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

Pneumatic actuator design matrix, Pneumatic Actuator Design Matrix: The ra...

Pneumatic Actuator Design Matrix: The range of actuator design parameters have been provisionally assessed and are presented in Table. You are required to determine the following

Regression coefficient, Regression Coefficient While analysing regressi...

Regression Coefficient While analysing regression in two related series, we calculate their regression coefficients also. There are two regression coefficients like two regress

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

Characteristics of index number, Characteristics of Index Number  On th...

Characteristics of Index Number  On the analysis of various definitions of index number the following may be its characteristics: 1.      Expressed in Number : Index number

Time series, what is the use of applied statistic in our daily routin life

what is the use of applied statistic in our daily routin life

Carry out a t-test, Suppose that before the minimum wage law change, the un...

Suppose that before the minimum wage law change, the underlying mean number of part-time employees per Burger King Restaurant in New Jersey was 20.3. It was thought that the increa

Perform a simple linear regression analysis, In New Jersey, banks have been...

In New Jersey, banks have been charged with withdrawing from counties having a high percentage of minorities. To substantiate this charge, data is presented in the table below conc

Solve the normal distribution problem, Assume that the normal distribution ...

Assume that the normal distribution applies and find the critical z value(s). A = 0.04; H1 is mean ≠ 98.6 degrees Fahrenheit. Dteremine the value of Z. Find the value of the

Evaluate minimum capability requirement, You are currently working wit...

You are currently working with a supplier who is producing a shaft whose diameter specification is 6.00 ± .003 inches.  Currently, the process is yielding shafts wit

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