Question
Download Solution PDFFind regression coefficient of y on x (byx) if correlation coefficient between x and y values is 0.75 and standard deviation of x and y are 5 and 6.4 respectively.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
Correlation coefficient between x on y = 0.75
Standard deviation of x and y = 5 and 6.4
Formula
Correlation coefficient ‘r’ = Cov(x,y)/SxSy
Cov(x,y) = Coveriance of x and y
Sx = Standard deviation of x
Sy = Standard deviation of y
Correlation coefficient of y on x = byx = Cov(x,y)/Sx2
Calculation
0.75 = Cov(x,y)/5 × 6.4
⇒ Cov(x,y) = 0.75 × 5 × 6.4
⇒ Cov(x,y) = 24
⇒ byx = 24/52
∴ byx = 24/25
∴ correlation coefficient of y on x is 0.96
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