HSC Commerce 12th Board ExamMaharashtra State Board
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for The Regression Equation of Y on X is Y = 2 9 Xand the Regression Equation of X on Y is X = Y 2 + 7 6 Find : (I) Correlation Coefficient Between X and Y. (Ii) σ 2 Y If σ 2 X = 4 - HSC Commerce 12th Board Exam - Mathematics and Statistics

Login
Create free account


      Forgot password?

Question

The regression equation of Y on X is y = `2/9` xand the regression equation of X on Y is `x=y/2+7/6` 

Find : (i) Correlation coefficient between X and Y. 

(ii) `σ_y^2 if σ _x^2=4`

Solution

The repression eqn. of y on x is y =`2/9x` 

Comparing with y − `barY = b_yx (x − barx)` 

Here              `  b_yx=2/9` 

Now the regression eqn. of x on y is x =`y/2+7/6` 

Comparing with` x-barx=bxy=1/2` 

(a) we have, correlation coefficient between x and y is 

`r=sqrt(b_(yx) b_(xy))` 

=`sqrt2/9xx1/2=sqrt1/9+-1/3` 

∴ `r=1/3 (∵b_(yx) and b_(xy) "are positive")` 

(b) `σ_x^2=4⇒ σ_x=2` 

We have `b_yx= r.σ_y/σ_x`  

∴ `2/9=1/3 σ_y/2` 

⇒ `σ_y=12/9` 

⇒ `σ_y=4/3`

 

  Is there an error in this question or solution?

APPEARS IN

 2017-2018 (March) (with solutions)
Question 4.5 | 2.00 marks
Solution The Regression Equation of Y on X is Y = 2 9 Xand the Regression Equation of X on Y is X = Y 2 + 7 6 Find : (I) Correlation Coefficient Between X and Y. (Ii) σ 2 Y If σ 2 X = 4 Concept: Statistics - Bivariate Frequency Distribution.
S
View in app×