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

Measurement errors models, How can we analyse data with four bilateral resp...

How can we analyse data with four bilateral response variables measured with errors and three covariated measured without errors?

Semiaverages and least square, how can we graph a trend line by semiaverage...

how can we graph a trend line by semiaverages and least square method?

Keno, Having 11 numbered balls -0 to 10 -into a basket and have 6 spaces t...

Having 11 numbered balls -0 to 10 -into a basket and have 6 spaces to be numbered with the balls selected in each 6 chances and it returned it back to the basket each time. Chanc

Level of significance, Level of Significance: α The main purpose of hyp...

Level of Significance: α The main purpose of hypothesis testing is not to question the computed value of the sample statistic, but to make judgment about the difference between

Different analyses of recurrent events data, Different analyses of recurren...

Different analyses of recurrent events data: The bladder cancer data listed in Wei, Lin, and Weissfeld (1989) is used in Example 54.8/49.8 of SAS to  illustrate different anal

Find relative maxima and minima, Q. Find relative maxima and minima? Wh...

Q. Find relative maxima and minima? When finding relative maxima and minima in the Chapters absolute extrema problem, don't forget to use the first or second derivative test to

Evaluation tracking system, BCBSRI was able to reduce MSD related Workers C...

BCBSRI was able to reduce MSD related Workers Compensation cases with lost workdays by implementing a New Ergonomic Program in March 2000 and increasing workstation evaluations. Ex

Calculating 40th percentile in ogive graph, how do i determine the 40th per...

how do i determine the 40th percentile in an ogive graph

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