ISI 2008 MATH PROBLEM...

[leon]

Am not able to solve this problem, please help

The correlation coefficients between two variables X and Y obtained from the two
equations 2x + 3y -1= 0 and 5x - 2y + 3 = 0 are
(a) equal but have opposite signs
(b)-2/3 and 2/5
(c) 1/2 and -3/5
(d) Cannot say

[Amrita]

the answer is (d) cannot say

[Amrita]

we can clearly say that they will be opposite in sign. but since neither the sd or variance of x or y is not given. we cannot determine the exact value.

[tanudas]

They'll have opposite signs. For the first equation it will be -1 and for the second it will be +1

[leon]

Thanks amrita and tanu.
Can you please explain how its 1 and -1?I don't know how to calculate them.

[Amrita]

dear leon,
          my bad. i read it as covariance.
the first equation is 2x+3y-1=0 ........1
so,
2(mean of x)+3(mean of y)-1=0........2
deduct eq 2 from 1
and write it in the form of variance
so you get the variance of x in terms of y.
formula for correlation coefficient is cov(x,y)/sd(x)sd(y)
replace all the equations in the formula and u wl get -1.

repeat the same procedure with the 2nd equation.

[Rajat]

Hi All,

I have a doubt. Wouldn't (a) be the answer always ? Regardless of the equations . Here, the equations which they have given are irrelevant to the question asked.

Please correct me if I am wrong.

[Amrita]

dear rajat,
 correlation coefficient measures the degree of linear relationship between two variables.
since here the equation is itself linear we will get -1 or +1.
like 2x+3y-1=0
here x and y have the same sign. so it wl be -1. again if it would had been 2x-3y-1=0 it would had been 1.

[leon]

Oh you're right. That was of great help. Thanks .