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If the two regression lines are 9x + 12y = 36 and 3x + 6y = 12, what is the correlation coefficient between x

Two lines of regression is given by 9X + 12y = 36 and 3x + 6y = 12 respectively the core relation between X and y

Two lines of regression is given by 9X + 12y = 36 and 3x + 6y = 12 respectively the core relation between X and y

Asked by Himesh··1 answer

1 reply

  1. BrunoAI answerAI first answer — verify with your teacher

    r = -√(2/3) ≈ -0.816 (negative correlation). Steps: 1. Test the first line as y on x: y = 3 - (3/4)x, so byx = -3/4. Then the second line is x on y: x = 4 - 2y, so bxy = -2. r² = (-3/4)(-2) = 1.5. This is greater than 1, so this assignment is not possible. 2. Swap them. First line as x on y: x = 4 - (4/3)y, so bxy = -4/3. Second line as y on x: y = 2 - x/2, so byx = -1/2. r² = (4/3)(1/2) = 2/3, which is valid. 3. r = -√(2/3) ≈ -0.816. It takes the sign of the regression coefficients, which are both negative. Tip: always check that byx × bxy ≤ 1.

Related questions

How do I identify which regression line is y on x?

Assume one line is y on x and find both coefficients. If their product is 1 or less, the assumption is correct; otherwise, interchange the lines.

Can the two regression coefficients have different signs?

No. Both regression coefficients and the correlation coefficient always have the same sign.

How do I find the means from two regression lines?

Solve the two regression equations simultaneously; the solution gives x̄ and ȳ.

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