Regression lines, Applied Statistics

Assignment Help:

Regression Lines

It has already been discussed that there are two regression lines and they show mutual relationship between two variable . The regression line Yon X gives   the most probable  value of y of given value of x whereas the regression  line x on y gives the most probable values  of y

Why there are two Regression Lines:

First Reason: For two mutually related series there are two regression lines. First line of regression is X on Y and second line of regression is X on Y.

While constructing line of regression of X on Y, Y is treated as independent variable whereas X is treated as dependent variable. This line gives most probable values of X for given  values of X for given values of Y. In   the same way line of regression of Y on variable. This line gives the most probable values of Y for given values of X. Practically  X and Y both variables may be required to be estimated, hence there is necessity  of two regression lines. One for best estimation of X and other for Y 

Second Reason: The regression lines are those best fit lines which are drawn on least squares assumption. Under least square method the line which are to be drawn should be in that manner so that the total of the squares of the deviations of the various points is minimum. The deviation of the various points of actual values up to the regression online can be measured by two ways (a) Horizontally i.e. parallel to X axis and (b) Vertically i.e. parallel to Y axis .Hence for minimising the total of squares separately there should be two regression lines.

The regression line Y and X is drawn in such a way that it minimises total of squares of the vertical deviations. In the same way   regression line X on Y   is drawn in such a way that it minimises the total squares of the horizontal deviations. Hence it is essential to have two regressio line under the assumptions of least square method.


Related Discussions:- Regression lines

Probability, HOW WOULD YOU INTERPRET THIS PROBABILITY:P(a)=1.05

HOW WOULD YOU INTERPRET THIS PROBABILITY:P(a)=1.05

Lorenz curve , Lorenz Curve   It is a graphic method of measur...

Lorenz Curve   It is a graphic method of measuring dispersion. This curve was devised by Dr. Max o Lorenz a famous statistician.  He used this technique for wealth it i

Advantages of sampling, Advantages of Sampling Why should we settle on ...

Advantages of Sampling Why should we settle on a sample instead of studying the entire population?  Sampling has the following advantages over a census (study of the entire pop

QUARTILE DEVIATION, Examples of grouped, simple and frequency distribution ...

Examples of grouped, simple and frequency distribution data

Ogive graphs, how many types of ogive are there

how many types of ogive are there

Decision making ., it is said that management is equivalent to decision mak...

it is said that management is equivalent to decision making? do you agree? explain

What are the charateristics of a population for which, what are characteris...

what are characteristics of a population for which it would be appropiate to use mean/median/mode

Simple linear regression, Simple Linear Regression   While correlati...

Simple Linear Regression   While correlation analysis determines the degree to which the variables are related, regression analysis develops the relationship between the var

Regression model, Using a random sample of 670 individuals for the populati...

Using a random sample of 670 individuals for the population of people in the workforce in 1976, we want to estimate the impact of education on wages. Let wage denote hourly wage in

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd