CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression
The two regression lines of a data set are 3X + 2Y = 26 and 6X + Y = 31. What are the means of X and Y respectively?
The means are X = 4 and Y = 7. Both regression lines pass through the point of means, so solving the two equations together gives that point. Check: 3×4 + 2×7 = 26 and 6×4 + 7 = 31, both satisfied.
- AX = 3, Y = 8.5
- BX = 4, Y = 7Correct
- CX = 5, Y = 0.5
- DX = 2, Y = 10
Explanation
Both lines pass through the means. Multiply the second by 2: 12X + 2Y = 62. Subtract the first: 9X = 36, so X = 4. Then 3(4) + 2Y = 26 gives Y = 7. Check in the second: 24 + 7 = 31. Option 3,8.5 satisfies only the first line.
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