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

Residual, regression line drawn as Y=C+1075x, when x was 2, and y was 239, ...

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Deviation measures, Deviation Measures The drawback of the range as a m...

Deviation Measures The drawback of the range as a measure of dispersion is that it takes into account the values of only two data points - the largest and the smallest. One

Determine the effects of stopping smoking on weight gain, Determine the Eff...

Determine the Effects of Stopping Smoking On Weight Gain As part of a study to determine the effects of stopping smoking on weight gain, nine females were weighed on the day t

Data project, Dr. Jim Mirabella UNIT EIGHT: DATA ANALYSIS PROJECT All Excel...

Dr. Jim Mirabella UNIT EIGHT: DATA ANALYSIS PROJECT All Excel output should be copied into a single Word document where you must enter all of your responses to the questions below.

Find a nash equilibrium, 2 bidders have identical valuations of an object f...

2 bidders have identical valuations of an object for sale. The value of the object is either 0; 50 or 100, with equal probabilities. The object is allocated to one of the bidders i

Muti linear regression model problem, Muti linear regression model problem ...

Muti linear regression model problem An investigator is studying the relationship between weight (in pounds) and height (in inches) using data from a sample of 126 high school

Data project, Choose any published database from the internet or Bethel lib...

Choose any published database from the internet or Bethel library (such as those from the Census Bureau or any financial sites). You may opt to use one of the data files provided b

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

Examples of grouped, simple and frequency distribution data

Find the unbiased estimators for mean and variance matrix, Is the random ve...

Is the random vector (Trunk Space, Length, Turning diameter) of US car normally distributed? Why? If yes, find the unbiased estimators for the mean and variance matrix of (Trunk Sp

Demand, A monopolist firm''s demand curve is given by P:100-2q. (a) Find it...

A monopolist firm''s demand curve is given by P:100-2q. (a) Find its marginal revenue function.

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