Assumed means deviations in f2 test, statistics, Basic Statistics

Assignment Help:

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


Related Discussions:- Assumed means deviations in f2 test, statistics

Accounting standards in word countries, Accounting Standards in word countr...

Accounting Standards in word countries: Diverse countries like Peru, Australia, Kuwait, South Africa etc. have all started adopting the IFRS. The SEC has suggested that all compan

Calculate s.d, Less than 5 yrs 22 5-10 18 10-20 5 20-30 4 More than 30 1

Less than 5 yrs 22 5-10 18 10-20 5 20-30 4 More than 30 1

Calculate permanent income, Suppose that permanent income, YP (t) is calcu...

Suppose that permanent income, YP (t) is calculated as the average of disposable income (YD t ) over the past 5 years, that is: YP (t) = 0.2(YD t + YD t-1 + YD t-2 + YD t-3

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

Cost of accounting, what are different method of classifying overhead? indi...

what are different method of classifying overhead? indicate the advantag

Statistic, any of your writer able to use the database given to generate th...

any of your writer able to use the database given to generate the null, alternative..etc.. into a power point presentation

Derive an expression for the autocorrelation, i)A sionusodial signal has t...

i)A sionusodial signal has the form x(t) = Asin?t Derive an expression for the autocorrelation Rxx(λ) II) Explain the significance of this result in term of the frequen

Time seires, explain time series analysis

explain time series analysis

Is the coin biased, A coin that is balanced should come up heads half the t...

A coin that is balanced should come up heads half the time in the long run. A coin is tossed 4040 times and gives 2085 heads. Is the coin biased? Use Alpha = .05. (State the Hypoth

Sketch the frequency resoponce, i) For a 3 term averagin filter, write a di...

i) For a 3 term averagin filter, write a difference eqatuon governing the filter and dervie the corresponding z transform Sketch a pole zero plot, would this filter be stable, why

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