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

Calculate strengths and weaknesses , In the 2009 baseball season, the team ...

In the 2009 baseball season, the team that finished the regular season with the best record in the National League was the Los Angeles Dodgers, with a record of 95-67. (For those o

Association of Attributes, In an examination 600 candidates appeared, boys ...

In an examination 600 candidates appeared, boys outnumbered girls by 16% of all candidates. number of passed candidates exceeded the number of failed candidates by 310. Boys failin

Iasb and fasb, Significant factors of financial accounting In financial...

Significant factors of financial accounting In financial accounting, The IASB and FASB considered that reconsidering all the ideas would not be a practical use of their underst

Homework, The probability a computer will boot is .08. What is the least nu...

The probability a computer will boot is .08. What is the least number needed so that the probability at least two will boot is greater than .99?

Accounting rate of return, Ghosh Ltd is considering expanding its business ...

Ghosh Ltd is considering expanding its business and has to decide between taking on Project A or Project B. Both projects have a life of four years. Equipment is expected to have

Biostatics, A national study found that treating people appropriately for h...

A national study found that treating people appropriately for high blood pressure reduced their overall mortality by 20%. Treating people adequately for hypertension has been diffi

Correlation analysis and coefficient, Individual Music scores Mathematics s...

Individual Music scores Mathematics scores Angela 2 8 Arthur 6 3 Peter 4 9 Mike 5 7 Barbara 7 2 Jane 7 3 Jean 2 9 Ruth 3 8 Alan 5 6 Theresa 4 7 Assess the data using a Correlation

Calculate the probability , In the 2009 Season, the Toronto Blue Jays finis...

In the 2009 Season, the Toronto Blue Jays finished the season with a record of 75-87. In 47 of those games, both the offense and defense performed adequately, and in 42 of them, ne

#title.- historigram, #question.differentiate between historigram and histo...

#question.differentiate between historigram and histogram.

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