IGNOU BCS 40 2026 2027 - The mean marks and standard deviations of students in two subjects are

Question

The mean marks and standard deviations of students in two subjects are given below:
Subject A: Mean = 36, Standard Deviation = 11
Subject B: Mean = 85, Standard Deviation = 8
Coefficient of correlation between A and B = ±0.66
Determine the two equations of regression and calculate the expected marks in Subject A corresponding to 75 marks obtained in Subject B.

08 Aug 2026

Answer :

Word Count : 614

The given data are: Subject A: Mean marks (\bar X = 36), Standard Deviation (\sigma_X = 11) Subject B: Mean marks (\bar Y = 85), Standard Deviation (\sigma_Y = 8) Coefficient of correlation: [ r = \pm 0.66 ] We have to determine the two regression equations and calculate the expected marks in Subject A when a student obtains 75 marks in Subject B. In statistical techniques, there are two regression equations: the regression equation of (A) on (B), which is used to estimate the marks in Subject A from the marks in Subject B, and the regression equation of (B) on (A), which is used to estimate the marks in Subject B from the marks in Subject A. The general regression equations are: [ X-\bar X=b_{XY}(Y-\bar Y) ] and [ Y-\bar Y=b_{YX}(X-\bar X) ] where the regression coefficients are: [ b_{XY}=r\frac{\sigma_X}{\sigma_Y} ] and [ b_{YX}=r\frac{\sigma_Y}{\sigma_X} ] For the regression of A on B: [ b_{AB}=r\frac{\sigma_A}{\sigma_B} ] Substituting the given

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