correlation coefficient

[Arushi]

Could someone please explain to me how to go about solving such questions. ISI 2007

24. For a given bivariate data set ) (xi , yi ; i =1, 2,..,n ), the squared correlation
coefficient  ( r^2) between x^2  and y is found to be 1. Which of the following statements is
the most appropriate?

(A) In the (x, y) scatter diagram, all points lie on a straight line.
(B) In the (x, y) scatter diagram, all points lie on the curve y = x^2
(C) In the (x, y) scatter diagram, all points lie on the curve y = a + bx^2
, a > 0, b > 0.
(D) In the (x, y) scatter diagram, all points lie on the curve y = a + bx^2
, a, b any real
numbers

15. The correlation coefficient r for the following five pairs of observations
x 5 1 4 3  2
y 0 4 2 0 -1
 satisfies
 
(A) r > 0; (B) r < −0.5; (C) −0.5 < r < 0; (D) r = 0.

Please reply. thanks

[Akshay Jain]

For ques no. 24
it is given that corr b/w y and x^2 is 1 mens that in a scatter diagram (x,y) the points lie on the curve y=x^2 but since corr coefficient is independent of change of origin and scale thus it shud b option d

[Arushi]

Yeah got it. What about the next question. The data looks independent so shouldn't r=0? How do we calculate r in that case?

[sarawagisruti]

Hi Akshay,  the graph of y=x^2 is a parabola so they should not be correlated? Also the answer posted by amit sir is option c).

Please reply

[Akshay Jain]

Here v have y=x^2 (since the coefficient of determination =1 b/w y and x^2)
and if v calculate the corr b/w y and x^2 will comw out to be 1
(underoot of coefficient of determination)
so if we plot x and y then it will comw out to be a parabola
but m not getting vy sir has given c  option....i dont no where m makin the mistake coz correlation is independent of origin and scale so a,b can be any real numbers

[Akshay Jain]

SIR pls correct me where m going wrong.....

[Homer Simpson]

i think its 15(B)

[vandita24x7]

Y = x^2. so y cannot take negative values. hence a,b>0

On Fri, May 9, 2014 at 6:12 PM, tsuki [via Discussion forum] <[hidden email]> wrote:

i think its 15(B)

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[sarawagisruti]

Haan..got it..Thanks

[sarawagisruti]

Thanks Vandita

[Amit Goyal]

You are right Akshay. The answer was wrongly posted as option (c) in the file but was later corrected to option (d). Check here: http://economicsentrance.weebly.com/lessons.html

[Akshay Jain]

Thank you sir.....me to tnsn me aa gya tha.... :P