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

Compute the roughness of several parametric densities, An approximation to ...

An approximation to the error of a Riemannian sum: where V g (a; b) is the total variation of g on [a, b] de ned by the sup over all partitions on [a, b], including (a; b

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?

Professional Counselor, A researcher hypothesized that the pulse rates of ...

A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He believed that the runners’ pulses would be slower. He obtained a ra

Simulation, Simulation When decisions are to be taken under conditions ...

Simulation When decisions are to be taken under conditions of uncertainty, simulation can be used. Simulation as a quantitative method requires the setting up of a mathematical

Find the rank correlation coefficient, 1. Calculate the mean and mode of: ...

1. Calculate the mean and mode of: Central size 15 25 35 45 55 65 75 85 Frequencies 5 9 13 21 20 15 8 3 The following data shows the monthly expenditure of 80 students of

Pie diagram, Circles or Pie Diagram: Circles or pie diagrams are alter...

Circles or Pie Diagram: Circles or pie diagrams are alternative to squares. These are used  for the same purpose i.e. when  the values are differing  widely in their magnitude

LINEAR PROGRAMMING FOR SOLVNG INEQUALITIES, To use Linear Programming for s...

To use Linear Programming for solving the following inequalities. Following Twin Conditions (as mandated by the Indian Regulatory Authority) Twin Condition I for TV Broadcasters

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

Luxury goods higher for men than for women, According to a recent study, wh...

According to a recent study, when shopping online for luxury goods, men spend a mean of $2,401, whereas women spend a mean of $1,527. Suppose that the study was based on a sample o

Calculate the length of the rope, The tension, T, in the tow rope pulling t...

The tension, T, in the tow rope pulling the car in Newtons is given in P8.  Determine the minimum length of the rope l, between A and B, so that the tension in either AB or AC equa

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