Assumed means deviations in f2 test, statistics, Basic Statistics

Assumed Means Deviations in F2 Test : When actual means of X and Y variables are in fractions the calculations can be simplified by taking the deviations from assumed means. When deviations are taken from assumed means the entire procedure of finding regression equations remains the same - the only difference is that instead of taking deviations from actual means, we take the deviations from assumed means. The two regression equations are:

X - X = r σx / σy ( y-y)

The value of σx/ σy will now be obtained as follows 

r σx/ σy = N Σ dx dy - (Σ dx x Σ dy)/N Σ d2y - (Σ dy)
2

dx = (X - A) and dy = (Y - A)

Similarly the regression equation of y on x is 

y - y = r σy/ σx (X - X)

r σy / σx = N Σ dx dy - Σ dx Σ dy / N Σ d x2 - (Σ dx)2

It should be noted that in both the cases the numerator is the same the only difference is in the denominator when the regression coefficients are calculated from correlation table their values are obtained as follows.

r σx/ σy = N Σ f dx dy - Σ f dx Σ dy /N Σ fd2y - (Σ f dy)2 x ix / iy

Ix= class interval of X variable and 

Iy = class interval of y variable

Similarly r σy/ σx = N Σ fd2x - (Σ f dx)2 X iy/ix

As is clear from above the formulae for calculating regression coefficients in a correlation table are the same - the only difference is that in a correlation table we are given frequencies also and hence we have multiplied every value by f.

Illustration: From the data of illustration calculate regression equation by taking deviations of X series from 5 and of y series form 7.

X (X - 5) dx 
d2x Y (Y-7)dy d2y dx dy
6 +1 1 9 +2 4 +2
2 -3 9 11 +4 16 -12
10 +5 25 25 -2 4 -10
4 -1 1 8 1 -1 -1
8 +3 9 7 0 0 0
ΣX=30 Σ dx=+5 Σ d2x=45 Σy =40 Σ dy = 5 Σ d2y = 25 Σ dxdy= - 21


Regression equation of X on Y; X-X = r σx /σy (Y-Y) 

X =  ΣX/N = 30/5 6; y = Σ y/N = 40/5 = 8 


r σx/σy = N Σ dxdy - Σ dx Σ dy/N Σ d2y - (Σdy)2 

= [5 (- 21) - (5)(5)]/(5)(25) - (5)2 = -105 - 25/(- 125 - 25) = - 130 / 100 = - 1.3 

X - 6 = - 1.3 (Y - 8)

X - 6 = - 1.3 Y + 10.4 or X = 16.4 - 1.3 y


Regression equation of Y on X ; Y - Y = r σy/ σx = N Σ dx dy - Σ dx Σ dy/N Σ d2x - (Σ dx)2

= 5 ( - 21) - (5) (5) / (5) (45) - (5)2 = - 105 - 25 / 200 = - 0.65

Y - 8 = - 0.65 (X - 6) 

Y - 8 = - 0.65 X + 3.9 or Y = 11.9 - 0.65 X >

Expertsmind.com offers unique solutions for statistics assignments, homework

Posted Date: 2/25/2012 4:33:41 AM | Location : United States







Related Discussions:- Assumed means deviations in f2 test, statistics, Assignment Help, Ask Question on Assumed means deviations in f2 test, statistics, Get Answer, Expert's Help, Assumed means deviations in f2 test, statistics Discussions

Write discussion on Assumed means deviations in f2 test, statistics
Your posts are moderated
Related Questions
I roll a fair die n times and don’t see the face 1 in the first r rolls (r


how would we find cumulative frequency for the median of discrete series

if sales is 6800 and variable costs are 2856 what is the variable cost percentage?


The average cost per night of a hotel room in New York City is $273 (SmartMoney, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard

So I can send you a word problem & you van send the answers back in excel for me?

One way to use contiguous allocation of the disk and not suffer from holes is to compact the disk every time a file is removed. Since all files are contiguous, copying a file requi

Allowance for uncollectible A contra-asset assessment consideration used to indicate the part of a / r that is approximated to be uncollectible.

The research should be Quantitative Research: A means for testing objective theories by examining the relationship among variables. These variables can be measured and analyzed