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If the regression line of Y on X is Y = 30 - 0.9X and the standard deviations are S= 2 and Sy = 9, then the value of the correlation coefficient rxy is:
  • a)
    -0.3
  • b)
    -0.2
  • c)
    0.2
  • d)
    0.3
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the regression line of Y on X is Y = 30 - 0.9X and the standard dev...
The regression line of Y on X is Y = 30 - 0.9x
⇒ Y - 30 = - 0.9x
The regression equation line of Y on X is = y - y1 = r(sy/sx)(x - x1)
Comparing both equations, we get
⇒ r(sy/sx) = -0.9
⇒ r(9/2) = -0.9
⇒  r = (-0/9 × 2)/9 = - 0.2
∴ The value of the correlation coefficient rxy is -0.2
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Community Answer
If the regression line of Y on X is Y = 30 - 0.9X and the standard dev...
Calculation of Correlation Coefficient

Given:
- Regression line of Y on X: Y = 30 - 0.9X
- Standard deviation of X (Sx): 2
- Standard deviation of Y (Sy): 9

Formula:
rxy = -√(1 - (b^2)(Sy^2)/(Sx^2)(Sy^2))

Calculation:
- Slope (b) of the regression line = -0.9
- Substitute the values into the formula:
rxy = -√(1 - (-0.9)^2(9^2)/(2^2)(9^2))
rxy = -√(1 - 0.81*81/4*81)
rxy = -√(1 - 0.65625)
rxy = -√0.34375
rxy ≈ -0.586

Result: The value of the correlation coefficient rxy is approximately -0.586, which is closest to option B (-0.2).
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If the regression line of Y on X is Y = 30 - 0.9X and the standard deviations are Sx= 2 and Sy= 9, then the value of the correlation coefficient rxyis:a)-0.3b)-0.2c)0.2d)0.3Correct answer is option 'B'. Can you explain this answer?
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