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

A new weight-watching company, A new weight-watching company, Weight Reduce...

A new weight-watching company, Weight Reducers International, advertises that those who join will lose, on the average, 10 pounds the first two weeks with a standard deviation of 2

Coefficient of variation, Coefficient of Variation or C.V. To compare t...

Coefficient of Variation or C.V. To compare the variability between or more series, coeffiecnt of variation is used, it is relative measure of dispersion, it innovated and used

Statistical process control, Statistical Process Control The variabilit...

Statistical Process Control The variability present in manufacturing process can either be eliminated completely or minimized to the extent possible. Eliminating the variabilit

Correlation coefficients, What type of correlation coefficient would you us...

What type of correlation coefficient would you use to examine the relationship between the following variables? Explain why you have selected the correlation coefficients. A. Re

Classical and modern regression, The data in the data frame asset are from ...

The data in the data frame asset are from Myers (1990), \Classical and Modern Regression with Applications (Second Edition)," Duxbury. The response y here is rm return on assets f

Techniques, Q. 1 a) Describe the important quantitative techniques used in ...

Q. 1 a) Describe the important quantitative techniques used in public system management. (10) b) Do you think the day will come when all decisions are made with the assistance of

Make a decision about the claim, Make a decision about the given claim. Do...

Make a decision about the given claim. Do not use any formal procedures and exact calculation. Use only the rare event rule. Claim: A coin favors head when tossed, and there

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

Business forecasting, Meaning and Definitions of Business Forecasting T...

Meaning and Definitions of Business Forecasting The problem of business  forecasting  refers to the  analysis  of the past and  present economic  conditions. With  the objectiv

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