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

Calculate the damping ratio for each system, (i) Plot the step responses of...

(i) Plot the step responses of the following second order systems and state the nature of each system. For each case, find the poles and plot the location of the poles in the compl

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

Evaluate the standard deviation, You have an assembly line which produces 1...

You have an assembly line which produces 1L bottles of seltzer with a standard deviation of 0.05L. • Assuming the distribution of volume is normal, what is the chance any single

Melissa Bakery, Melissa Bakery is preparing for the coming thanksgiving fes...

Melissa Bakery is preparing for the coming thanksgiving festival. The bakery plans to bake and sell its favourite cookies; butter cookies, chocolate cookies and almond cookies. A k

Regression analysis and experimental design, For many decades, there has be...

For many decades, there has been considerable attention paid to identifying various factors that help to reduce the number of fatalities on Australian roads. In 1964 Victoria and S

HLT 362, What is an interaction? Describe an example and identify the varia...

What is an interaction? Describe an example and identify the variables within your population (work, social, academic, etc.) for which you might expect interactions?

Sample standard deviation, Sample Standard Deviation So far, we discu...

Sample Standard Deviation So far, we discussed the population standard deviation. Now, let us switch to sample standard deviation(s) that is analogous to the population stand

Compute the output of correlation, Q. Compute the output of correlation? ...

Q. Compute the output of correlation? The following figure shows (a) a 3-bit image of size 5-by-5 image in the square, with x and y coordinates specified, (b) a Laplacian

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