Two random variables x and y have the following regression equations – 3x + 2y…
2021
Two random variables x and y have the following regression equations –
3x + 2y − 26 = 0
6x + y − 31 = 0
then, the mean values of x and y are respectively:
- A.
7, 4
- B.
6, 4
- C.
4, 7
- D.
4, 6
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Correct answer: C
The intersection point of two regression lines represents the mean values x and y. We solve the system of equations: 3x + 2y = 26 and 6x + y = 31. From the second equation, y = 31 - 6x. Substituting into the first: 3x + 2(31 - 6x) = 26 => 3x + 62 - 12x = 26 => -9x = -36 => x = 4. Then y = 31 - 24 = 7. The mean values are x=4 and y=7.