If \( Y = \frac{x}{2} + 2 \) and \( X = \frac{y}{8} - 1 \) are regression lines of Y on X and X on Y respectively, then the correlation coefficient between X and Y is equal to:
1/4
1. Y on X: \( Y = \frac{1}{2}X + 2 \) ⇒ \( b_{yx} = \frac{1}{2} \)
2. X on Y: \( X = \frac{1}{8}Y - 1 \) ⇒ \( b_{xy} = \frac{1}{8} \)
The correlation coefficient (r) is given by:
\( r = \pm\sqrt{b_{yx} \times b_{xy}} \)
Substituting the values:
\( r = \pm\sqrt{\frac{1}{2} \times \frac{1}{8}} = \pm\sqrt{\frac{1}{16}} = \pm\frac{1}{4} \)
Since both regression coefficients are positive, we take the positive value:
\( r = \frac{1}{4} \)
Correct Answer: Option 3. \(\frac{1}{4}\)
Similar Questions
The two regression lines y = c + mx and x = a + dy always pass through:
If the correlation coefficient is the geometric mean of regression coefficients, then:
The limits of a multiple correlation coefficient R1.23 are:
For three variables X1, X2 and X3, the following information is available:
s1 = 10, r12 = 0.90
s2 = 5, r13 = 0.75
s3 = 3, r23 = 0.70
Then partial regression coefficient (b13,2) of X2 on X1 and X3 is:If the correlation coefficient between two variables is zero, then the two lines of regression will be:
Using usual notations, the correlation coefficient between two random variables, X and Y, is given by:
In Spearman's rank correlation coefficient, squared differences of ranks are used to:
In Spearman's rank correlation coefficient:
\[ r_s = 1 - \frac{6\sum_{i=1}^n d_i^2}{n(n^2-1)} \]The maximum value of \(\sum_{i=1}^n d_i^2\) in case of untied ranks is:
The Karl Pearson’s correlation coefficient (r) between two random variables, X and Y, is computed by:
For three random variables X1 , X2 and X3, the pairwise correlation coefficients are r12 = r13 = r23 = r. The multiple correlation coefficient \(\rm R_{1.2.3}^2\) is
Important Questions from Correlation and Regression
If two lines of regression are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, then what is the value of x when y = -3 ?
A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ?
Two variates, x and y, are uncorrelated and have standard deviations σ xand σ yrespectively. What is the correlation coefficient between x + y and x – y?
If the covariance between x and y is 30, variance of x is 25 and variance of y is 144, then what is the correlation coefficient?
The coefficient of correlation when coefficients of regression are 0.2 and 1.8 is
