Regression lines, Applied Statistics

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.

Posted Date: 9/27/2012 6:27:28 AM | Location : United States







Related Discussions:- Regression lines, Assignment Help, Ask Question on Regression lines, Get Answer, Expert's Help, Regression lines Discussions

Write discussion on Regression lines
Your posts are moderated
Related Questions
First Moment of Dispersion or Mean Deviation Mean deviation or the average deviation is the measure if dispersion which   is based upon all the items in a variable .It is the a

The data le for this assignment is brain-body-wts.txt, which lists the averages brain weights (gm) and body weights (kg) for a number of animal species. Your task is to t an appr

Level of Significance: α The main purpose of hypothesis testing is not to question the computed value of the sample statistic, but to make judgment about the difference between

Suppose both the Repair record 1978 and Company headquarters are believed to be significant in explaining the vector (Price, Mileage, Weight). Here, because of the limited sample s

Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Find the replacement time that separates the top 20% from the

Standard Error The measure of reliability of the estimating equation that we have developed is given by standard error of estimate. The standard error of estimate represented b

Question: (a) (i) Define the term multicollinearity. (ii) Explain why it is important to guard against multicollinearity. (b) (i) Sometimes we encounter missing values

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

Hi There, I have a question regarding R, and I am wondering if anyone can help me. Here is a code that I would like to understand: squareFunc g f(x)^2 } return(g) } sin

how can we graph a trend line by semiaverages and least square method?