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 (x̄, ȳ)?
The means are x̄ = 4 and ȳ = 7. Both regression lines pass through the point of means, so solving the two equations simultaneously gives that point. Substituting x = 4, y = 7 satisfies both 3x + 2y = 26 and 6x + y = 31.
- A(4, 7)Correct
- B(7, 4)
- C(5, 6)
- D(3, 8)
Explanation
Both regression lines pass through the point of means, so solve them together. From 6x + y = 31, y = 31 - 6x. Substituting in 3x + 2y = 26 gives 3x + 62 - 12x = 26, so x = 4 and y = 7. The pair (7, 4) merely swaps the values.
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