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

Standard deviation for grouped data, Grouped data  For ...

Grouped data  For grouped data, the formula applied is  σ = Where f = frequency of the variable, μ= population mea

Find probability of remaining paint free - ball duel, In a three-cornered p...

In a three-cornered paint ball duel, A, B, and C successively take shots at each other until only one of them remains paint free. Once hit, a player is out of the game and gets no

Problem on standard deviation, Your organization purchases bottles of ...

Your organization purchases bottles of a popular commercial solvent for resale.  Each bottle is labeled as containing 32 fluid ounces of the solvent.  Your cont

Regression analysis, Of the 6,325 kindergarten students who participated in...

Of the 6,325 kindergarten students who participated in the study, almost half or 3,052 were eligible for a free lunch program. The categorical variable sesk (1 == free lunch, 2 = n

Range, Range Official Exports Target 2000-2001 ...

Range Official Exports Target 2000-2001 Product ($ million) Plantation 500 Agriculture and Alli

Mean and median, The amounts of money won by the top ten finishers in a fam...

The amounts of money won by the top ten finishers in a famous car race are listed below. $1,172,246    $163,659    $440,584    $350,634     $290,596 $186,731    $145,809     $143,2

Confidence interval, a) List down several measures of central tendency and ...

a) List down several measures of central tendency and define the difference among them? b) What do you mean by confidence interval, and why it is useful? What is a confidence lev

Regression analysis, Meaning and Definitions of Regression The dictiona...

Meaning and Definitions of Regression The dictionary meaning of regression is just opposite the meaning of progression. Progression means to move forward while regression means

Evaluate standard deviation, Consider an MBA program as a processing networ...

Consider an MBA program as a processing network where the flow unit consists of a student in the program.  Suppose the organizations that hire and promote MBAs are considered to be

Analysis of variance for the data, Analysis of Variance for the data: ...

Analysis of Variance for the data: Draw a random sample of size 25 from the following data : (a) With Replacement and   (b) Without Replacement and obtain Mean and Varia

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