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

Probability, 1 A penny is tossed 5 times. a. Find the chance that the 5th t...

1 A penny is tossed 5 times. a. Find the chance that the 5th toss is a head b. Find the chance that the 5th toss is a head, given the first 4 are tails.

Classification of universe, Classification of Universe The universe may...

Classification of Universe The universe may be classified either on the basis of number of units and on the basis   of existence of units as is clear from the following chart :

., Theories of Business forecasting

Theories of Business forecasting

Find the minimum constant workforce, Find the minimum constant workforce: ...

Find the minimum constant workforce: ABC Company, a manufacturer of roofing supplies, has developed monthly forecasts for roofing tiles. The forecasted demand and the expected

Principles of data analysis, For the data analysis project, you will addres...

For the data analysis project, you will address some questions that interest you with the statistical methodology we are learning in class.   You choose the questions; you decide h

PERCENTAGES, CALCULATE THE PERCENTAGE OF REFUNDS EXPECTED TO EXCEED $1000 U...

CALCULATE THE PERCENTAGE OF REFUNDS EXPECTED TO EXCEED $1000 UNDER THE CURRENT WITHHOLDING GUIDELINES

Correlation, prove that coefficient of correlation lies between -1 and+1

prove that coefficient of correlation lies between -1 and+1

Correlation coefficient, Consider three stocks A, B and C costing $100 each...

Consider three stocks A, B and C costing $100 each. The annual returns on the three stocks have mean $5 and variance $10. a. Suppose that the returns on the three stocks are i.i

Agreement, Agreement The degree to which different observers, raters or ...

Agreement The degree to which different observers, raters or diagnostic the tests agree on the binary classification. Measures of agreement like that of the kappa coefficient qu

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