correlation coefficient

Posted by Arushi on May 05, 2014; 1:06pm
URL: http://discussion-forum.276.s1.nabble.com/correlation-coefficient-tp7588637.html

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