if the relation between x and u is 3x + 4u + 7 = 0 and the correlation coefficient between x and y is -0.6, then what is correlation coefficient u and y
a)-0.6 b)0.8 c)0.6 d)-0.8
Kuch samaj nahi aata last step
To find the correlation coefficient between u and y, we first need to find the value of u.
Given the relation between x and u:
3x + 4u + 7 = 0
Let's isolate u in this equation:
4u = -3x - 7
u = (-3x - 7)/4
Now, let's substitute this expression for u in terms of x into the correlation coefficient formula:
r_xy = Σ[(x - x̄)(y - ȳ)] / √[Σ(x - x̄)² * Σ(y - ȳ)²]
Since the correlation coefficient between x and y is given as -0.6, we can use this value in the equation.
Therefore, the correlation coefficient between u and y is given by replacing x with (-3x - 7)/4:
r_uy = Σ[((-3x - 7)/4 - x̄)(y - ȳ)] / √[Σ(((-3x - 7)/4) - x̄)² * Σ(y - ȳ)²]
Simplifying this equation further will allow us to determine the correlation coefficient between u and y.
To find the correlation coefficient between u and y, we need to determine their relationship. Given that the relation between x and u is 3x + 4u + 7 = 0, we can solve this equation for u in terms of x:
3x + 4u + 7 = 0
4u = -3x - 7
u = (-3x - 7) / 4
Now, we need to find the relationship between y and u. Given that x and y have a correlation coefficient of -0.6, we know that there exists a linear relationship between them in the form of y = mx + b, where m represents the slope and b represents the y-intercept.
Recall that u can be expressed in terms of x as u = (-3x - 7) / 4. Substituting this into the equation y = mx + b, we get:
y = m((-3x - 7) / 4) + b
This means that the correlation coefficient between u and y is actually equal to the correlation coefficient between x and y, since they are related through the same equation. Therefore, the correlation coefficient between u and y is -0.6.
So, the answer is a) -0.6.
U= (-3/4)x-7/3
Thus a perfect negative correlation between u and x
So correlation between u and y= (-0.6*(-3/4)/(-3/4)= 0.6