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

Bionomial, The Quality Manager of a battery manufacturing plant reviewed th...

The Quality Manager of a battery manufacturing plant reviewed the warranty records within his department and found that 4% of the low maintenance batteries produced at the plant ov

Hypothesis testing, the president of a certain firm concerned about the saf...

the president of a certain firm concerned about the safety record of the firms employee sets aside $50 million a year for safety education. the firms accountant believes that more

Determine the closed loop speed transfer function, In the case of permanent...

In the case of permanent magnet DC motor whose stator consists of a permanent magnet we can take the field current to be constant (i.e. a constant magnetic field) and it can be sho

Regression constants, The regression line should be drawn on the scatter di...

The regression line should be drawn on the scatter diagram in such a way that when the squared values of the vertical distance from each plotted point to the line are added, the to

Aviation legislation - SUPPLEMENTAL TYPE CERTIFICATION, JAR 21 SUPPLEMENTAL...

JAR 21 SUPPLEMENTAL TYPE CERTIFICATION JAR 21 Part E introduces the need for Supplemental Type Certification when a manufacturer wishes to make major changes to the Type Desig

Regression, The 4 assumptions of regression: 1.       Variables are norm...

The 4 assumptions of regression: 1.       Variables are normally distributed 2.       Linear relationship between the independent and dependent variables 3.       Homosced

Business statistics, Betting on sporting events is big business both in the...

Betting on sporting events is big business both in the US and abroad. Consider, for instance, next winter’s American football tournament known as the Superbowl. Billions of dollars

Time series, merits and demerits of methods to determin trends

merits and demerits of methods to determin trends

Weight distribution, What does the confidence level of a confidence interva...

What does the confidence level of a confidence interval tell you? Suppose that a population has mean, µ, and standard deviation, σ.  What does the central limit theorem tell us

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