zero which is incorrect. Sales Volume cannot be 0.

In this situation, we fix it by adding other coefficient b0. Here b0 is called intercept or constant.

Then below will be the formula

Statistical Analysis Regression 3

This is called Multi Linear Regression.

Here:

  • is called intercept or constant
  • b1,b2,b3,b4 are called coefficients

Regression Scatterplot graph in Excel

Lets us learn how to plot graphs in excel with the below problem statement.

Problem Statement:

X (No. of products sold) Y (Amount received)
2 3000
2 2500
3 4000
4 3500
6 5000
7 5500
7 6000
9 6000
11 7000
12 6500

We have two columns in the above table X and Y.

X is the number of products sold and Y is the amount received after selling the products.

So in this problem, the first-row state’s number of products sold is 2 and the amount received after selling the product is ₹3000.

The second row states that the number of products sold is 2 and the amount received after selling the product is ₹2500 and so on.

We can now run simple descriptive statistics on this data.

We need to be sure that we have data analysis available in excel.

And if you don’t have this you’ll simply need to:

  • Go to file then click on excel options.

Statistical Analysis Regression excel options

  • Select Add-ins and press OK.

Statistical Analysis Regression Add-ins

  • Then click on add-ins under Manage select Excel Add-ins and click on GO.

Excel Add-ins

  • Then click on go and be sure that you select Analysis ToolPak.

Statistical Analysis Regression Analysis ToolPak

  • You will then get the option of data analysis in the toolbar.

data analysis in tool bar

Now that we have data analysis options in excel lets run descriptive statistics.

  • Click on the data analysis option and select Descriptive Statistics and then OK.

select Descriptive Statistics

  • Select the input range as complete X i.e., the number of products sold in the below case from C3 to C12. Select Summary Statistics. If you want you can select the output range in this sheet (it’s optional), then click OK.

Select Summary Statistics

Select Summary Statistics 2

  • We will get the result in Column 1, where we get all the central tendency and other details.

central tendency

Plotting Regression Analysis in Excel

  • Select the complete excel of X & Y. Go to insert < select scatter < choose first option.

complete excel of X & Y

  • The below chart pop-ups.

chart pop-ups

  • Click on chart < go to layout and select Trendline. Choose Linear Trendline.

Linear Trendline

  • We can now find the trendline below.

Linear Trendline chart

Advantages of Statistical Analysis Regression

Now that we know how statistical analysis regression is performed, we need to understand the advantages after performing the regression analysis.

Below are a few advantages of statistical analysis regression:

  • Predictive analytics: Regression analysis results can define the business outputs. It helps to predict sales in the near and long term.
  • Business Operation efficiency: For a small business, it determines which factor matters the most and which factor can be ignored. It can be used to understand inventory levels, supply and demand levels.

Conclusion

We can now understand that Regression analysis is a family of statistical tools that can help business analysts build models to predict trends, make tradeoff decisions, and model the real world for decision-making support. Regression analysis helps to make better decisions for the business currently and for the future. Regression forecasting is used to determine the relationship between variables. Data provides fresh and new insights into the business which can help find the relationship between different variables to uncover patterns.

Recommended Articles

This is a guide to Statistical Analysis Regression. Here we discuss the needs, advantages of Statistical analysis regression and how to perform it. You can also go through our other suggested articles to learn more –

  1. Statistical Analysis Methods
  2. Statistical Analysis Types
  3. Learn the 17 Different Statistical Analysis Tools
  4. Guide to Statistical Analysis in R

Statistical Analysis Training (10 Courses, 5+ Projects)

10 Online Courses

5 Hands-on Projects

126+ Hours

Verifiable Certificate of Completion

Lifetime Access

Learn More

0 Shares
Share
Tweet
Share
Primary Sidebar
Big Data Tutorial
  • Statistical Analysis
    • Statistical Analysis
    • Statistical Analysis Types
    • Statistical Analysis Softwares
    • Free Statistical Analysis Software in the market
    • Types of Data in Statistics
    • Statistical Analysis Tools
    • Statistical Data Analysis Techniques
    • Statistical Analysis Methods
    • Exploratory Data Analysis
    • Statistical Analysis Regression
  • Big Data Basics
    • Introduction To Big Data
    • What is Big Data
    • Big Data Architecture
    • Big data Concepts
    • Careers in Big Data
    • Is Big Data a Database
    • Trends Of Big Data
    • Big Data Technologies
    • Big Data Programming Languages
    • Challenges of Big Data Analytics
    • What is Big Data Technology
    • Most Critical Aspect of Big Data
    • What is Big data and Hadoop
    • What Is NOSQL
    • Big Data Techniques
    • Big Data in Banking
    • Big Data interview questions
  • Big data and analytics
    • What is Big data analytics
    • What is Data Analysis
    • What is Data Analyst
    • What is Data Analytics
    • Careers in Data Analytics
    • Data Analysis Process
    • Who is a Data Scientist
    • What is Data Visualization
    • Types of Data Visualization
    • Types of Qualitative Data
    • Secondary Data Analysis
    • Data Visualization Tools
    • Benefits of Data Visualization
    • Best Data Visualization Tools
    • What is a Data Scientist?
    • What do Data Scientists Do
    • Skills Required for Data Scientist
    • Data Scientist Skills
    • How to Become a Data Scientist
    • Data Analyst Associate
    • Big Data Analytics
    • Big Data Analytics Examples
    • Big Data Analytics Jobs
    • Customer Data
    • Big Data Analytics Salary
    • Big Data Analytics Software
    • Big Data Analytics Techniques
    • Big Data Analytics Tools
    • Data Analysis Techniques
    • Data Analysis Software
    • Data Quality Tools
    • Data Analysis Tools
    • Data Analysis Tools Research
    • Types of Data Analysis
    • Types of Quantitative Research
    • What is Qualitative Data Analysis
    • Free Data Analysis Tools
    • Data Analytics Trends in 2019
    • Types of Data Analysis Techniques
    • Data Analytics Interview Questions
    • Data Analyst Interview Questions

Related Courses

Hadoop Certification Training

MapReduce Training

Splunk Training Certification

Apache Pig Training

Footer
About Us
  • Blog
  • Who is EDUCBA?
  • Sign Up
  • Corporate Training
  • Certificate from Top Institutions
  • Contact Us
  • Verifiable Certificate
  • Reviews
  • Terms and Conditions
  • Privacy Policy
  •  
Apps
  • iPhone & iPad
  • Android
Resources
  • Free Courses
  • Database Management
  • Machine Learning
  • All Tutorials
Certification Courses
  • All Courses
  • Data Science Course - All in One Bundle
  • Machine Learning Course
  • Hadoop Certification Training
  • Cloud Computing Training Course
  • R Programming Course
  • AWS Training Course
  • SAS Training Course

© 2020 - EDUCBA. ALL RIGHTS RESERVED. THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS.

EDUCBA Login

Forgot Password?

EDUCBA
Free Data Science Course

Hadoop, Data Science, Statistics & others

*Please provide your correct email id. Login details for this Free course will be emailed to you
Book Your One Instructor : One Learner Free Class

Let’s Get Started

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you
EDUCBA
Free Data Science Course

Hadoop, Data Science, Statistics & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

Special Offer - Statistical Analysis Training (10 Courses, 5+ Projects) Learn More