F2 test x, y arithmetic means, statistics, Basic Statistics

Assignment Help:

What is F2 Test,  X, Y Arithmetic Means The above method of finding out regression equation is tedious. The calculations can very much be simplified if instead of dealing with the actual values of X and Y we take the deviations of X and Y series form their respective means. In such a case the two regression equations are written as follows:
    
Regression equation  of x on Y ; X - X = r σx / σy (Y - Y)
 
X is the mean of X series. Y is then mean of y series

R σx/ σy is known as the regression coefficient of X on Y.

The regression coefficient of X on Y is denoted by the symbol b xy or b1. It measures the change in X corresponding to a unit change in Y. when deviations are taken from the means of X and Y, the regression coefficient of X on Y is obtained as follows:

b xy or r σ/ σy = Σ x y / Σ y2

Instead of finding out the value of correlation coefficient σx, σ y etc, we can find the value of regression coefficient by calculating Σ x y and Σ y2 and dividing the former by the latter.
    
Regression equation of y on X; Y - Y =r σy/ σx (X - X)

R σy/ σx is the regression coefficient of Y on X it is denoted by b xy or b2. It measures the change in Y corresponding to a unit change in X. when deviators are taken from  actual means the regression coefficient of Y on X can be obtained as follows.

R σy/ σx = Σ xy / Σ x
2

It should be noted that ht ender- root of the product of two regression coefficients given us the value of correlation coefficient. Symbolically,

R = √bxy X b xy

Proof, 
B xy = r σx / σy and b xy = r σy/σx

B xy x b xy = r σx/σy x r σy/ σx = r2 , ∴ r = √bxy X b yx

The following points should be noted about the regression coefficients 
     
Both the regression coefficients will have the same sign. Either they will be positive or negative. It is never possible that one of the regression coefficients is negative and the other positive. 
    
Since the value of the coefficients of correlation cannot exceed one, one of the regression coefficients must be less than one or, in other  words both the regression coefficients cannot be greater than one. For example, if b xy = 1.2 and b xy = 1.4 the value of correlating to coefficient would be √(1.2 x 1.4) = 1.296 which is not possible.
    
The coefficients of correlation will have the same sign as that of regression coefficients if regress coefficients have a negative sign r will also be negative and if regression coefficients have a positive sign, r would also be positive. For example if b xy = - 0.8 and b xy = - 1.2 r would be √(- 0.8 x-1.2) = - 0.98and not + 0.98.
    
Since b xy = r σx / σy we can find out any of the four values given the other three. For example if we know that r = 0.6 σx = 4 and b xy = 0.8, we can find σy.

B xy = r σx/ σy

Substituting the given values: 0.8 = 0.6 x 4 / σy or σy= 2.4 / 0.8 = 3.

Regression coefficients are independent of change of origin but two of scale. 

Expertsmind.com offers unique solutions for statistics assignments, homework


Related Discussions:- F2 test x, y arithmetic means, statistics

Probability, Consider the two events A and B with P(A) = 0.4 and P(B) = 0.3...

Consider the two events A and B with P(A) = 0.4 and P(B) = 0.3. (a) If A and B are independent then compute the probability that Both A and B happen

Logistic regression model, Model 1:  Let's consider the logistic regression...

Model 1:  Let's consider the logistic regression model, which we will refer to as Model 1, given by log(pi / [1-pi]) = 0.25 + 0.32*X1 + 0.70*X2 + 0.50*X3

What is budget control, Definition of budget control as management of costs...

Definition of budget control as management of costs & expenses with examples. Budget control is the management of costs & expenses in accordance with an underlying budget.

Least squares analysis, Least squares method of fitting a line ( the line o...

Least squares method of fitting a line ( the line of best fit or the regression line) through the scatter diagram is a method which minimizes the sum of squared vertical deviations

BUSINESS FORECASTING., a) What is analysis of variance? What are the assump...

a) What is analysis of variance? What are the assumptions of this technique? b) Three samples below have been obtained from normal populations with equal variances. Test the hypoth

12 questions, normal distribution and the sampling distributions of sample ...

normal distribution and the sampling distributions of sample proportions and sample means, but without confidence interval

Asset, what''s the asset?

what''s the asset?

Card custodian, Card custodian An person who is assigned responsibility of...

Card custodian An person who is assigned responsibility of purchase card security & issuance of cards to authorized users,

Estimate stand-up time using the rmr system, SCENARIO It is proposed to...

SCENARIO It is proposed to construct a 3m diameter, 50m long tunnel, heading 0950, through the andesite lava flow at Maori Bay (Muriwai). As part of the preliminary investigati

QUANTITATIVE METHODS., A LARGE SHIPPPING COMPANY RECORDED THE NUMBERS OF TO...

A LARGE SHIPPPING COMPANY RECORDED THE NUMBERS OF TONS SHIPPED WEEKLY ACROSS THE PACIFIC FOR 50 WEEKS. ARRANGE DATA IN A LESS THAN CUMULATIVE DISTRIBUTION USING SEVEN CLASSES OF E

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