Correlation — Important Questions
ICSE · Class 11 · Economics
64 important questions from Correlation for ICSE Class 11 Economics, with answers. Includes multiple choice, true false and multiple correct questions.
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Important Questions from Correlation
A rank-correlation problem has tied groups of sizes 3, 2, and 2. The uncorrrected sum of squared rank differences is \sum D^2 = 41 and N=10. What is the corrected rank correlation coefficient?
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0.73
Add the tie adjustments: (1/12)(3^3 - 3) = 2, and each (1/12)(2^3 - 2) = 0.5. Total adjustment = 3. So corrected sum = 41 + 3 = 44. Then r = 1 - [6 x 44] / [10(100 - 1)] = 1 - 264/990 = 0.73.
A linear relation is written as y = a + bx. If the intercept is 12 and the slope is 4, what is the value of y when x = 7?
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40
Substitute into y = a + bx. So y = 12 + 4 x 7 = 12 + 28 = 40.
Two variables have covariance C=18, standard deviations \sigma_x = 3 and \sigma_y = 6. What is Karl Pearson's coefficient of correlation?
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1
Use r = C / (sigma_x sigma_y). So r = 18 / (3 x 6) = 18 / 18 = 1. Covariance has a unit, but r is unit-free.
A data set gives \sum x y = 24, \sum x^2 = 36, and \sum y^2 = 64. What is the direct-method value of r?
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0.50
Use r = sum xy / sqrt(sum x^2 x sum y^2). Thus r = 24 / sqrt(36 x 64) = 24 / 48 = 0.50.
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