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Question

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:

This question was previously asked in
SSC CGL 2023 (Tier-II) Paper 1 Previous Year Paper (26-Oct-2023) (Shift-1)
The correct answer is

1/3 n(n2 - 1)

The maximum value of Σni=1di2 in case of untied ranks in Spearman's rank correlation coefficient formula is 1/3 n(n2 - 1).

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Similar Questions

  1. The two regression lines y = c + mx and x = a + dy always pass through:

  2. If the correlation coefficient is the geometric mean of regression coefficients, then:

  3. The limits of a multiple correlation coefficient R1.23 are:

  4. 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:

  5. If the correlation coefficient between two variables is zero, then the two lines of regression will be:

  6. Using usual notations, the correlation coefficient between two random variables, X and Y, is given by:

  7. In Spearman's rank correlation coefficient, squared differences of ranks are used to:

  8. The Karl Pearson’s correlation coefficient (r) between two random variables, X and Y, is computed by:

  9. 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

  10. If the correlation between X and Y is 0.3, then correlation coefficient between 2X and 3Y is:  


Important Questions from Correlation and Regression

  1. 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 ?

  2. A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ?

  3. 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?

  4. 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?

  5. The coefficient of correlation when coefficients of regression are 0.2 and 1.8 is

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