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

#binomial probability, they gave me n=30 and p=.23 to get the answers for P...

they gave me n=30 and p=.23 to get the answers for P(20,x,23)= and P(x.23)=

Ifrs financial instruments, journal entries of a loan swap with different c...

journal entries of a loan swap with different currency

What is accounting system , The methods and records established to recogniz...

The methods and records established to recognize, set up, evaluate, move, record, and report the state’s purchases and to maintain responsibility for its obligations and resources

Cash accounting, Accounting system is one prevalent among agencies in volun...

Accounting system is one prevalent among agencies in voluntary sector. Transactions are registered in journals only when cash is in fact paid out or taken in. The primary virtue of

Biostatistics, I need the following exercises done by March 19th at 11:59pm...

I need the following exercises done by March 19th at 11:59pm: 4.4, 4.6, 4.8, 4.10, 4.14, 4.18, 4.26, 4.28. On pages 198-205

Prepare the journal entries, 1. Unrestricted cash contributions receiv...

1. Unrestricted cash contributions received during the year, $300,000. 2. Restricted cash contributions were received during the year for the following: Education

Distribution of the sample mean, 1. Suppose that a population has mean, µ, ...

1. Suppose that a population has mean, µ, and standard deviation, σ. What does the central limit theorem tell us about the distribution of the sample mean?

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