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CA Foundation · Quantitative Aptitude · Correlation and Regression

The two regression lines of a sample are 3x + 2y = 26 and 6x + y = 31. What are the mean values of x and y respectively?

The means are x̄ = 4 and ȳ = 7. Both regression lines pass through the point of means, so solving the two equations simultaneously gives the values: substituting y = 31 − 6x into 3x + 2y = 26 gives x = 4, and then y = 7.

  1. Ax̄ = 7, ȳ = 4
  2. Bx̄ = 4, ȳ = 7Correct
  3. Cx̄ = 5, ȳ = 5.5
  4. Dx̄ = 3, ȳ = 6.5

Explanation

Both regression lines pass through the point of means (x̄, ȳ), so solve them together. From 6x + y = 31 we get y = 31 − 6x. Substituting in 3x + 2y = 26 gives 3x + 62 − 12x = 26, so x = 4 and y = 7. Option 7 and 4 simply swaps the two means.

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