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Question
The following data pertains to the marks in subjects A and B in a certain examination. Mean marks in A = 39.5, Mean marks in B = 47.5 standard deviation of marks in A = 10.8 and Standard deviation of marks in B = 16.8. coefficient of correlation between marks in A and marks in B is 0.42. Give the estimate of marks in B for the candidate who secured 52 marks in A.
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Solution
Let X represent the marks in subject A and Y represent the marks in subject B.
Given `bar"X"` = 39.5, `bar"Y"` = 47.5
σX = 10.8, σY = 16.8
r(X, Y) = 0.42
∴ Regression coefficient of Y on X
byx = `"r" . (sigma_"Y")/(sigma_"X")`
= `0.42 (16.8/10.8)`
= `7.056/10.8`
= 0.653
∴ Regression line of Y on X is
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y − 47.5 = 0.653 (X − 39.5)
Y − 47.5 = 0.653X − 25.79
Y = 0.653X + 21.71
When X = 52, Y = 0.653(52) + 21.71
Y = 33.956 + 21.71
Y = 55.67
Hence, the estimate of marks in B for the candidate who secured 52 marks in A is 55.67
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