Goseeko blog
  • Home
  • Engineering
    • Civil
    • Electronics
    • Computers
  • Science
    • Chemistry
    • Maths
    • Physics
  • Commerce
  • Arts
  • E-Learning
  • Career
  • Exams
  • Scholarships
  • Hiring News
  • Goseeko- Smart Study Material
@2021 - All Right Reserved. Designed and Developed by PenciDesign
Top Posts
Goseeko launches its own certifications for engineering and...
Online certifications which you can get in a...
What is Race around Condition?
What is a Development Plan ?
What is a Co-operative Bank?
What are the properties of Laser?
Top 5 Websites for Academic Research
What is regula-falsi method?
Top 10 Engineering YouTube Channels for Engineers
What is Lorentz Transformation?
What are Toposheets?
What is Pumping and its types?
Maths

What is regression analysis?

by Harpreet_Physics 30/10/2021
written by Harpreet_Physics 30/10/2021 0 comment

Overview(regression analysis)

First time the term regression analysis was used by a British Biometrician Sir Francis Galton. He found that the offspring of tall or short parents tend to regress to the average height.

The term ‘regression’ means some sort of functional relationship between two or more related variables.

Regression is the estimation of unknown values of one variable from known values of another variable. We can also state the regression analysis as below-

Regression is the measure of average relationship between independent and dependent variable. We can used for two or more than two variables. There are two types of variables in this analysis-

1. Independent variable

2. Dependent variable

The variable which is used for prediction is called independent variable.

It is known as predictor or regressor.

The variable whose value is predicted by independent variable is called dependent variable or regressed or explained variable.

The scatter diagram shows relationship between independent and dependent variable, then the scatter diagram will be more or less concentrated round a curve, which is called the curve of regression.

When we find the curve as a straight line then it is known as line of regression and the regression is called linear regression.

What is correlation?

When two variables are related in such a way that change in the value of one variable affects the value of the other variable, then these two variables are said to be correlated and there is correlation between two variables.

Example- Height and weight of the persons of a group.

The correlation is said to be perfect correlation if two variables vary in such a way that their ratio is constant always.

Curve and regression of equation

If the scatter diagram indicates some relationship between two variables and , then the dots of the scatter diagram will be concentrated round a curve. This curve is called the curve of regression.

Regression analysis is the method used for estimating the unknown values of one variable corresponding to the known value of another variable.

The mathematical equation of the regression curve is called regression equation.

Note- regression line is the best fit line which expresses the average relation between variables.

LINE OF REGRSSION

When we get the curve as a straight line that curve is called a line of regression. A line of regression is the straight line which gives the best fit in the least square sense to the given frequency.

Difference between regression and correlation

1. Correlation is the linear relationship between two variables and regression is the average relationship between two or more variables.

2. There are only limited applications of correlation as it gives the strength of linear relationship and the regression is to predict the value of the dependent varibale for the given values of independent variables.

3. Correlation does not consider dependent and independent variables and regression consider one dependent variable and other indpendent variables.

Equation of the line of regression

Let 

is the equation of the line of y on x.

Let be the estimated value of yi for the given value of x = xi

According to the principle of least squares, we have the determined ‘a’ and ‘b’, sum of squares of deviations of observed values of y from expected values of y,

That means-

Or

Is minimum.

Form the concept of maxima and minima, we partially differentiate U with respect to ‘a’ and ‘b’ and equate to zero.

Which means 

And

These equations (3) and (4) are known as normal equation for straight line.

Divide equation (3) by n, we get-

This indicates that the regression line of y on x passes through the point

.

As we know that-

The variance of variable x can be expressed as-

Now, dividing equation (4) by n, we get-

from the equations (6), (7) and (8)

Multiply (5) by , we get-

Subtracting equation (10) from equation (9), we get-

Since ‘b’ is the slope of the line of regression y on x and the line of regression passes through the point , so that the equation of the line of regression of y on x is-

Which is known as regression line of y on x.

Note-

  1. are the coefficients of regression.

Solved examples of regression analysis

Example: Find the regression line of y on x for the given dataset.

X4.34.55.95.66.15.23.82.1
Y12.612.111.611.811.411.813.214.1

Sol.

Let y = a + bx is the line of regression of y on x, where ‘a’ and ‘b’ are given as-

Construct the following table

xyxyx^2
4.312.654.1818.49
4.512.154.4520.25
5.911.668.4434.81
5.611.866.0831.36
6.111.469.5437.21
5.211.861.3627.04
3.813.250.1614.44
2.114.129.614.41
Sum = 37.598.6453.82188.01

Using the above equations we get-

So that on solving these both equations-

a = 15.49 and b = -0.675

Hence, the regression line will be

y = 15.49 – 0.675x 

Interested in learning about similar topics? Here are a few hand-picked blogs for you!

  • What is conditional probability?
  • Bayes theorem.
  • Probability distributions?
  • Linear programming.
Share
0
FacebookTwitterPinterestLinkedinTumblr
previous post
List of The Top 10 B.Com Colleges across India
next post
What is method of variation of parameters?

You may also like

What are matrices and their types?

16/05/2022

What is graph theory?

16/05/2022

What is a ring?

16/05/2022

What are the definite and indefinite integrals? Explained...

29/04/2022

What is the Pigeonhole principle?

20/04/2022

What is a bar diagram?

20/04/2022

What is simplex method?

20/04/2022

What is maxima and minima?

20/04/2022

What is the sample space and types of...

20/04/2022

What is integration?

15/04/2022

Leave a Comment Cancel Reply

Save my name, email, and website in this browser for the next time I comment.

Keep in touch

Facebook Twitter Instagram Youtube

Popular Posts

  • 1

    What is Race around Condition?

    03/08/2021
  • 2

    What is a Development Plan ?

    02/08/2021
  • 3

    What is a Co-operative Bank?

    03/08/2021
  • 4

    What are the properties of Laser?

    02/07/2021
  • 5

    Top 5 Websites for Academic Research

    11/07/2021
  • 6

    What is regula-falsi method?

    03/08/2021
  • 7

    Top 10 Engineering YouTube Channels for Engineers

    10/07/2021
  • 8

    What is Lorentz Transformation?

    02/07/2021
  • 9

    What are Toposheets?

    07/07/2021
  • 10

    What is Pumping and its types?

    03/08/2021

Categories

  • Arts
  • Career
  • Chemistry
  • Civil
  • Commerce
  • Computers
  • E-Learning
  • Electronics
  • Engineering
  • Exams
  • Hiring News
  • Maths
  • Physics
  • Scholarships
  • Uncategorized

Read alsox

How to solve a differential equation?

12/07/2021

What is Linear Programming?

26/05/2021

What is permutation?

21/03/2022